PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                              1  

A  Tale  of  Two  Motorsports:  A  Graphical-­‐Statistical  Analysis  of  How  Practice,  Qualifying,  and  Past  Success  Relate  to  Finish  Position  in  NASCAR  and  Formula  One  Racing*    Kathleen  M.  Silva  and  Francisco  J.  Silva    Department  of  Psychology,  University  of  Redlands,  Redlands,  California  92373-­0999  USA  

ABSTRACT  

We  analyzed  data  from  the  2009  National  Association  for  Stock  Car  Auto  Racing  (NASCAR)  and  Formula  One  (F1)   racing   seasons   to   examine   the   relationships   between  drivers’   finish  positions   and   their   performances  during   the   final   practice,   qualifying,   and  past   races.    NASCAR  drivers’   performances   in   practice,   qualifying,  and   past   races   were   usually   positively   correlated   with   their   finish   positions.     In   F1   racing,   only   drivers’  performances   during   qualifying   and,   to   a   lesser   extent,   in   past   races  were   positively   correlated  with   their  finish  positions.    In  contrast,  there  was  rarely  a  significant  correlation  between  the  finish  positions  of  the  best  NASCAR  drivers  and  their  performances  in  practice,  qualifying,  or  previous  races.    We  discuss  the  results  in  the  context  of  the  demands  and  characteristics  of  NASCAR  and  F1  racing.    Keywords:  correlation,  Formula  One,  motorsports,  NASCAR,  practice,  qualifying,  regression,  Sprint  Cup  

In terms of their environments or physical features (e.g., cars, racetracks), National Association for Stock Car Auto Racing (NASCAR) and Formula One (F1) racing are very different forms of automotive racing (Blount, 2009; Collantine, 2006; Hook, 2010; “NASCAR’s Jeff Gordon on Formula One racing,” 2004). For example, the premier NASCAR series, currently known as the Sprint Cup Series, consisted of 36 races in 2009.1 Of these races, all were run at tracks in the United States and all but two of the races were on run on speedways shaped like ovals or distorted ovals (e.g., rounded triangles or D’s). In contrast, the F1 Grand Prix series consisted of 17 races in 2009, each of which was run in a different country and all of which consisted of irregularly shaped circuits and road courses. Table 1 presents a summary of some key physical differences between NASCAR and F1 racing.

                                                                                                               * © 2010 Kathleen M. Silva and Francisco J. Silva. All right reserved.

Cite as: Silva, K. M., & Silva, F. J. (2010). A tale of two motorsports: A graphical-statistical analysis of how practice, qualifying, and past success relate to finish position in NASCAR and Formula One racing. Retrieved from http://newton.uor.edu/FacultyFolder/Silva/NASCARvF1.pdf

Address correspondence to K. Silva or F. Silva, Department of Psychology, University of Redlands, Redlands, California 92373-0999 USA (email: kathleen_silva@redlands.edu or francisco_silva@redlands.edu). 1 Throughout the manuscript, any reference to NASCAR will mean, more specifically, a reference to NASCAR’s Sprint Cup Series and never to its other series (e.g., Nationwide Series, Camping World Truck Series, K&N Pro Series). Although Sprint Cup Series is more accurate, the name of NASCAR’s premier racing series changes as a function of corporate sponsorship. The Sprint Cup Series was previously known as the Nextel Cup Series and, before that, the Winston Cup Series. Thus, although less precise than Sprint Cup Series, it is commonplace to refer to this racing series simply as NASCAR (e.g., NASCAR on Fox and NASCAR TNT Summer Series, both of which refer to television programs that cover of Sprint Cup races).

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        2  

Despite these differences, there are noteworthy similarities between the two motorsports. For example, both NASCAR and F1 award points commensurate with when a driver finishes a race to determine who is the best driver, overall, at the end of the racing season. Also, both NASCAR and F1 set a driver’s starting position for a race based on his2 time during qualifying. The drivers’ qualifying times are ranked such that there is normally a perfect and positive                                                                                                                2 All drivers during all of the races analyzed in the present article were men.

Table 1 Physical Variables: Similarities and Differences Between NASCAR and F1 Racing in 2009 Characteristic Motorsport NASCAR F1 Number of Drivers 43 20 Number of Crew Members During Pit Stops

7 20

Number of Races 36 17 Design of Cars front-engine, “stock" car,

heavy (1500 kg) mid-engine, open-wheel, light (600

kg) Technological Sophistication of Cars

basic; relatively simple engineering

sophisticated; advanced engineering

Racing Tracks and Circuits oval-shaped speedways circuits and road courses Width of Tracks and Circuits

relatively wide, side-by-side racing is common

relatively narrow, side-by-side racing is rare

Length of Tracks and Circuits

relatively short (0.85 km to 4.18 km)

relatively long (3.34 km to 7.00 km)

Location of Races 23 locations in USA 17 countries in Asia, Australia,

Europe, South America Turning all left turns 34 of 36 races left and right turning Overtaking and Lead Changes

relatively common relatively rare

Qualifying 1 session consisting of 1 or 2

laps 3 sessions consisting of several

(e.g., 7, 12) laps in each Final Practice occurs after qualifying occurs before qualifying Ability to race in wet weather

cannot race in rain under any circumstances

can race in rain with tires designed for this purpose

Time Limit none 2 hours

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        3  

correlation between a driver’s rank during qualifying and his starting position (e.g., fastest in qualifying = 1st or pole position to start a race; slowest in qualifying = last position on the starting grid).3 Finally, both NASCAR and F1 racing allow drivers to practice their driving, and teams to set up their cars for the conditions of the speedway or circuit. But, even here, the two motorsports differ: NASCAR’s final practice session normally occurs the day after qualifying; F1 racing’s final practice occurs before qualifying.

In this article, we examine whether there are similarities and differences between NASCAR and F1 racing in terms of performance features – i.e., those factors tied to the drivers’ and their teams’ performance rather than the physical features of the two motorsports (e.g. see Table 1). We examined these performance features by answering six questions. (1) What is the relationship between a driver’s performance during the final practice before a race and his finish position? (2) What is the relationship between a driver’s performance during qualifying (and thus his position at the start of a race) and his finish position? (3) What is the relationship between a driver’s points-standing before a race (i.e., a measure of his overall success) and his finish position? (4) How do the relationships in (1) through (3) change across races? (5) What is a more reliable predictor of a driver’s finish position: His performance during practice, his performance during qualifying, his overall success prior to a race, or a combination of these variables? (6) What factors are related to the degree that a driver’s finish position is predictable from his performance in practice, qualifying, and his success up to that point in the season? To answer these questions, we analyzed the results of the 2009 NASCAR and F1 racing seasons using a combination of visual inspection of graphed data (see, e.g., Kazdin, 1982) and inferential statistics (primarily correlation and regression).

Published research that investigated NASCAR drivers’ performance is rare. Most of the studies that do exist take the form of working papers available through the authors’ personal archives. However, two exploratory studies of whether reliable predictors exist for the outcomes of NASCAR races hint at answers to some of the preceding six questions. One project examined the results from 14 races from the 2003 NASCAR season to see whether the outcome of a race was predicted from a variety of performance variables, such as how drivers performed in the practice session closest to the start of the race, the drivers’ performance during qualifying, the drivers’ overall success leading up to a race, the number of laps a driver completed in all races during the previous season, how often a driver did not finish a race, the drivers’ finish positions at the same race the year before, and the drivers’ finish positions in the preceding race. The results showed that drivers’ performance during practice and qualifying, as well as their overall success leading up to a particular race and the number of laps they completed during the previous season, were correlated with their finish position (Pfitzner & Rishel, 2005). A similar project that used the results of 38 races in the 2002 NASCAR season found that the drivers’                                                                                                                3 Although there is normally a perfect and positive correlation between the rank of a driver’s qualifying time and his starting position, there are occasions when this is not the case. For example, a driver may produce the fastest time during qualifying (and thus be ranked first following qualifying) and yet start a race at the rear of the field for any of several reasons (e.g., changing an engine after qualifying; having his qualifying time disallowed because of a rules violation). These sorts of events, though, are uncommon. Also, in NASCAR, qualifying is sometimes cancelled because of rain. When this happens, the starting positions for a race are determined by so-called “car owner points,” which are usually but not always the same as a driver’s points-standing. Nevertheless, for most intents and purposes (including those of the present article), there is a perfect and positive correlation between a driver’s rank following qualifying and his starting position. During the 2009 NASCAR season, qualifying was cancelled at the following races: Martinsville, Pocono, New Hampshire, *Daytona, *Pocono.

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        4  

performances during qualifying (and thus their starting positions) and their number of years of NASCAR driving experience were important predictors of their finish positions (Allender, 2008). Published studies that investigated the performance of F1 drivers are non-existent.

The present study attempts to fill a void by providing the first comprehensive, quantitative, and comparative analysis of the performance of NASCAR and F1 drivers across an entire racing season. Our ultimate goal is to create a table (comparable to Table 1), based on the answers to the six questions posed above, which highlights the similarities and differences between NASCAR and F1 drivers in relation to key performance variables of these motorsports.

Method   The data that we analyzed were downloaded from the official websites of NASCAR and F1 racing: nascar.com and formulaone.com. For each points-awarding race in 2009,4 we obtained each driver’s rank during the final practice session before a race, each driver’s rank in qualifying (and, thus, his starting position), each driver’s points-standings (i.e., his ranking based on the number of points he accrued before the start of a race, which is a measure of his overall success up to that race), and each driver’s finish position.5 For short, we refer to these variables as Practice, Qualifying, Points, and Finish.

