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Example Math Projects in Basketball

Example Math Projects in Basketball Dean Oliver Author, Basketball on Paper Consultant to the Seattle Supersonics Math in Sports Symposium Seattle, WA May 13, 2006 Possible Math Uses in Basketball Checking data Evaluating players Evaluating contracts Developing analysis tools

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Example Math Projects in Basketball

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  1. Example Math Projects in Basketball Dean Oliver Author, Basketball on Paper Consultant to the Seattle Supersonics Math in Sports Symposium Seattle, WA May 13, 2006

  2. Possible Math Uses in Basketball • Checking data • Evaluating players • Evaluating contracts • Developing analysis tools • Checking tactics • Estimation of missing data, etc. • …anything… Dean Oliver deano@rawbw.com

  3. Where to Get Data • Newspaper • Books • Sporting News, NBA Guide, NBA Register • Total Basketball • Internet • Dougstats.com • NBA.com • Basketball-Reference.com • 82games.com • Ask me Dean Oliver deano@rawbw.com

  4. What Data Look Like • Who? • Player or player type • Ref • Team • Franchise • League • What? • Traditional stats • Calculated stats • Collect-your-own stats • Physical attributes • Financial data • When? • Career • Season • Game • Quarter • Possession • What level? • High school • College • Minor league • International • NBA Dean Oliver deano@rawbw.com

  5. Analysis • Come up with questions • 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?) • Cast things in terms of concepts • What statistics reflect winning? • Gather data • Seasonal and boxscore data readily available • Make estimates • Track own data • Do analyses • Set up equalities, inequalities • Set up time frame • Report in concrete terms • How to convince a non-math person? • Room for soft things, not measured Dean Oliver deano@rawbw.com

  6. Example 1: Checking Data • Data from Dougstats.com Dean Oliver deano@rawbw.com

  7. Example 1: Checking Data • Minutes Team = Minutes Opponents • 1442 ≠ 1444 • Sum of Individuals = Team? • Minutes: 116+…+ 121 = 1142 • Sum of Games Started/5 = Games? • (6+6+6+6+6)/5 = 6 • Minutes/5/Games = 48 if no overtime? • 1442/30 = 48.066667 ≠ 48 • Points = 2*FGM + FG3M + FTM • Team FGA – FGM >= Team OREB + Opp DREB Dean Oliver deano@rawbw.com

  8. Example 2: Basic Analysis • Continuing with data from Dougstats.com • Why did Chicago lose to Miami? • “Bulls couldn’t handle Shaq” • “Tyson Chandler’s injury” • Big picture to little picture Dean Oliver deano@rawbw.com

  9. Example 2: Basic Analysis • Offense or defense? • Possessions = FGA – OR + 0.4*FTA + TOV • Average estimates to get 570.3 • Rating: Pts/Poss*100 • Offense: 590/570.3*100 = 103.5 • Defense: 608/570.3*100 = 106.6 • Playoff Avg: 107.4 Dean Oliver deano@rawbw.com

  10. Example 2: Basic Analysis • Four Factor Analysis • eFG%: (FGM + 0.5 * FG3M)/FGA • O: 0.497 • D: 0.514 • Avg: 0.498 • TOV%: TOV/Poss • O: 0.161 • D: 0.167 • Avg: 0.146 Dean Oliver deano@rawbw.com

  11. Example 2: Basic Analysis • Four Factor Analysis (cont.) • OR%: OR/(OR + OppDR) • O: 0.216 • D: 0.268 • Avg: 0.260 • FTratio: FTM/FGA • O: 0.295 • D: 0.261 • Avg: 0.275 Dean Oliver deano@rawbw.com

  12. Example 2: Basic Analysis • Breaking down eFG% • Was it Shaq? • What was wrong with the Bulls? Dean Oliver deano@rawbw.com

  13. Example 2: Basic Analysis • Was it Shaq? Dean Oliver deano@rawbw.com

  14. Example 2: Basic Analysis • What was wrong with the Bulls? Dean Oliver deano@rawbw.com

  15. Example 3: Estimation of Rebounds • College data for Dwyane Wade (basketball-reference.com) • How many offensive and defensive rebounds? Dean Oliver deano@rawbw.com

  16. Example 3: Rebound Estimation • Basic: • Offensive rebounds are typically about 30% of total • Oreb = 0.30*420 = 126 • Dreb = 420 – 126 = 294 Dean Oliver deano@rawbw.com

  17. Example 3: Rebound Estimation • More detailed: • From Chicago example, we see breakdown by position: • Use PG info: • Oreb = 0.05*420 = 21 • Dreb = 420-21 = 399 Dean Oliver deano@rawbw.com

  18. Example 3: Rebound Estimation • More information: • In 2003, in 28 games, Wade had 52 offensive rebounds and 176 total rebounds • Set OREB = x • x/209 = 52/176 => x = 61.75 ~ 62 • Dreb = 209 – x • Percentage = 61.75/209 = 29.5% • Assume that percentage • OREB in 2002 = 0.295*211 = 62 • DREB in 2002 = 211-62 = 149 Dean Oliver deano@rawbw.com

  19. Example 4: Opponent Rebound Estimation • Available information from ESPN.com: • 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? Dean Oliver deano@rawbw.com

  20. Example 4: Opponent Rebound Estimation • Scale and assume 30%? • Scale up: TREB/31 = 898/26 • TREB = 1071, OREB = 321, DREB = 750 • But… • Team FGA – FGM >= Team OREB + Opp DREB • Arizona: 1878-868 >= 334 + 750? • 1010 < 1084 • Opp: (1723-764)*31/26 >= 321 + 711? • 1143 >=1032 Dean Oliver deano@rawbw.com

  21. Example 4: Opponent Rebound Estimation • Assume same proportion of Total Rebounds to Missed Shots for Arizona and opponents • (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 • Opp OR = 412, Opp DR = 658 • OR are 38% of total • (next year, actual was 35%) Dean Oliver deano@rawbw.com

  22. Example 5: Unit Conversion • Lots of units in basketball: • Per Game • Per 48 minutes • Per 40 minutes • Per Minute • Per Team Possession • Per Individual Possession Dean Oliver deano@rawbw.com

  23. Example 6: Percentage of Shots Assisted • 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 • Minutes played • Assists by teammates • FGM by teammates Dean Oliver deano@rawbw.com

  24. Example 6: Percentage of Shots Assisted • One (bad) estimate: • Asstd FG= (Assists by teammates)/(Minutes by teammates)*(Minutes by Player) • =(TmAST – AST)/(TmMin – Min)*Min • =(1483-289)/(19755-3069)*3069 • =220 • Doesn’t consider FGM by player Dean Oliver deano@rawbw.com

  25. Example 6: Percentage of Shots Assisted • Better estimate: • %Asstd: Assists by teammates/FGM by teammates • Assists by teammates = (TmAst/TmMin*5*Min – Ast) • FGM by teammates = (TmFGM/TmMin*5*Min – FGM) • Considers all info, at least indirectly Dean Oliver deano@rawbw.com

  26. Example 6: Percentage of Shots Assisted • Better estimate: • Sum of chances of each player assisting others • =0.472 (Actual 47%) • See Basketball on Paper, Appendix 1 Dean Oliver deano@rawbw.com

  27. Finally… • Repeated experiments! • Use the structure of Basketball on Paper • Are players similar? • Play games • Chart games for data • Other suggestions? Dean Oliver deano@rawbw.com

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