Winning at BasketballWinning at BasketballDarren BloomingdaleDarren Bloomingdale

Michelle BomerMichelle BomerPeter MartinPeter MartinJosh PatseyJosh PatseyMatt Mason Matt Mason

The Problem…The Problem…

Does Field Goal percentage and average Does Field Goal percentage and average turnovers per game effect the number of turnovers per game effect the number of games won during a single season?games won during a single season?

Thought it was interesting because the Thought it was interesting because the Suns are for sale. New owners might be Suns are for sale. New owners might be interested in team performance.interested in team performance.

Our DataOur Data(espn.com)(espn.com)

Teams WinsSeason Field Goal Percentage (FG%)

Average Turnovers Per

Game (TO)Correlati

on

  y x1 x2 x1x2

Minnesota Timber wolves 58 0.461 12.2 5.6242

San Antonio Spurs 57 0.442 14 6.188

Dallas Mavericks 52 0.46 11.8 5.428

Memphis Grizzlies 50 0.446 14.4 6.4224

Houston Rockets 45 0.442 15.8 6.9836

Denver Nuggets 43 0.444 14.6 6.4824

Utah Jazz 42 0.436 15.3 6.6708

Los Angeles Lakers 56 0.454 13.4 6.0836

Sacramento Kings 55 0.463 13.5 6.2505

Portland Trailblazers 41 0.448 13.8 6.1824

Golden State Warriors 37 0.442 14.1 6.2322

Seattle SuperSonics 37 0.445 13.8 6.141

Phoenix Suns 29 0.443 14.6 6.4678

ResultsResultsFitted Regression Equation:Fitted Regression Equation:

ŷ = 203 – 293x1 – 26.6x2 + 55.4x1x2 ŷ = 203 – 293x1 – 26.6x2 + 55.4x1x2

ReRefitted regression equationfitted regression equation

ŷ = 74.5 - 17.4 X2 + 34.4 X1X2 ŷ = 74.5 - 17.4 X2 + 34.4 X1X2

where x1=FG%, & x2=TO/Gamewhere x1=FG%, & x2=TO/Game

HypothesisHypothesis

H0: β1 = β2 = β3 = β4 = 0H0: β1 = β2 = β3 = β4 = 0

H1: At least on β ≠ 0.H1: At least on β ≠ 0.

Regression AnalysisRegression AnalysisThe regression equation isThe regression equation isWins = 74.5 - 17.4 TO/Game + 34.4 CorrelationWins = 74.5 - 17.4 TO/Game + 34.4 CorrelationPredictor Coef StDev T PPredictor Coef StDev T PConstant 74.53 22.15 3.37 0.002Constant 74.53 22.15 3.37 0.002TO/Game -17.404 3.984 -4.37 0.000TO/Game -17.404 3.984 -4.37 0.000Correlat 34.36 10.07 3.41 0.002Correlat 34.36 10.07 3.41 0.002S = 8.439 R-Sq = 46.8% R-Sq(adj) = 42.7%S = 8.439 R-Sq = 46.8% R-Sq(adj) = 42.7%

Analysis of VarianceAnalysis of VarianceSource DF SS MS F PSource DF SS MS F PRegression 2 1630.16 815.08 11.44 0.000Regression 2 1630.16 815.08 11.44 0.000Residual Error 26 1851.84 71.22Residual Error 26 1851.84 71.22Total 28 3482.00Total 28 3482.00Source DF Seq SSSource DF Seq SSTO/Game 1 801.59TO/Game 1 801.59Correlat 1 828.57Correlat 1 828.57

Unusual ObservationsUnusual ObservationsObs TO/Game Wins Fit StDev Fit Residual St ResidObs TO/Game Wins Fit StDev Fit Residual St Resid 21 13.0 21.00 39.90 3.10 -18.90 -2.41R 21 13.0 21.00 39.90 3.10 -18.90 -2.41R 22 13.6 61.00 41.57 1.95 19.43 2.37R 22 13.6 61.00 41.57 1.95 19.43 2.37R

R denotes an observation with a large standardized residual R denotes an observation with a large standardized residual

Matrix of scatter plots for the FG% Matrix of scatter plots for the FG% TO/Game data TO/Game data

51

31

0.45075

0.42625

5131

15.55

13.05

0.45075

0.4262515.55

13.05

Wins

FG%

TO/Game

-20 -10 0 10 20

-2

-1

0

1

2

No

rma

l Sco

re

Residual

Normal Probability Plot of the Residuals(response is Wins)

Normal Probability Plot of the residuals

Residuals Versus the fitted valuesResiduals Versus the fitted values

55453525

20

10

0

-10

-20

Fitted Value

Res

idua

l

Residuals Versus the Fitted Values(response is Wins)

Residuals vs. the Fitted Values Residuals vs. the Fitted Values Response is ln(Wins) Response is ln(Wins)

4.053.953.853.753.653.553.453.353.25

0.5

0.0

-0.5

Fitted Value

Res

idua

l

Residuals Versus the Fitted Values(response is lnWins)

ConclusionConclusion

Best fits the data is:Best fits the data is:

ŷ = 74.5 - 17.4* TO/Game + 34.4* FG%*TO/Gameŷ = 74.5 - 17.4* TO/Game + 34.4* FG%*TO/Game

RR22 value of only 46.8% suggests this model value of only 46.8% suggests this model is a poor fitis a poor fit

Plots of the transformations indicated that Plots of the transformations indicated that the residuals are not completely random the residuals are not completely random

To answer the question…To answer the question…

Yes - Yes - field goal percentage and the average field goal percentage and the average number of turnovers per game, during a number of turnovers per game, during a season, have an effect on the number of season, have an effect on the number of games a team wins that season,games a team wins that season, however however additional factors and possibly correlations additional factors and possibly correlations are necessary to model the data well enough are necessary to model the data well enough to make future predictions. to make future predictions. For future research we suggest another For future research we suggest another model that includes such factors as Free model that includes such factors as Free Throw %, Rebounds, Blocks, Steals or Throw %, Rebounds, Blocks, Steals or Assists.Assists.