In NASCAR, the final practice session normally occurs after qualifying. In F1 racing, the final practice session normally occurs before qualifying. Thus, for NASCAR, the final practice is the last time a driver is on the speedway before the start of the race; for F1 racing, qualifying is the last time a driver spends any substantial amount of time on the racing circuit before the start of a grand prix.6

The primary results were obtained by calculating Spearman rank correlation coefficients (known as Spearman’s rs) between Practice and Finish, Qualifying and Finish, and Points and Finish for each NASCAR and F1 race. We chose to calculate Spearman’s rs instead of Pearson’s product moment correlation coefficients or r for three main reasons. One, we calculated a total of 159 correlation coefficients (36 for NASCAR + 17 for F1 x 3 relationships, explained below). Rather than worry about whether the characteristics of any set if data violated one or more assumptions necessary to calculate Pearson’s r, we opted for the assumption-free Spearman’s rs.                                                                                                                4 All of the 36 NASCAR and 17 F1 races analyzed in the present article award drivers points commensurate with their performance in a race. These points are awarded exclusively on the basis of a driver’s finish position in F1 racing and primarily on the basis of a driver’s finish position in NASCAR. Other factors that contribute to a NASCAR driver’s points include leading the most laps in a race and leading a lap during a race. Races that did not contribute to the drivers’ points total (e.g., all-star race) were excluded from the analyses.

5 The one exception was the first race for each of the NASCAR and F1 seasons. Because all drivers start the first race of the season with 0 points, we used the drivers’ final points-standing from the previous season. For 2009 rookie drivers who did not race in 2008, we assigned a value of 0 points to their points-total before the first race of the 2009 season and ranked them accordingly.

6 In NASCAR, there are two notable exceptions to this schedule. Because NASCAR cars cannot race in wet weather (drizzle, showers, rain), final practice is sometimes cancelled because of precipitation. In these circumstances, the final practice occurs before qualifying. Also, 3 of the 36 NASCAR races held in 2009 were so-called impound races. At both Talladega races and the second Daytona race, NASCAR officials impound cars following qualifying. This means that drivers cannot drive their cars and teams cannot work on their cars between the end of qualifying and the start of a race. At impound races, the final practice also occurs before qualifying.

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        5  

Two, the number of data points used in some analyses was relatively small (n = 20). Pearson correlation coefficients can be misleading when sample sizes are small (Aliaga & Gunderson, 2006). Third, the ranked Practice, Qualifying, and Finish data seemed ideally suited to a Spearman analysis, which converts data to ranks before rs is calculated. We used α < .05 to determine the statistical significance of all two-tailed analyses.

To determine how combinations of Practice, Qualifying, and Points correlated with Finish, we tested the following four models:

(1) Finish = α + β1Practice + β2Qualifying (2) Finish = α + β1Practice + β2Points (3) Finish = α + β1Qualifying + β2Points (4) Finish = α + β1Practice + β2Qualifying + β3Points For each analysis, we were interested only in (a) the multiple correlation coefficient or R,

which expresses the correlation between Finish and a combination of the predictor variables (Practice, Qualifying, Points) in the equation, and (b) the accompanying F statistic and p value, which provide information about the degree that the combination of variables in the model is significantly correlated with Finish.

Given the number of races for which we tested the models listed above,7 “by the book” evaluations of each model for each race – which normally consists of specifying the model, identifying multicollinearity, disentangling partial correlations, removing nonsignificant variables, specifying a new model, evaluating it, and so on (Keith, 2006; Younger, 1985) – were not reasonable. Instead, we relied on visual inspection of graphed data to form generalizations about the four models and their relation to NASCAR and F1 racing. We will explain more completely in the Results section how we evaluated the models by graphical inspection, and how we used chi-square tests of independence to provide corroborating support for our evaluations.

Results   Correlations:  NASCAR   Figure 1 shows how Finish was correlated with Practice, Qualifying and Points across the 2009 NASCAR season. Values in the grey area are not statistically significant; values in the white area are statistically significant. An asterisk before the location of the race means it was the second time during the season that a race was held at that location. For all but one race, the data from 43 drivers were used to calculate each rs. Appendix A shows Spearman’s rs values and their associated two-tailed p values used to construct Figure 1.

An analysis of NASCAR drivers’ ranking in final practice and their finish positions throughout the 2009 season revealed statistically meaningful correlations between their practice

                                                                                                               7 Data from 36 NASCAR and 17 F1 races were analyzed. However, as explained in the Results section, we also analyzed the data of the top 20 points-leaders leading up to each NASCAR race. Thus, two sets of data were analyzed for each NASCAR race: one set that included every driver in the race (n = 43) and one set that included only the top 20 points-leaders before the race (n = 20). In total, 89 sets of data were analyzed: 36 NASCAR races, 17 F1 grands prix, and 36 NASCAR races for the top 20 points-leaders.

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        6  

performance and their finish positions in 29 of the 36 (81%) races. The better someone performed in practice, the better his finish position. For 27 of the 36 (75%) races, the drivers’ performances in the final practice and in qualifying were significantly correlated with their finish positions in a race. For most races, the correlations between Practice and Finish and between Qualifying and Finish were similar. However, there were some notable exceptions. At Bristol and Kansas, the correlations between Practice and Finish were statistically significant, but the correlations between Qualifying and Finish were not. The reverse was true in the second races held at Daytona and Atlanta. During these races, the correlations between Practice and Finish were not statistically significant, but those between Qualifying and Finish were significant. Finally, Talladega is notable for the fact that it was the only speedway that hosted two races for which the correlations between Practice and Finish and between Qualifying and Finish were not statistically significant in either race.

Figure 1. A graph of the correlations (rs) between Practice and Finish, Qualifying and Finish, and Points and Finish for each race in the 2009 NASCAR season. An asterisk before the name of a race means it was the second time during the season that a race was held at that location. Forty-three drivers started all races except for the first race at Pocono, where 42 drivers started the race. Thus, df = 41 for most races and df = 40 for one race. In general, the values in the grey area are not statistically significant and the values in the white area are statistically significant. However, because of limitations in the graphing software, the plot symbols of some marginally significant/insignificant values are not entirely within the grey or white areas. To see precisely which Spearman’s rank correlation coefficients were statistically significant, see Appendix A.

Figure 1 also shows that there were statistically significant correlations between the

drivers’ finish positions and their points-standings before a race in 31 of the 36 races (86%). Drivers ranked higher in the standings tended to finish a race before drivers ranked lower in the standings. Although this relationship was not evident during the first three races of the season, it occurred reliably thereafter except at both races held at Talladega. Moreover, if we compare the correlations between Finish and each of Practice, Qualifying, and Points, we see that the

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        7  

correlations between Points and Finish are generally greater than those between Practice and Finish and those between Qualifying and Finish.

To get a visualization of the raw data used to calculate the correlations shown in Figure 1, Figure 2 shows scatter plots of the strongest and weakest associations in Figure 1. The top graph illustrates the strong linear relationship between Points and Finish, which occurred in the second race held at Richmond. The bottom graph illustrates the almost-zero correlation between Practice and Finish from the first race held at Talladega.

 

 Figure 2. Scatter plots showing the strongest (top graph) and weakest (bottom graph) associations among the correlations in Figure 1. The top graph illustrates the relationship between Points and Finish for the second race held at Richmond [rs(41) = .809]. The bottom graph illustrates the relationship between Practice and Finish for the first race held at Talladega [rs(41) = -.013]. Note: Although 45 drivers participated in the final practice at Talladega (which occurs before qualifying at this race), only 43 drivers qualified for the race.

Correlations:  F1   Figure 3 shows how Finish was correlated with Practice, Qualifying, and Points across the 2009 F1 racing season. Values in the grey area are not statistically significant; values in the white area are statistically significant. For most grands prix, the data from 20 drivers were used to calculate

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        8  

each rs. Appendix B shows Spearman’s rs values and their associated two-tailed p values used to construct Figure 3.

Figure 3. A graph of the correlations (rs) between Practice and Finish, Qualifying and Finish, and Points and Finish for each grand prix in the 2009 F1 season. Twenty drivers started each grand prix except Hungary (18 drivers) and Japan (19 drivers), thus df = 18 for all grands prix except Hungary (df = 16) and Japan (df = 17). Details are the same as for Figure 1. To see precisely which Spearman’s rank correlation coefficients were statistically significant, see Appendix B.

In general, and in contrast to the NASCAR drivers, only the correlations between F1 drivers’ qualifying positions and their finish positions and between the F1 drivers’ points-standing and their finish positions were statistically significant. Statistically significant correlations between Practice and Finish were rare, occurring in only 7 of the 17 races (41%). Statistically significant correlations between Qualifying and Finish were observed in 14 of the 17 (82%) races, and between Points and Finish in 10 of the 17 races (59%). Also, unlike the NASCAR drivers, the correlations between Practice and Finish and between Qualifying and Finish were often dissimilar. Finally, with the exception of an upward trend in the correlations between Practice and Finish that started with the grand prix held in China and ended with the grand prix held in Great Britain, there were no strong trends in the correlations between Finish and each of Practice, Qualifying, and Points across the racing season.

To get a visualization of the raw data used to calculate the correlations shown in Figure 3, Figure 4 shows scatter plots of the strongest and weakest associations in Figure 3. The top graph illustrates the strong relationship between Qualifying and Finish from the Japanese Grand Prix. The bottom graph illustrates the near-zero correlation between Qualifying and Finish from the Brazilian Grand Prix.

