Example Math Projects in Basketball

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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

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Possible Math Uses in Basketball

• Checking data
• Evaluating players
• Evaluating contracts
• Developing analysis tools
• Checking tactics
• Estimation of missing data, etc.
• anything

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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

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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

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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 ONeal? (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

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Example 1 Checking Data

• Data from Dougstats.com

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Example 1 Checking Data

• Minutes Team Minutes Opponents
• 1442 ? 1444
• Sum of Individuals Team?
• Minutes 116 121 1142
• Sum of Games Started/5 Games?
• (66666)/5 6
• Minutes/5/Games 48 if no overtime?
• 1442/30 48.066667 ? 48
• Points 2FGM FG3M FTM
• Team FGA FGM gt Team OREB Opp DREB

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Example 2 Basic Analysis

• Continuing with data from Dougstats.com
• Why did Chicago lose to Miami?
• Bulls couldnt handle Shaq
• Tyson Chandlers injury
• Big picture to little picture

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Example 2 Basic Analysis

• Offense or defense?
• Possessions FGA OR 0.4FTA TOV
• Average estimates to get 570.3
• Rating Pts/Poss100
• Offense 590/570.3100 103.5
• Defense 608/570.3100 106.6
• Playoff Avg 107.4

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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

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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

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Example 2 Basic Analysis

• Breaking down eFG
• Was it Shaq?
• What was wrong with the Bulls?

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Example 2 Basic Analysis

• Was it Shaq?

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Example 2 Basic Analysis

• What was wrong with the Bulls?

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Example 3 Estimation of Rebounds

• College data for Dwyane Wade (basketball-reference
  .com)
• How many offensive and defensive rebounds?

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Example 3 Rebound Estimation

• Basic
• Offensive rebounds are typically about 30 of
  total
• Oreb 0.30420 126
• Dreb 420 126 294

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Example 3 Rebound Estimation

• More detailed
• From Chicago example, we see breakdown by
  position
• Use PG info
• Oreb 0.05420 21
• Dreb 420-21 399

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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 gt x 61.75 62
• Dreb 209 x
• Percentage 61.75/209 29.5
• Assume that percentage
• OREB in 2002 0.295211 62
• DREB in 2002 211-62 149

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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?

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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 gt Team OREB Opp DREB
• Arizona 1878-868 gt 334 750?
• 1010 lt 1084
• Opp (1723-764)31/26 gt 321 711?
• 1143 gt1032

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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)

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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

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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

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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
• Doesnt consider FGM by player

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Example 6 Percentage of Shots Assisted

• Better estimate
• Asstd Assists by teammates/FGM by teammates
• Assists by teammates (TmAst/TmMin5Min Ast)
• FGM by teammates (TmFGM/TmMin5Min FGM)
• Considers all info, at least indirectly

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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

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Finally

• Repeated experiments!
• Use the structure of Basketball on Paper
• Are players similar?
• Play games
• Chart games for data
• Other suggestions?