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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 Possible Math Uses in Basketball Checking data Evaluating players Evaluating contracts Developing analysis tools

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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
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

where to get data
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

what data look like
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

analysis
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

example 1 checking data
Example 1: Checking Data
  • Data from Dougstats.com

Dean Oliver

deano@rawbw.com

example 1 checking data7
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

example 2 basic analysis
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

example 2 basic analysis9
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

example 2 basic analysis10
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

example 2 basic analysis11
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

example 2 basic analysis12
Example 2: Basic Analysis
  • Breaking down eFG%
    • Was it Shaq?
    • What was wrong with the Bulls?

Dean Oliver

deano@rawbw.com

example 2 basic analysis13
Example 2: Basic Analysis
  • Was it Shaq?

Dean Oliver

deano@rawbw.com

example 2 basic analysis14
Example 2: Basic Analysis
  • What was wrong with the Bulls?

Dean Oliver

deano@rawbw.com

example 3 estimation of rebounds
Example 3: Estimation of Rebounds
  • College data for Dwyane Wade (basketball-reference.com)
  • How many offensive and defensive rebounds?

Dean Oliver

deano@rawbw.com

example 3 rebound estimation
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

example 3 rebound estimation17
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

example 3 rebound estimation18
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

example 4 opponent rebound estimation
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

example 4 opponent rebound estimation20
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

example 4 opponent rebound estimation21
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

example 5 unit conversion
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

example 6 percentage of shots assisted
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

example 6 percentage of shots assisted24
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

example 6 percentage of shots assisted25
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

example 6 percentage of shots assisted26
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

finally
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