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        9  

 

 Figure 4. Scatter plots showing the strongest (top graph) and weakest (bottom graph) associations among the correlations in Figure 3. The top graph illustrates the relationship between Qualifying and Finish for the grand prix held in Japan [rs(17) = .849]. The bottom graph illustrates the relationship between Qualifying and Finish for the grand prix held in Brazil [rs(18) = -.007]. Correlations:  NASCAR’s  Top  20  Points-­Leaders   Because correlation coefficients are affected by sample size, the differences in the results shown in Figures 1 and 3 may have occurred because Spearman’s rank correlation coefficients were calculated across different numbers of drivers (43 NASCAR drivers vs. 20 F1 drivers). If we calculated correlation coefficients for only 20 NASCAR drivers, the results of the analyses of the NASCAR and F1 drivers may have been more alike. To evaluate this possibility, we calculated

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        10  

Spearman’s rank correlation coefficients between Practice and Finish, Qualifying and Finish, and Points and Finish for the top 20 points-leading drivers before each NASCAR race.8

Figure 5 shows how Finish was correlated with Practice, Qualifying, and Points across the 2009 NASCAR season for the top 20 points-leaders before each race. Most striking is that there were few statistically significant correlations between Finish and each of Practice, Qualifying, and Points. This contrasts with the F1 drivers’ data for which there were statistically

Figure 5. A graph of the correlations (rs) between Practice and Finish, Qualifying and Finish, and Points and Finish for the top 20 points-leaders before each race in the 2009 NASCAR season. For all races, df = 18. Details are the same as for Figure 1. To see precisely which Spearman’s rank correlation coefficients were statistically significant, see Appendix C. significant correlations between Practice and Finish, between Qualifying and Finish, and between Points and Finish in 41%, 82%, 59% of the grands prix, respectively. For the top 20 points-leaders in NASCAR, statistically significant correlations between Practice and Finish, Qualifying and Finish, and Points and Finish occurred in only 8 of 36 (22%), 10 of 36 (28%), 7

                                                                                                               8 It could be argued that taking a random sample of NASCAR drivers, rather than taking a sample of the best NASCAR drivers, is the best way to assess whether the differences between the results of the NASCAR and F1 drivers were because of the difference in the sample sizes. Although this may be true, we chose to use the Top 20 NASCAR drivers instead of a random sample of them because using the best NASCAR drivers may actually be a better way to assess the role of sample sizes in the observed differences between the 43 NASCAR drivers and the 20 F1 drivers. Why? Because the 20 F1 drivers are not a random sample of F1 drivers; they are the best F1 drivers. A comparable sample of NASCAR drivers consists of the 20 best NASCAR drivers, not a random sample of them.

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        11  

of 36 (19%) races, respectively. Appendix C shows Spearman’s rs values and their associated two-tailed p values used to construct Figure 5.

To get a visualization of the raw data used to calculate the correlations shown in Figure 5, Figure 6 shows scatter plots of the strongest and weakest associations in Figure 5. The top graph illustrates the strong relationship between Qualifying and Finish, which occurred in the second race held at Richmond. The bottom graph illustrates the almost-zero correlation between Points and Finish from the first race held at Charlotte.

 

Figure 6. Scatter plots showing the strongest (top graph) and weakest (bottom graph) associations among the correlations in Figure 5. The top graph illustrates the relationship between Qualifying and Finish for the second race held at Richmond [rs(18) = .699]. The bottom graph illustrates the relationship between Points and Finish for the first race held at Charlotte [rs(18) = .001]. Regression:  NASCAR   Figure 7 shows the values of the multiple correlation coefficient for each of the four models listed in the Method section plotted across the races of the 2009 NASCAR season. For the models with the combinations Practice and Qualifying, Practice and Points, and Qualifying and Points, the R values plotted in the white area are statistically significant and those in the grey area are not. For the model with the combination Practice, Qualifying, and Points, only values

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        12  

above the dashed horizontal line are statistically significant. Appendix D shows the R values and the associated F statistics and p values used to construct Figure 7.

Figure 7. A graph of the multiple correlation coefficient (R) for each race in the 2009 NASCAR season. The R values plotted in the white area are statistically significant and those in the grey area are not, except for the model with the combination Practice, Qualifying, and Points. For this model, only values above the dashed horizontal line are statistically significant. However, because of limitations in the graphing software, the plot symbols of some marginally significant/insignificant values are not entirely within the grey or white areas. To see precisely which R values were statistically significant, see Appendix D. The degrees of freedom for the models with two predictor variables were (2, 40) for all races except for the second Pocono race (df = 2, 39). For the model with three predictor variables, the degrees of freedom were (3, 39) for all races except for the second Pocono race (df = 3, 38). There are five noteworthy features in the graph. One, most R values were statistically significant. Two, the R values were similar across races. Three, the two races at Talladega produced the lowest R values. Four, the R values for the model with only Practice and Qualifying were often smaller than the R values of the other three models. Five, there was considerable overlap among the R values for the models with Practice and Points, Qualifying and Points, and Practice, Qualifying, and Points. Given that there is a lot of overlap among these three models and that the common variable to all three models is Points, we can conclude that a model with Points as the only predictor variable is as good as any model with it plus Practice and/or Qualifying. In other words, the best predictor of a driver’s finish is his success up to that point in the racing season, and additional information about how he performed in practice and qualifying does little to help predict his finish position in most races.

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        13  

Regression:  F1   Figure 8 shows the R values for each of the four models listed in the Method section plotted across the grands prix of the 2009 F1 season. Appendix E shows the R values and the associated F statistics and p values used to construct Figure 8. Similar to the NASCAR drivers, there was relatively little change in the R values across grands prix. In contrast to the NASCAR drivers’ data, the model with Practice and Points generated lower R values than the other models. Also, there was considerable overlap between the model with Practice, Qualifying, and Points and the models with Practice and Qualifying and with Qualifying and Points. Given that there was a lot of overlap among these three models and that the common variable to all three models is Qualifying, we can conclude that a model with Qualifying as the only predictor variable is as good as any model with it plus Practice and/or Points. In other words, the best predictor of a driver’s finish is his performance during qualifying, and additional information about his success in the season and how he performed in practice does little to help predict his finish position in most grands prix.

Figure 8. A graph of the multiple correlation coefficient (R) for each grand prix in the 2009 F1 racing season. The R values plotted in the white area are statistically significant and those in the grey area are not, except for the model with the combination Practice, Qualifying, and Points. For this model, only values above the dashed horizontal line are statistically significant. However, because of limitations in the graphing software, the plot symbols of some marginally significant/insignificant values are not entirely within the grey or white areas. To see precisely which R values were statistically significant, see Appendix E. The degrees of freedom for the models with two predictor variables were (2, 17) for all grands prix except Hungary (df = 2, 15) and Japan (df = 2, 16). For the model with three predictor variables, the degrees of freedom were (3, 16) for all grands prix except Hungary (df = 3, 14) and Japan (df = 3, 15).

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        14  

Regression:  NASCAR’s  Top  20  Points-­Leaders   Figure 9 shows the R values for each of the four models listed in the Method section plotted across the 2009 NASCAR season for the top 20 points-leaders before each race. Appendix F shows the R values and the associated F statistics and p values used to construct Figure 9. Except for two clusters late in the season (*Michigan, *Bristol, *Atlanta in one cluster and *Talladega, *Texas, *Phoenix in the other cluster) where the R values were near or below .20, there was no trend in the R values across races. Also, in contrast to the data of the F1 drivers and the 43 drivers who comprise the broader NASCAR field, few of the R values from any of the four models reached statistical significance for the top 20 NASCAR points-leaders. Also in contrast to the data of the F1 drivers and the broader NASCAR field, there was no consistent overlap between any of the models across races. Given that none of the four models resulted in R values that were consistently statistically significant and that there was no consistent overlap between any of the models, we can conclude that no combinations of Practice, Qualifying, and/or Points can predict Finish for the top 20 points-leaders in most races.

Figure 9. A graph of the multiple correlation coefficient (R) for the top 20 points-leaders before each race in the 2009 NASCAR season. The R values plotted in the white area are statistically significant and those in the grey area are not, except for the model with the combination Practice, Qualifying, and Points. For this model, only values above the dashed horizontal line are statistically significant. However, because of limitations in the graphing software, the plot symbols of some marginally significant/insignificant values are not entirely within the grey or white areas. To see precisely which R values were statistically significant, see Appendix F. The degrees of freedom for the models with two predictor variables were (2, 17) for all races. For the model with three predictor variables, the degrees of freedom were (3, 16) for all races.

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        15  

Contingency  Table  Analyses   For many reasons, regression can be a complicated procedure (see Keith, 2006; Younger, 1985). Our brute-force approach that relied on visual analysis of the graphed R values is one way to simplify the testing of regression models. Another approach to evaluating the relative importance of Practice, Qualifying, and Points to predicting Finish is to use a chi-square test of independence. This approach involves ranking the magnitude of the correlations in each of the pairs of variables “Practice and Finish,” “Qualifying and Finish,” and “Points and Finish” for each race, and then tallying how often the largest correlation was associated with each pair of variables, how often the median correlation was associated with each pair of variables, and how often the smallest correlation was associated with each pair of variables. This produces a 3 x 3 contingency table with three rows for the pairs of variables (“Practice and Finish,” “Qualifying and Finish,” and “Points and Finish”) and three columns for the rank of a correlation (largest, median, smallest).

