Sports Statistics:First Class Meeting

Dale Zimmerman

January 20, 2017

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First things

• Go through syllabus

• Discuss assignment

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Some important dates in the history of sports statis-tics

• 1952 — First sports statistics paper published in a major statisicsjournal (Frederick Mosteller’s analysis of World Series data inJASA)

• 1992 — Creation of the Statistics in Sports section within theASA

• 1994 — September issue of JASA devoted entirely to sportsstatistics

• 2005 — Inaugural issue published of the ASA journal Journalof Quantitative Analysis in Sports

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Some sports statistics books

• Anthology of Statistics in Sports, (2005), Albert, J., Bennett,J., and Cochran, J.J. (eds.), Philadephia: SIAM.

• Analyzing Baseball Data with R, (2014), Marchi, M. and Al-bert, J. Boca Raton, FL: CRC Press.

• Handbook of Statistical Methods and Analyses in Sports, (2016),Albert, J., Glickman, M.E., Swartz, T.B., and Koning, R.H.(eds.), Boca Raton, FL: Chapman & Hall/CRC.(https://www.crcpress.com/Handbook-of-Statistical-Methods-and-Analyses-in-Sports/Albert-Glickman-Swartz-Koning/p/book/9781498737364)

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Some interesting sports statistics graphics

1. Score progression plots

• Not that illuminating for most major team sports (football,baseball, soccer, hockey)

• First proposed for use in basketball by P.H. Westfall, “Graph-ical presentation of a basketball game,” The American Statis-tician, 44:305–307 (1990).

• Westfall’s idea was to display the difference in score as thegame progresses.

• Example: Iowa’s men’s basketball team first 6 losses in the2014-15 season (next page):

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Iowa vs Texas

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Iowa vs Syracuse

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Iowa vs Iowa State

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Iowa vs UNI

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Iowa vs Michigan State

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Iowa vs Wisconsin

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• Some websites now display scores of the two teams in cdf-likeform for the game.

• There appears to be no published statistical analysis yet ofthese types of plots. However, the following paper is relevant:Gabel, A. and Redner, S., “Random walk picture of basket-ball scoring,” Journal of Quantitative Analysis in Sports, 8(1),1416 (2012).

• A functional principal component analysis to uncover the dom-inant pattern of curves for a given team in a given season couldbe interesting.

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2. Continous-time win probability plots

• Common now for NFL, NCAA football, and NBA games.

• Go to

http://live.advancednflstats.com/index.php?gameid1=2015020100

to see how the win probability evolved over time in the 2015Super Bowl between the Seattle Seahawks and the New Eng-land Patriots.

• We will learn one way these plots may be constructed (viarandom forests) in a few weeks.

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3. Basketball shot charts

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• It appears that one statistical analysis of shot chart data hasbeen published: “A spatial analysis of basketball shot chartdata,” by B.J. Reich, J. Hodges, B.P. Carlin, and A.M. Reich,The American Statistician, 60:3–12 (2006).

• The authors analyze the shot chart for Sam Cassell, a guardfor the Minnesota Timberwolves, in 2003–2004. They reducethe shot chart to counts (and probabilities of made shots) in an11×11 grid in polar coordinates, plus the semicircle within 2feet of the basket.

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• Authors’ objective: Understand how several covariates (whetherat home or away, behind or ahead, 1st half or 2nd half, . . . ) af-fect Cassell’s shot success.

• Because some of the 122 cells have ≤ 4 shot attempts, bor-rowing strength from (smoothing over) neighboring cells isimportant for obtaining stable estimates of covariate effects.

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Shot success: Model

• Shooting percentage was modeled with separate logistic re-gressions at each of the 122 cells.

• The logit of the success probability was modeled as a linearfunction of the covariates, and the regression coefficients wereallowed to vary over cells.

• A spatial model known as a CAR (Conditional AutoRegres-sive model) prior was placed on the regression coefficients,which smooths them spatially.

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Shot locations: Results

• Significant covariate effects: NOKG (whether Kevin Garnettwas not in the game), NOKG×NOLS (interaction of NOKGand whether Latrell Sprewell was not in the game), TEAM-FGA (whether the Timberwolves took more than 80 shots thatgame)

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4. Baseball spray charts

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• A google search suggests that no statistical analysis of spraycharts has been published yet.

• Last year, Emily Eck did her Creative Component on this topicunder my supervision.

• She analyzed data from all hitters (combined) for the the en-tire 2014 MLB season. Among several other findings, shefound that the distribution of balls put into play by RH battersis significantly different from (a) that of LH batters (no sur-prise there!), and (b) the mirror image of that of LH batters(somewhat surprising).

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5. Baseball pitch location plots

Next two slides: Locations of balls and called strikes for all 370,673called pitches from the 2014 MLB season (and postseason). Therule-book strike zone (which is a rectangle) is superimposed on bothplots.

I will present a detailed analysis of the called strike zone in a fewweeks.

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Reading assignment for next week

• The paper by Gabel and Redner cited on page 7.

• “The home-court advantage in basketball: How large is it, anddoes it vary from team to team?” by D.A. Harville and M.H.Smith, The American Statistician, 48:22–28 (1994).

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