Example Math Projects in Basketball BASKETBALL ON PAPER
Example Math Projects in Basketball BASKETBALL ON PAPER Dean Oliver Author, Basketball on Paper Consultant to the Seattle Supersonics Math in Sports Symposium Seattle, WA May 13, 2006 1
Possible Math Uses in Basketball n n n n Checking data Evaluating players Evaluating contracts Developing analysis tools Checking tactics Estimation of missing data, etc. …anything… BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 2
Where to Get Data n n Newspaper Books n n n Internet n n n Sporting News, NBA Guide, NBA Register Total Basketball Dougstats. com NBA. com Basketball-Reference. com 82 games. com Ask me BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 3
What Data Look Like n Who? n n n n Player or player type Ref Team Franchise League n n n What? n n n Traditional stats Calculated stats Collect-your-own stats Physical attributes Financial data BASKETBALL ON PAPER When? Career Season Game Quarter Possession What level? n n n High school College Minor league International NBA Dean Oliver deano@rawbw. com 4
Analysis n Come up with questions n n n Cast things in terms of concepts n n Seasonal and boxscore data readily available Make estimates Track own data Do analyses n n n What statistics reflect winning? Gather data n n Who is better? (Right now? Individual production or help team to win by doing role? ) Should you double-team Shaquille O’Neal? (How much? Reduce team or his efficiency? ) Are the Sixers better off without Allen Iverson? (Short or long term? ) How important is a bench or big contracts or biggest contract or a superstar? (To winning a championship? ) Set up equalities, inequalities Set up time frame Report in concrete terms n n How to convince a non-math person? Room for soft things, not measured BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 5
Example 1: Checking Data n Data from Dougstats. com BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 6
Example 1: Checking Data n Minutes Team = Minutes Opponents n n Sum of Individuals = Team? n n n (6+6+6)/5 = 6 Minutes/5/Games = 48 if no overtime? n n Minutes: 116+…+ 121 = 1142 Sum of Games Started/5 = Games? n n 1442 ≠ 1444 1442/30 = 48. 066667 ≠ 48 Points = 2*FGM + FG 3 M + FTM Team FGA – FGM >= Team OREB + Opp DREB BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 7
Example 2: Basic Analysis n n Continuing with data from Dougstats. com Why did Chicago lose to Miami? n n n “Bulls couldn’t handle Shaq” “Tyson Chandler’s injury” Big picture to little picture BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 8
Example 2: Basic Analysis n Offense or defense? n Possessions = FGA – OR + 0. 4*FTA + TOV n n Average estimates to get 570. 3 Rating: Pts/Poss*100 n n n Offense: 590/570. 3*100 = 103. 5 Defense: 608/570. 3*100 = 106. 6 Playoff Avg: 107. 4 BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 9
Example 2: Basic Analysis n Four Factor Analysis n e. FG%: (FGM + 0. 5 * FG 3 M)/FGA n n O: 0. 497 D: 0. 514 Avg: 0. 498 TOV%: TOV/Poss n n n O: 0. 161 D: 0. 167 Avg: 0. 146 BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 10
Example 2: Basic Analysis n Four Factor Analysis (cont. ) n OR%: OR/(OR + Opp. DR) n n O: 0. 216 D: 0. 268 Avg: 0. 260 FTratio: FTM/FGA n n n O: 0. 295 D: 0. 261 Avg: 0. 275 BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 11
Example 2: Basic Analysis n Breaking down e. FG% n n Was it Shaq? What was wrong with the Bulls? BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 12
Example 2: Basic Analysis n Was it Shaq? BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 13
Example 2: Basic Analysis n What was wrong with the Bulls? BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 14
Example 3: Estimation of Rebounds n n College data for Dwyane Wade (basketball-reference. com) How many offensive and defensive rebounds? BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 15
Example 3: Rebound Estimation n Basic: n n n Offensive rebounds are typically about 30% of total Oreb = 0. 30*420 = 126 Dreb = 420 – 126 = 294 BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 16
Example 3: Rebound Estimation n More detailed: n n From Chicago example, we see breakdown by position: Use PG info: n n Oreb = 0. 05*420 = 21 Dreb = 420 -21 = 399 BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 17
Example 3: Rebound Estimation n More information: n n In 2003, in 28 games, Wade had 52 offensive rebounds and 176 total rebounds Set OREB = x n n x/209 = 52/176 => x = 61. 75 ~ 62 Dreb = 209 – x Percentage = 61. 75/209 = 29. 5% Assume that percentage n n OREB in 2002 = 0. 295*211 = 62 DREB in 2002 = 211 -62 = 149 BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 18
Example 4: Opponent Rebound Estimation n Available information from ESPN. com: n n n In 31 games, Arizona 2002 had 334 offensive rebounds, 711 defensive rebounds (1045 total), and went 868 -1878 from the field In 26 games, Arizona 2002 opponents had 898 total rebounds and went 764 -1723 from the field What is their opponents’ offensive rebounding percentage? BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 19
Example 4: Opponent Rebound Estimation n Scale and assume 30%? n Scale up: TREB/31 = 898/26 n n TREB = 1071, OREB = 321, DREB = 750 But… n n Team FGA – FGM >= Team OREB + Opp DREB Arizona: 1878 -868 >= 334 + 750? n n 1010 < 1084 Opp: (1723 -764)*31/26 >= 321 + 711? n 1143 >=1032 BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 20
Example 4: Opponent Rebound Estimation n Assume same proportion of Total Rebounds to Missed Shots for Arizona and opponents n n n (AZ OR + Opp DR)/(AZ FGA – AZ FGM) = (Opp OR + AZ DR)/(Opp FGA – Opp FGM) Opp DR + Opp OR = 1071 2 equations and 2 unknowns n n n Opp OR = 412, Opp DR = 658 OR are 38% of total (next year, actual was 35%) BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 21
Example 5: Unit Conversion n Lots of units in basketball: n n n Per Per Per Game 48 minutes 40 minutes Minute Team Possession Individual Possession BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 22
Example 6: Percentage of Shots Assisted n n Data from NBA. com or Dougstats. com Ray Allen 640 -1494 FG, 289 AST, 3069 Minutes Seattle team 2882 -6495 FG, 1483 AST, 19755 Minutes Multiple factors affect %asstd n n n Minutes played Assists by teammates FGM by teammates BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 23
Example 6: Percentage of Shots Assisted n One (bad) estimate: n Asstd FG= (Assists by teammates)/(Minutes by teammates)*(Minutes by Player) n n =(Tm. AST – AST)/(Tm. Min – Min)*Min =(1483 -289)/(19755 -3069)*3069 =220 Doesn’t consider FGM by player BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 24
Example 6: Percentage of Shots Assisted n Better estimate: n n %Asstd: Assists by teammates/FGM by teammates Assists by teammates = (Tm. Ast/Tm. Min*5*Min – Ast) FGM by teammates = (Tm. FGM/Tm. Min*5*Min – FGM) Considers all info, at least indirectly BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 25
Example 6: Percentage of Shots Assisted n Better estimate: n Sum of chances of each player assisting others n n =0. 472 (Actual 47%) See Basketball on Paper, Appendix 1 BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 26
Finally… n n n Repeated experiments! Use the structure of Basketball on Paper Are players similar? Play games Chart games for data Other suggestions? BASKETBALL ON PAPER Dean Oliver deano@rawbw. com 27
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