The results of the contingency table analyses are shown in Table 2. For the 43 drivers who normally start a NASCAR race (top panel), the largest correlations occurred most often between “Points and Finish” (28 of the 36 races). The correlations between “Practice and Finish” and between “Qualifying and Finish” were the median and smallest correlations in 15 to 17 of the 36 races. A chi-square test of independence confirmed that the pairs of variables and the correlation-ranks were not independent [χ2(4) = 48.50, p < .001] and that the largest correlations occurred most often in “Points and Finish” [χ2(2) = 32.17, p < .001].

Table 2 Three Panels Showing 3 x 3 Contingency Tables

Drivers Rank of rs

Variable Correlated With Finish 1st 2nd 3rd

Practice 5 16 15 NASCAR Qualifying 3 17 16 Points 28 3 5 Practice 4 3 10 F1 Qualifying 11 4 2 Points 2 10 5 Practice 12 7 17 NASCAR (Top 20) Qualifying 13 15 7 Points 11 14 12

For the F1 drivers (middle panel), the largest correlations occurred most often between

“Qualifying and Finish” (11 of the 17 grands prix). The correlations between “Practice and Finish” and between “Points and Finish” were the median and smallest correlations in 10 of the 17 races. A chi-square test of independence confirmed that the pairs of variables and the correlation-ranks were not independent [χ2(4) = 18.71, p < .001] and that the largest correlations occurred most often in “Qualifying and Finish” [χ2(2) = 7.88, p = .01].

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        16  

For the top 20 points-leaders before each NASCAR race (bottom panel), the results showed that, in contrast to the broader NASCAR field and the F1 drivers, there was no relationship between categories and the correlation-ranks [χ2(4) = 7.33, p = .12].

Thus, the 3 x 3 contingency table analyses corroborated our visual analyses of the graphed R values from the four models listed in the Method section. For the 43 NASCAR drivers who started a race, the best predictor of a driver’s finish was his overall success up to that point in the racing season (i.e., his points-standing). For the F1 drivers, the best predictor of a driver’s finish was his performance during qualifying. For the top 20 points-leaders in NASCAR, none of the variables (Practice, Qualifying, Points) were useful predictors of a driver’s finish position. How  Lead  Changes  and  Cautions  Relate  to  Predictability  of  Finish  

The analyses above quantified the correlation between Finish and each of Practice, Qualifying, and Points. Because correlation and prediction are closely related (the latter dependent on the former), we could say that the values of Spearman’s rs measured the degree that a driver’s finish position was predictable from his performance during practice, his performance during qualifying, and his overall success leading up a race. What we attempt to address next is, what factors are related to the predictability of Finish from Practice, Qualifying, and Points? We focused on two factors that occur during a race: lead changes and cautions. To answer the question, we correlated the values of Spearman’s rs from the analyses above with how often lead changes and cautions occurred in a race. In this context, we refer to the values of Spearman’s rs as Predictability of Finish.

Because many races had the same number of lead changes or cautions, we calculated the relationship between Predictability of Finish and each of Lead Changes and Cautions using Pearson’s product moment correlation coefficient (r). This measure of the association between variables works better than Spearman’s rs when many values in the data are the same. Spearman’s rs, but not Pearson’s r, requires that all raw data be converted to ranks, something that can be problematic if there are many values in the data that are the same.

NASCAR. The mean number of lead changes in a 2009 NASCAR race was 20 (SD = 11.46) and the mean number of cautions was 8.47 (SD = 3.40). Table 3 shows the correlations between Lead Changes and Predictability of Finish from each of the variables Practice, Qualifying, and Points, as well as between Cautions and Predictability of Finish from Practice, Qualifying, and Points.

The results showed that there were statistically significant inverse (negative) correlations between Lead Changes and Predictability of Finish from Practice, Qualifying, and Points. More intuitively, these results show that the more lead changes that occurred during a race, the more difficult it was to predict a driver’s finish position from his performance during practice, his performance during qualifying, or his points-standing. In short, an increase in lead changes meant a decrease in the Predictability of Finish from Practice, Qualifying, and Points. There were no statistically significant relationships between Cautions and Predictability of Finish from Practice, Qualifying, or Points.9

                                                                                                               9 The correlation between the number of cautions and the number of lead changes was not statistically significant (r = .03, p < .88).

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        17  

Table 3 Correlations (r) Between Lead Changes and Predictability of Finish and Cautions and Predictability of Finish

Drivers Variable Predictability of Finish from Practice Qualifying Points NASCAR Lead Changes -0.636* -0.356* -0.553* Cautions -0.218 -0.110 -0.061 F1 Lead Changes -0.129 0.277 -0.261 Cautions n/a n/a n/a NASCAR (Top 20) Lead Changes -0.433* -0.313 -0.412* Cautions 0.091 0.119 0.108 Note. For both groups of NASCAR drivers, n = 36; for F1 drivers, n = 17. * p < .05.

F1. The mean number of lead changes in an F1 grand prix was 4.53 (SD = 2.45),

significantly fewer than the 20 that typically occurred in a NASCAR race [t(51) = 5.48, p < .001]. In contrast to NASCAR races, there were no statistically significant correlations between Lead Changes and Predictability of Finish from Practice, Qualifying, or Points in F1 racing. (Information about the number of cautions in F1 grands prix was not available from formulaone.com, and thus no analyses involving Cautions were possible.)10

NASCAR  Top  20  Points-­Leaders. The results for the top 20 points-leaders before each NASCAR race were similar to the results of the broader 43-driver field. However, there was one exception: The correlation between Lead Changes and Predictability of Finish from Qualifying approached but did not reach statistical significance (p = .06). Thus, for the top 20 points-leaders, an increase in lead changes meant a decrease in the Predictability of Finish from Practice and Points.

Discussion   We used the results of the 2009 NASCAR and F1 seasons to answer six questions related to drivers’ performances in these two motorsports, which differ considerably in terms of their physical features. In what follows, we restate the questions and discuss the answers to each. What   is   the   relationship   between   a   driver’s   performance   during   the   final   practice  before  a  race  and  his  finish  position?                                                                                                                  10 Also, yellow- and red-flag cautions in F1 racing are different from those in NASCAR. In NASCAR, all yellow- and red-flag cautions apply to the entire speedway. In F1 racing, a red-flag caution also applies to the entire race circuit, but a yellow-flag caution may apply to only a particular section of the circuit (termed a “local caution”) or it may apply to the whole course (termed a “full-course caution”).

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        18  

For the 43 drivers who comprise the starting field of a NASCAR race there was a statistically significant relationship between their performances during the final practice and their finish positions in most races (see also Pfitzner & Rishel, 2005). For these statistically significant correlations, the rs values were generally between .4 and .6. This was not the case for the 20 drivers who comprise the starting field of an F1 grand prix. For these drivers, there was no reliable relationship between their performances during final practice and their finish positions; the rs values for most grands prix were between .2 and .4.

If we limit our analysis to the top 20 drivers in the NASCAR points-standings, there was no reliable relationship between a driver’s performance in final practice and his finish position. Moreover, in contrast to the F1 drivers, there was more variability in the rs values from race to race. In sum, a NASCAR driver’s performance during final practice is related to his finish position if the entire 43-driver field is entered into the analysis; the better a driver performed in practice, the better he performed in the race. This relationship was not evident for F1 drivers or for the top 20 points-leaders in NASCAR.

One possible reason for the difference between the standard 43-driver NASCAR field and the F1 drivers relates to when the final practice session occurs. In NASCAR, the final practice session normally occurs after qualifying. In F1 racing, the final practice session occurs before qualifying. These two motorsports thus differ in terms of how contiguous the final practice session is with the start of the race. In NASCAR, the purpose of the final practice is to set up the car for the conditions expected during a race. In F1 racing, the purpose is to set up a car for optimal performance during qualifying conditions, which may not necessarily be the conditions during the race. These differences between the two motorsports reflect what is known about contingencies of reinforcement and the allocation of behavior: People and other animals generally respond to satisfy the requirements of the more immediate consequence (Pear, 2001).

Alternatively, the similarity of the results for the top 20 NASCAR points-leaders and the F1 drivers suggests that performance in final practice, regardless of when it occurs, may not relate much to the race-day performance of elite drivers. Perhaps it is that the best NASCAR drivers and their teams are excellent at adapting during a race, that their improvisational skills are better than those of the 23 drivers who comprise the rest of the starting field. In relation to their finish position, how a top 20 points-leading NASCAR driver and his team adapt during a race may be more important than what they do during practice. Or, perhaps what they do during practice is not so much about producing the fastest laps during practice (a short-term payoff) but about testing configurations and strategies that may help them produce consistently fast laps across a variety of race conditions (a long-term payoff). As a result, there were few statistically significant correlations between these drivers’ performance during final practice and their finish positions. Whether this explanation or the difference in the timing of the final practice sessions (or both) best explains the differences among the broader NASCAR field, the best NASCAR driver, and the F1 drivers, we cannot say. What  is  the  relationship  between  a  driver’s  performance  during  qualifying  (and  thus  his  position  at  the  start  of  a  race)  and  his  finish  position?   A driver’s starting position is normally determined by his performance during qualifying. The better a driver performs in qualifying, the closer to the front of the field he will start a race. For the 43 drivers who comprise the starting field of a NASCAR race, there was a statistically significant relationship between their performances in qualifying and their finish positions in

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        19  

most races (see also Allender, 2008; Pfitzner & Rishel, 2005). For these statistically significant correlations, the rs values were generally between .4 and .6. Similar results were noted for the F1 drivers, except that the typical rs values were greater (between .6 and .8). This was not the case for the top 20 drivers in the NASCAR points-standings. For these drivers, there was no reliable relationship between a driver’s performance in qualifying and his finish position. Why this relationship was absent for these drivers is unclear. Perhaps here, too, how a top 20 points-leading driver and his team adapt during a race may be more important to their finish positions than where these drivers start a race. Alternatively, for the best drivers in NASCAR, perhaps it is that individual drivers and their teams are better suited to particular speedways or race conditions (Grace, Reeves, & Fitzgerald, 2003), and it is this fit between driver and environment that is more related to a driver’s finish position than his performance in qualifying.

If the difference in the importance of qualifying between NASCAR and F1 racing reflects differences in the demands of these two motorsports, then we might expect the importance of qualifying to be more similar in the two types of racing when the demands of each motorsport are more similar. Such is the case at NASCAR’s Sonoma and Watkins Glen races, both of which are run at road courses similar to the circuits used in F1 racing. The results, though, were inconsistent with this expectation. For the top 20 points-leading NASCAR drivers, the correlations between their qualifying performances and their finish positions were not statistically significant at either Sonoma or Watkins Glen. What  is  the  relationship  between  the  number  of  points  a  driver  has  accrued  in  a  season  (i.e.,  his  overall  success)  and  his  finish  position?   For the 43-driver NASCAR field, the more points a driver had accrued before a race, the better his finish position (see also Pfitzner & Rishel, 2005). This relationship got stronger as the season progressed with the correlation between Points and Finish approaching rs = .8 for several races in the last quarter of the season. In contrast, the relationship between Points and Finish was not as reliable for F1 drivers, and there was rarely a statistically significant correlation between these variables for the top 20 points-leaders in NASCAR.

In relation to NASCAR racing, the different results for the 43-driver field versus the top 20 points-leaders suggests again some sort of fundamental differences between the best drivers and the rest of the field. We speculated above that one of these differences might be the drivers’ and their teams’ abilities to make adjustments throughout the race, perhaps similar to a team who makes adjustments at halftime or alters their behavior as a function of variations that occur during a game (e.g., the other team’s strategy, injuries, weather conditions). That the results of the top 20 points-leading drivers in NASCAR were similar to those of the F1 drivers – all of whom could be considered elite in the sense that the starting field consists of only 20 drivers – adds some support to this speculation. How  do  the  three  relationships  above  (i.e.,  between  Practice  and  Finish,  Qualifying  and  Finish,  and  Points  and  Finish)  change  across  races?  

In general, there were no trends across the racing seasons in the correlations between drivers’ finish positions and their performances in final practice and qualifying, as well as how successful they were in previous races. This was true for NASCAR and F1 racing. The one exception was

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        20  

that the correlations between NASCAR drivers’ finish positions and their points-standing before a race became somewhat larger as the NASCAR season progressed.

It was interesting to note that the weakest correlations in NASCAR occurred during the two races at Talladega. During both of these races, NASCAR requires that all cars use restrictor plates that limit the amount of horsepower the engines can produce. The net effect of using a restrictor plate is a reduction in the maximum speed that a car can attain, which then results in a clustering of the cars as they travel around the speedway. Drivers have lamented and columnists have written about the unpredictability of Talladega races (Caraviello, 2009; McGee, 2009; Snider, 2009), which may be partly the result of a situation where a driver’s particular skills are less important. That is, somewhat independent of what a driver does, his car will not go much faster or slower than any other car. Although races at Daytona also require the use of restrictor plates, only the first Daytona race was unpredictable. This result may have as much to do with the use of restrictor plates as it does with Daytona being the first race of the season and its atypical qualifying sessions (known in 2009 as the Gatorade Duels).

In F1 racing, the presence of wet weather allows us to evaluate the influence of an uncommon environmental condition on the drivers’ finish positions. If rain is disruptive, we should observe noticeably lower correlations between Practice and Finish and between Qualifying and Finish, and perhaps even Points and Finish. The opportunity to evaluate the influence of rain occurred during the grands prix held in Malaysia and China. At the Malaysian Grand Prix, the practice and qualifying sessions were conducted in dry weather, but the grand prix took place in heavy rain. Despite the different conditions in practice and qualifying versus the grand prix, the correlations between the drivers’ finish positions and their performances in practice, qualifying, and the previous grand prix were all statistically significant. The results were different for the grand prix in China, where it also rained during the grand prix but not during practice or qualifying. At this grand prix, only the correlation between Qualifying and Finish was statistically significant. Although different from the result in Malaysia, the results from the Chinese Grand Prix are consistent with the other grands prix in the 2009 season. It seems that, overall, the relationship between F1 drivers’ performance in practice, qualifying, and previous races and their finish positions is about the same regardless of whether there were very different conditions in the practice and qualifying sessions versus the grand prix.

For any particular race, a driver’s performance in practice, qualifying, or previous races, may be better predictors of his finish position. For example, some racing analysts argue that qualifying is key at NASCAR’s Dover races because qualifying well gives a driver both a good starting position and a good pit selection (McReynolds, 2007). This analysis was not supported by the results from the two Dover races in 2009. For the first race at Dover, the correlations between Finish and each of Practice, Qualifying, and Points were rs = .58, .49, and .49, respectively. Practice was a better predictor of Finish than either Qualifying or Points. For the second race at Dover, the correlations between Finish and each of Practice, Qualifying, and Points were rs = .49, .59, and .74, respectively. For this race, Points was a better predictor than either Practice or Qualifying. If we restrict our analysis to the top 20 points-leaders, the only statistically significant correlation occurred between Points and Finish (rs = .56) in the second race at Dover.

Similarly, some NASCAR drivers contend that the final practice before a race is critically important to success (“NASCAR Sprint Cup Series: News and Notes – Lowe’s Motor Speedway,” 2009). But here, too, the results from 2009 only partially support this contention. Although Practice was significantly correlated with Finish in many races, the regression

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        21  

analyses and contingency table analyses showed that Practice was not as important as Points for predicting a NASCAR driver’s success. Among the top 20 points-leaders in NASCAR, the prevailing result was the unpredictability of the drivers’ finishing positions. What  is  a  more  reliable  predictor  of  a  driver’s  finish  position:  His  performance  during  practice,   his   performance   during   qualifying,   his   overall   success   prior   to   a   race,   or   a  combination  of  these  variables?       Overall, two different analyses – the visual inspection of the R values from the four regression models evaluated and the contingency table analyses – showed that the best predictor of a NASCAR driver’s finish position was his points-standing. For F1 drivers, the best predictor of their finish position was their performance during qualifying and thus their position at the start of a grand prix. For the top 20 points-leaders in NASCAR, there was no reliable predictor across races held in 2009.

One reason for this difference between NASCAR and F1 racing is probably related to differences in overtaking (i.e., passing another driver) in these two motorsports. Overtaking in NASCAR is a common occurrence; overtaking in F1 racing is rare. For this reason, lead changes in NASCAR are more prevalent than lead changes in F1 racing. The relative difficulty of overtaking in F1 means that a driver’s starting position is likely to have an important influence on a driver’s finish position (“Hungarian Grand Prix,” 2009). Given the importance of starting position in F1 racing, it should not surprise us that the most reliable correlation was between a driver’s performance in qualifying and his finish position. The lack of reliable predictors for the finish positions of NASCAR’s top 20 points-leaders going into a race is puzzling in light of the reliable predictors noted for the broader 43-driver field that starts most NASCAR races and the 20-driver field that starts most F1 grands prix. We speculated above that predicting the outcome of a NASCAR race based on the top 20 points-leaders’ performance in practice, qualifying, or past races is difficult because what these elite drivers and their teams do during a race may be what distinguishes the best drivers and teams at any given race. What might tip the scale towards a better finish position for a top 20 points-leading NASCAR driver and his team during a race? Any number of variables may be involved: faster pit stops, better mechanical adjustments to the car, more effective pit strategies (e.g., changing two vs. four tires), more effective communication between a driver and his crew chief, the superiority of a driver’s physical fitness in a demanding race, the superiority of a driver’s ability to concentrate in different circumstances, a better fit between the demands of race and a driver’s skills, a greater willingness on the part of a driver to incur risks to produce faster laps times or overtake other cars, and the like. What   factors   are   related   to   the   predictability   of   a   driver’s   finish   position   from   his  performance  in  practice,  qualifying,  and  his  success  up  to  that  point  in  the  season?   For the 43 drivers who normally start a NASCAR race, the results showed that an increase in lead changes, but not cautions, was correlated with an increase in the difficulty of predicting a driver’s finish position from his performance during practice, qualifying, and previous races. This result was similar for the top 20 points-leaders in NASCAR. However, for F1 drivers, there was no relationship between lead changes and the predictability of the finish positions from

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        22  

drivers’ performances during practice, qualifying, or how they had performed up to that point in the racing season.

Intuitively, this result makes sense. By definition, an increase in lead changes means that drivers in the lead are having a difficult time maintaining their position. As variability (of position) increases, predictability (of finish) decreases. This effect was absent in F1 racing because there are many fewer lead changes than in NASCAR.

That cautions were unrelated to the predictability of finish position from practice, qualifying, or past success is puzzling. Cautions lead to restarts in which all of the cars are lined up close together. One might think that restarts would cause lead changes because the gaps (distances) between cars are minimized during a restart. Given that there are as many restarts as there are cautions, one might expect a correlation between the number of cautions and the number of lead changes, and yet no such relationship occurred in the 2009 NASCAR season. Conclusions   We began this paper with a summary of some key physical differences between NASCAR and F1 racing (see Table 1). We can now create a new table of performance differences based on the results of the analyses of the 2009 races. As shown in Table 4, the most significant difference between these two forms of racing is that the finish positions in NASCAR are related to more variables than the finish positions in F1 racing. NASCAR drivers’ performances in practice, qualifying, and past races were usually positively correlated with their finish positions. In F1 racing, only drivers’ performances during qualifying and, to a lesser extent, in past races were positively correlated with their finish positions. Surprising (at least to us), there was rarely a significant correlation between the finish positions of the best NASCAR drivers and their performances in practice, qualifying, or previous races. Predicting these drivers’ finish positions from any combination of their performances in practice, qualifying, or previous races was usually unsuccessful. It seems that in NASCAR, the best drivers predictably win a race, but who among these drivers will win is not predictable from how they performed in practice, qualifying, or in previous races. It remains for future research to identify and study variables associated with these elite drivers’ finish positions and to identify what makes their performances different from those of drivers in F1 racing.

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        23  

References  

Aliaga, M., & Gunderson, B. (2006). Interactive statistics (3rd ed.). Upper Saddle River, NJ: Prentice Hall. Allender, M. (2008). Predicting the outcome of NASCAR races: The role of driver experience. Journal of

Business & Economic Research, 6, 79-84. Blount, T. (2009. March 31). F1, Cup made for wildly different day. ESPN.com. Retrieved from

cvchttp://sports.espn.go.com/rpm/nascar/cup/columns/story?columnist=blount_terry&id=4029638 Caraviello, D. (2009, November 4). Like an unwelcome journey into NASCAR’s difficult past. NASCAR.com.

Retrieved from http://www.nascar.com/2009/news/opinion/11/04/inside.line.dcaraviello.talladega.past/index.html

Collantine, K. (2006, July 22). F1 vs NASCAR [Web log post]. Retrieved from http://www.f1fanatic.co.uk/2006/07/22/f1-vs-nascar

Graves, T., Reese, C. S., & Fitzgerald, M. (2003). Hierarchical models for permutations: Analysis of auto racing results. Journal of the American Statistical Association, 98, 282-291.

Hook, N. (2010, June 12). NASCAR vs. Formula One. Examiner.com. Retrieved from http://www.examiner.com/x-4026-Minneapolis-Autos-Examiner~y2009m6d12-NASCAR-vs-Formula-One

Hungarian Grand Prix – Team and Driver Preview Quotes (2009, July 21). Formula1.com. Retrieved from http://www.formula1.com/news/headlines/2009/7/9631.html

Kazdin, A. E. (1982). Single-case research designs: Methods for clinical and applied settings. New York: Oxford University Press.

Keith, T. Z. (2006). Multiple regression and beyond. Boston, MA: Allyn and Bacon.

Table 4

Performance Variables: Similarities and Differences Between NASCAR and F1 in 2009

Characteristic Drivers

NASCAR F1 NASCAR (Top 20) Finish position generally correlated with practice performance

Yes, 81% of races No, 41% of grands prix No, 22% of races

Finish position generally correlated with qualifying performance/starting position

Yes, 75% of races Yes, 82% of grands prix No, 28% of races

Finish position generally correlated with overall success in season

Yes, 86% of races Somewhat, 59% of grands prix

No, 19% of races

Best overall predictor(s) of finish position

Points-standing before a race

Qualifying performance (starting position)

None of the performance variables studied

Relationship between lead changes and predictability of finish position

↑ lead changes, ↓ predictability

None based on performance variables studied

↑ lead changes, ↓ predictability based on practice performance and overall success in season

Relationship between cautions and predictability of finish position

None based on performance variables studied

(Data not available) None based on performance variables studied

Changes in correlations across season

Slight increase in correlation between Finish and Points

Transitory increase in correlation between Finish and Practice

None based on performance variables studied

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        24  

McGee, R. (2009, October 30). A Talladega twist of fate. ESPN.com. Retrieved from http://insider.espn.go.com/espn/blog/index?entryID=4608684&name=mcgee_ryan&action=login&appRedirect=http%3a%2f%2finsider.espn.go.com%2fespn%2fblog%2findex%3fentryID%3d4608684%26name%3dmcgee_ryan

McReynolds, L. (2007, September 21). Mac Track: Past can’t predict future success. msn.foxsports.com. Retrieved from http://foxsports.foxnews.com/nascar/story/7243656/Mac-Track:-Past-can't-predict-future-success

NASCAR’s Jeff Gordon on Formula One Racing (2004, June 17). Formula1.com. Retrieved from http://www.formula1.com/news/features/2004/6/1745.html

NASCAR Sprint Cup Series: News and Notes – Lowe’s Motor Speedway (2009, October 14). Retrieved from http://www.autoracingdaily.com/news/nascar-sprint-cup-series/nascar-sprint-cup-series-news-notes-lowes-motor-speedway1

Pear, J. J. (2001). The science of learning. Philadelphia, PA: Psychology Press. Pfitzner, B., & Rishel, T. (2005). Do reliable predictors exist for the outcomes of NASCAR races? The Sport

Journal, 8(2). Retrieved from http://www.thesportjournal.org/article/do-reliable-predictors-exist-outcomes-nascar-races

Snider, M. (2009, October 30). Chasers have a lot on their plate as Talladega calls. NASCAR.com. Retrieved from http://www.nascar.com/2009/news/features/10/30/chase.tiering.talladega/index.html

Younger, M. S. (1985). A first course in linear regression (2nd ed.). Boston, MA: Duxbury Press.

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        25  

Appendix  A  

Spearman rs (and their p values) used to construct Figure 1 Race Variables Finish and Practice Finish and Qualifying Finish and Points Spearman's rs p Spearman's rs p Spearman's rs p Daytona 0.119 0.447 -0.085 0.587 0.263 0.087 Fontana 0.557 0.000 0.489 0.000 0.299 0.051 Las Vegas 0.328 0.031 0.270 0.080 0.131 0.401 Atlanta 0.499 0.000 0.392 0.009 0.585 0.000 Bristol 0.469 0.001 0.187 0.231 0.488 0.000 Martinsville 0.560 0.000 0.645 0.000 0.645 0.000 Texas 0.402 0.007 0.549 0.000 0.595 0.000 Phoenix 0.627 0.000 0.529 0.000 0.622 0.000 Talladega -0.013 0.931 0.084 0.590 -0.137 0.381 Richmond 0.402 0.007 0.320 0.036 0.597 0.000 Darlington 0.164 0.292 0.280 0.069 0.407 0.006 Charlotte 0.613 0.000 0.460 0.001 0.423 0.004 Dover 0.580 0.000 0.493 0.000 0.488 0.000 Pocono 0.498 0.000 0.688 0.000 0.692 0.000 Michigan 0.640 0.000 0.450 0.002 0.693 0.000 Sonoma 0.426 0.004 0.476 0.001 0.475 0.001 New Hampshire 0.450 0.002 0.607 0.000 0.586 0.000 *Daytona 0.236 0.126 0.557 0.000 0.577 0.000 Chicago 0.614 0.000 0.456 0.002 0.722 0.000 Indianapolis 0.588 0.000 0.549 0.000 0.633 0.000 *Pocono 0.711 0.000 0.783 0.000 0.783 0.000 Watkins Glen 0.516 0.000 0.514 0.000 0.558 0.000 *Michigan 0.349 0.021 0.322 0.034 0.477 0.001 *Bristol 0.431 0.003 0.300 0.050 0.602 0.000 *Atlanta 0.105 0.504 0.398 0.008 0.503 0.000 *Richmond 0.460 0.001 0.591 0.000 0.809 0.000 *New Hampshire 0.596 0.000 0.460 0.001 0.756 0.000 *Dover 0.485 0.000 0.592 0.000 0.794 0.000 Kansas 0.471 0.001 0.191 0.220 0.665 0.000 *Fontana 0.443 0.002 0.397 0.008 0.630 0.000 *Charlotte 0.510 0.000 0.568 0.000 0.452 0.002 *Martinsville 0.443 0.020 0.467 0.001 0.801 0.000 *Talladega 0.127 0.414 0.215 0.165 0.221 0.152 *Texas 0.168 0.280 0.259 0.092 0.528 0.000 *Phoenix 0.614 0.000 0.594 0.000 0.754 0.000 Homestead 0.589 0.000 0.353 0.020 0.651 0.000 Note. The degrees of freedom for all races was 41, except for Pocono (df= 40) The * denotes that drivers had raced at that track earlier in the season.

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        26  

Appendix  B  

Spearman rs (and their p values) used to construct Figure 3 Grand Prix Variables Finish and Practice Finish and Qualifying Finish and Points Spearman's rs p Spearman's rs p Spearman's rs p Australia 0.300 0.197 0.087 0.714 -0.440 0.051 Malaysia 0.427 0.060 0.630 0.002 0.558 0.010 China -0.260 0.267 0.514 0.020 0.288 0.216 Bahrain 0.130 0.582 0.739 0.000 0.665 0.001 Spain 0.251 0.285 0.804 0.000 0.558 0.010 Monaco 0.515 0.019 0.476 0.030 0.424 0.062 Turkey 0.523 0.017 0.730 0.000 0.577 0.007 Great Britain 0.654 0.001 0.830 0.000 0.695 0.000 Germany 0.320 0.168 0.452 0.045 0.595 0.005 Hungary 0.496 0.030 0.370 0.118 0.334 0.175 Europe 0.281 0.229 0.720 0.000 0.474 0.034 Belgium 0.067 0.776 0.621 0.003 0.162 0.494 Italy 0.529 0.016 0.524 0.017 0.366 0.111 Singapore 0.505 0.023 0.715 0.000 0.459 0.041 Japan 0.349 0.142 0.849 0.000 0.658 0.002 Brazil -0.515 0.019 -0.007 0.974 0.390 0.088 Abu Dhabi 0.425 0.061 0.628 0.002 0.566 0.009 Note. The degrees of freedom for all races was 18 except for Hungary (df= 16) and Japan (df = 17).

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        27  

Appendix  C  

Spearman rs (and their p values) used to construct Figure 5 Race Variables Finish and Practice Finish and Qualifying Finish and Points Spearman's rs p Spearman's rs p Spearman's rs p Daytona 0.067 0.776 -0.255 0.276 0.192 0.416 Fontana 0.514 0.020 0.392 0.086 -0.073 0.757 Las Vegas 0.544 0.013 0.478 0.032 0.018 0.939 Atlanta 0.369 0.108 0.187 0.427 0.230 0.328 Bristol 0.386 0.092 0.073 0.757 0.242 0.302 Martinsville 0.630 0.002 0.350 0.129 0.350 0.129 Texas 0.333 0.150 0.569 0.008 0.470 0.036 Phoenix 0.460 0.041 0.578 0.007 0.285 0.222 Talladega -0.048 0.840 0.069 0.771 -0.279 0.232 Richmond -0.144 0.543 0.272 0.245 0.169 0.475 Darlington 0.186 0.431 0.172 0.465 0.374 0.103 Charlotte 0.517 0.019 0.467 0.037 0.001 0.994 Dover 0.285 0.222 0.269 0.251 -0.010 0.964 Pocono -0.031 0.894 0.209 0.376 0.209 0.376 Michigan 0.323 0.164 -0.070 0.767 0.269 0.251 Sonoma 0.209 0.376 0.362 0.116 0.031 0.894 New Hampshire 0.530 0.016 0.547 0.012 0.547 0.012 *Daytona -0.239 0.309 0.535 0.014 0.535 0.014 Chicago 0.219 0.352 0.431 0.057 0.294 0.207 Indianapolis 0.192 0.416 0.541 0.013 0.204 0.387 *Pocono 0.428 0.059 0.436 0.054 0.436 0.054 Watkins Glen 0.615 0.003 0.326 0.160 0.279 0.232 *Michigan 0.033 0.889 -0.115 0.626 -0.022 0.924 *Bristol 0.254 0.279 0.230 0.329 -0.103 0.663 *Atlanta -0.052 0.825 0.081 0.733 0.067 0.776 *Richmond 0.261 0.265 0.699 0.006 0.436 0.054 *New Hampshire 0.694 0.000 0.449 0.046 0.434 0.055 *Dover 0.377 0.100 0.204 0.387 0.555 0.010 Kansas -0.040 0.865 0.395 0.084 0.559 0.010 *Fontana 0.287 0.219 0.317 0.172 0.500 0.024 *Charlotte 0.183 0.438 0.550 0.011 -0.126 0.595 *Martinsville 0.261 0.265 0.335 0.148 0.493 0.027 *Talladega 0.021 0.929 -0.240 0.306 -0.240 0.306 *Texas 0.046 0.845 0.021 0.929 0.043 0.855 *Phoenix 0.204 0.387 0.293 0.209 0.390 0.088 Homestead 0.156 0.510 -0.141 0.552 0.299 0.199 Note. The degrees of freedom for all races was 18. The * denotes that drivers had raced at that track earlier in the season.

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        28  

Appendix  D  

R values (and their related F statistics and p values) used to construct Figure 9 Race Model Finish = α + β1Practice + β2Qualifying Finish = α + β1Practice + β2Points R F p R F p Daytona 0.169 0.589 0.559 0.293 1.883 0.165 Fontana 0.609 11.817 0.000 0.594 10.943 0.000 Las Vegas 0.359 2.963 0.063 0.332 2.485 0.096 Atlanta 0.537 8.120 0.001 0.658 15.275 0.000 Bristol 0.478 5.929 0.005 0.591 10.779 0.000 Martinsville 0.720 21.572 0.000 0.741 24.496 0.000 Texas 0.591 10.735 0.000 0.575 9.882 0.000 Phoenix 0.642 14.055 0.000 0.719 21.429 0.000 Talladega 0.084 0.144 0.866 0.135 0.374 0.690 Richmond 0.404 3.921 0.027 0.654 14.954 0.000 Darlington 0.289 1.825 0.174 0.432 4.614 0.015 Charlotte 0.652 14.854 0.000 0.650 14.654 0.000 Dover 0.626 12.932 0.000 0.609 11.848 0.000 Pocono 0.691 17.829 0.000 0.699 18.649 0.000 Michigan 0.706 19.934 0.000 0.743 24.775 0.000 Sonoma 0.576 9.941 0.000 0.557 9.014 0.000 New Hampshire 0.623 12.689 0.000 0.594 10.908 0.000 *Daytona 0.569 9.580 0.000 0.579 10.117 0.000 Chicago 0.624 12.762 0.000 0.738 24.030 0.000 Indianapolis 0.638 13.763 0.000 0.667 16.089 0.000 *Pocono 0.823 42.177 0.000 0.812 38.863 0.000 Watkins Glen 0.586 10.463 0.000 0.621 12.614 0.000 *Michigan 0.383 3.453 0.041 0.528 7.734 0.001 *Bristol 0.440 4.818 0.013 0.629 13.130 0.000 *Atlanta 0.398 3.779 0.031 0.567 9.492 0.000 *Richmond 0.595 10.968 0.000 0.798 35.141 0.000 *New Hampshire 0.602 11.404 0.000 0.740 24.339 0.000 *Dover 0.599 11.235 0.000 0.797 34.917 0.000 Kansas 0.477 5.893 0.005 0.652 14.792 0.000 *Fontana 0.494 6.490 0.003 0.617 12.323 0.000 *Charlotte 0.585 10.448 0.000 0.526 7.689 0.001 *Martinsville 0.508 6.989 0.000 0.772 29.671 0.000 *Talladega 0.219 1.016 0.371 0.219 1.016 0.371 *Texas 0.273 1.612 0.212 0.472 5.734 0.006 *Phoenix 0.674 16.701 0.000 0.725 22.241 0.000 Homestead 0.590 10.725 0.000 0.697 18.917 0.000

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        29  

Appendix  D  (continued)  

Race Model Finish = α + β1Qualifying + β2Points Finish = α + β1Practice + β2Qualifying + β3Points R F p R F p Daytona 0.337 2.573 0.008 0.342 1.726 0.177 Fontana 0.532 7.902 0.001 0.631 8.606 0.000 Las Vegas 0.305 2.058 0.141 0.364 1.994 0.130 Atlanta 0.650 14.656 0.000 0.671 10.676 0.000 Bristol 0.578 10.044 0.002 0.608 7.627 0.000 Martinsville 0.687 17.944 0.000 0.742 15.926 0.000 Texas 0.630 13.211 0.000 0.635 8.818 0.000 Phoenix 0.676 16.876 0.000 0.719 13.974 0.000 Talladega 0.162 0.542 0.586 0.166 0.372 0.733 Richmond 0.655 15.044 0.000 0.655 7.153 0.000 Darlington 0.430 4.540 0.016 0.514 3.427 0.017 Charlotte 0.580 10.179 0.000 0.681 11.296 0.000 Dover 0.552 8.785 0.000 0.638 8.962 0.000 Pocono 0.708 19.703 0.000 0.716 9.741 0.000 Michigan 0.681 17.347 0.000 0.754 17.131 0.000 Sonoma 0.527 7.704 0.001 0.616 7.952 0.000 New Hampshire 0.607 11.672 0.000 0.623 8.249 0.000 *Daytona 0.565 9.427 0.000 0.586 6.821 0.000 Chicago 0.762 27.735 0.000 0.762 18.047 0.000 Indianapolis 0.711 20.450 0.000 0.712 13.371 0.000 *Pocono 0.796 34.635 0.000 0.826 28.086 0.000 Watkins Glen 0.642 14.052 0.000 0.667 10.443 0.000 *Michigan 0.518 7.344 0.001 0.532 5.137 0.004 *Bristol 0.631 13.255 0.000 0.643 9.187 0.000 *Atlanta 0.566 9.432 0.000 0.567 6.170 0.001 *Richmond 0.814 39.286 0.000 0.818 26.336 0.000 *New Hampshire 0.736 23.777 0.000 0.741 15.852 0.000 *Dover 0.796 34.720 0.000 0.798 22.948 0.000 Kansas 0.652 14.812 0.000 0.652 9.629 0.000 *Fontana 0.625 12.857 0.000 0.631 8.605 0.000 *Charlotte 0.575 9.913 0.000 0.589 6.923 0.000 *Martinsville 0.776 30.424 0.000 0.779 20.101 0.000 *Talladega 0.217 0.997 0.377 0.222 0.678 0.570 *Texas 0.478 5.943 0.005 0.478 3.864 0.016 *Phoenix 0.717 21.214 0.000 0.736 15.377 0.000 Homestead 0.628 13.051 0.000 0.697 12.308 0.000 Note. The degrees of freedom for the two- and three-variable models were (2, 40) and (3, 39), respectively, for all races except Pocono (df = 2, 39 and 3, 38). The * denotes that drivers had raced at that track earlier in the season.

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        30  

Appendix  E  

R values (and their related F statistics and p values) used to construct Figure 8 Grand Prix Model Finish = α + β1Practice + β2Qualifying Finish = α + β1Practice + β2Points R F p R F p Australia 0.300 0.845 0.446 0.579 4.308 0.030 Malaysia 0.630 5.597 0.013 0.681 7.353 0.005 China 0.635 5.773 0.012 0.418 1.804 0.194 Bahrain 0.789 14.108 0.000 0.730 9.705 0.001 Spain 0.810 16.231 0.000 0.589 4.538 0.026 Monaco 0.536 3.432 0.055 0.572 4.147 0.034 Turkey 0.749 10.881 0.000 0.612 5.113 0.018 Great Britain 0.837 20.019 0.000 0.809 16.159 0.000 Germany 0.478 2.524 0.109 0.608 5.003 0.019 Hungary 0.501 2.523 0.113 0.523 2.826 0.090 Europe 0.741 10.441 0.001 0.467 2.380 0.122 Belgium 0.660 6.574 0.007 0.103 0.091 0.913 Italy 0.587 4.490 0.027 0.612 5.102 0.018 Singapore 0.718 9.053 0.002 0.575 4.210 0.032 Japan 0.866 24.111 0.000 0.576 3.986 0.039 Brazil 0.542 3.551 0.051 0.707 8.522 0.002 Abu Dhabi 0.633 5.702 0.012 0.623 5.407 0.015

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        31  

Appendix  E  (continued)  

Grand Prix Model Finish = α + β1Qualifying + β2Points Finish = α + β1Practice + β2Qualifying + β3Points R F p R F p Australia 0.523 3.217 0.065 0.583 2.755 0.076 Malaysia 0.694 7.925 0.003 0.702 5.183 0.010 China 0.523 3.203 0.066 0.651 3.937 0.027 Bahrain 0.801 15.234 0.000 0.805 9.882 0.000 Spain 0.805 15.690 0.000 0.811 10.289 0.000 Monaco 0.538 3.467 0.054 0.579 2.701 0.080 Turkey 0.740 10.331 0.001 0.755 7.087 0.003 Great Britain 0.839 20.265 0.000 0.855 14.518 0.000 Germany 0.603 4.863 0.021 0.613 3.222 0.051 Hungary 0.320 0.859 0.443 0.529 1.822 0.189 Europe 0.730 9.700 0.001 0.745 6.653 0.003 Belgium 0.626 5.478 0.014 0.685 4.724 0.015 Italy 0.547 3.643 0.048 0.626 3.452 0.041 Singapore 0.721 9.254 0.001 0.724 5.889 0.006 Japan 0.879 27.418 0.000 0.896 20.498 0.000 Brazil 0.447 2.127 0.149 0.713 5.516 0.008 Abu Dhabi 0.662 6.664 0.007 0.664 4.226 0.022 Note. The degrees of freedom for the two- and three-variable models were (2, 17) and (3, 16), respectively, for all grands prix except Hungary (df = 2, 15 and 3 ,14) and Japan (df = 2, 16 and 3, 15).

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        32  

Appendix  F  

R values (and their related F statistics and p values) used to construct Figure 9 Race Model Finish = α + β1Practice + β2Qualifying Finish = α + β1Practice + β2Points R F p R F p Daytona 0.273 0.689 0.515 0.196 0.340 0.716 Fontana 0.460 2.283 0.132 0.435 1.990 0.167 Las Vegas 0.547 3.641 0.048 0.544 3.573 0.050 Atlanta 0.421 1.840 0.189 0.336 1.085 0.360 Bristol 0.306 0.883 0.432 0.351 1.195 0.326 Martinsville 0.639 5.879 0.011 0.640 5.903 0.011 Texas 0.597 4.726 0.023 0.532 3.359 0.058 Phoenix 0.587 4.479 0.027 0.463 2.320 0.128 Talladega 0.085 0.063 0.939 0.288 0.769 0.478 Richmond 0.513 3.036 0.074 0.242 0.532 0.597 Darlington 0.317 0.952 0.405 0.555 3.788 0.043 Charlotte 0.596 4.706 0.023 0.433 1.965 0.170 Dover 0.427 1.902 0.179 0.415 1.777 0.199 Pocono 0.241 0.528 0.599 0.292 0.795 0.467 Michigan 0.396 1.589 0.232 0.539 3.491 0.053 Sonoma 0.466 2.362 0.124 0.352 1.205 0.324 New Hampshire 0.672 7.024 0.005 0.680 7.314 0.005 *Daytona 0.504 2.909 0.081 0.443 2.082 0.155 Chicago 0.462 2.319 0.128 0.334 1.074 0.363 Indianapolis 0.465 2.356 0.125 0.244 0.540 0.592 *Pocono 0.552 3.740 0.045 0.541 3.527 0.052 Watkins Glen 0.544 3.582 0.050 0.524 3.219 0.065 *Michigan 0.145 0.184 0.833 0.066 0.038 0.962 *Bristol 0.259 0.611 0.554 0.230 0.477 0.628 *Atlanta 0.105 0.095 0.909 0.160 0.225 0.800 *Richmond 0.736 10.058 0.001 0.445 2.103 0.152 *New Hampshire 0.541 3.532 0.052 0.544 3.583 0.050 *Dover 0.156 0.213 0.810 0.551 3.721 0.045 Kansas 0.543 3.562 0.057 0.564 3.967 0.038 *Fontana 0.330 1.040 0.375 0.271 0.679 0.520 *Charlotte 0.418 1.800 0.195 0.400 1.620 0.227 *Martinsville 0.308 0.894 0.427 0.342 1.131 0.345 *Talladega 0.204 0.371 0.695 0.134 0.158 0.855 *Texas 0.113 0.111 0.895 0.206 0.378 0.690 *Phoenix 0.191 0.322 0.729 0.108 0.101 0.904 Homestead 0.273 0.689 0.515 0.205 0.375 0.692

PRACTICE,  QUALIFYING,  AND  PAST  SUCCESS  IN  NASCAR  AND  F1                                                                                                                                                                        33  

Appendix  F  (continued)  

R values (and their related F statistics and p values) used to construct Figure 9 Race Model Finish = α + β1Practice + β2Qualifying Finish = α + β1Practice + β2Points R F p R F p Daytona 0.338 1.102 0.354 0.338 0.692 0.570 Fontana 0.345 1.153 0.339 0.460 1.433 0.270 Las Vegas 0.434 1.981 0.168 0.578 2.681 0.081 Atlanta 0.390 1.532 0.244 0.447 1.339 0.296 Bristol 0.275 0.697 0.511 0.351 0.754 0.536 Martinsville 0.343 1.134 0.344 0.640 3.704 0.033 Texas 0.633 5.703 0.012 0.655 4.021 0.026 Phoenix 0.577 4.246 0.031 0.589 2.846 0.070 Talladega 0.287 0.767 0.479 0.288 0.483 0.699 Richmond 0.302 0.857 0.442 0.530 2.087 0.142 Darlington 0.475 2.479 0.113 0.535 2.378 0.108 Charlotte 0.494 2.749 0.092 0.597 2.968 0.063 Dover 0.359 1.261 0.308 0.447 1.332 0.298 Pocono 0.360 1.271 0.305 0.384 0.927 0.450 Michigan 0.350 1.189 0.328 0.552 2.341 0.111 Sonoma 0.430 1.939 0.174 0.476 1.564 0.236 New Hampshire 0.549 3.680 0.047 0.680 4.591 0.016 *Daytona 0.519 3.134 0.069 0.543 2.238 0.123 Chicago 0.536 3.431 0.056 0.543 2.232 0.123 Indianapolis 0.527 3.285 0.062 0.528 2.067 0.144 *Pocono 0.493 2.737 0.093 0.552 2.347 0.111 Watkins Glen 0.425 1.879 0.183 0.544 2.253 0.121 *Michigan 0.159 0.221 0.803 0.159 0.139 0.935 *Bristol 0.242 0.532 0.597 0.278 0.448 0.722 *Atlanta 0.146 0.187 0.830 0.163 0.147 0.930 *Richmond 0.749 10.875 0.000 0.753 7.001 0.003 *New Hampshire 0.382 1.457 0.260 0.548 2.299 0.116 *Dover 0.573 4.166 0.033 0.583 2.750 0.076 Kansas 0.461 2.301 0.130 0.678 4.545 0.017 *Fontana 0.325 1.005 0.386 0.355 0.772 0.526 *Charlotte 0.626 5.489 0.014 0.643 3.771 0.031 *Martinsville 0.401 1.633 0.224 0.404 1.043 0.400 *Talladega 0.248 0.559 0.581 0.253 0.366 0.778 *Texas 0.203 0.366 0.699 0.206 0.237 0.868 *Phoenix 0.177 0.277 0.761 0.191 0.203 0.892 Homestead 0.266 0.651 0.534 0.363 0.812 0.505

Note. The degrees of freedom for the two- and three-variable models were (2, 17) and (3, 16), respectively, for all races. The * denotes that drivers had raced at that track earlier in the season.