Basketball and $#^! Complexity

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

                         Dean Oliver
BASKETBALL ON PAPER   deano@rawbw.com   2
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
BASKETBALL ON PAPER      deano@rawbw.com          3
What Data Look Like
   Who?                               When?
        Player or player type              Career
        Ref                                Season
        Team                               Game
        Franchise                          Quarter
        League                             Possession
   What?                              What level?
        Traditional stats                  High school
        Calculated stats                   College
        Collect-your-own stats             Minor league
        Physical attributes                International
        Financial data                     NBA

                                    Dean Oliver
BASKETBALL ON PAPER              deano@rawbw.com             4
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
BASKETBALL ON PAPER                        deano@rawbw.com                                  5
              Example 1: Checking Data
                  Data from Dougstats.com
Player             Team   PS GP Min FGM FGA 3M 3A FTM FTA OR TR AS ST TO BK PF DQ PTS TC EJ FF Sta
allen,malik        chi    PF  6 116   14  30 0 0     0  1 5 18 7 2 10 6 16 0 28 0 0 0            6
chandler,tyson     chi    C   6 104    4   6 0 0     3 10 8 27 3 2 6 2 29 1 11 0 0 0             0
deng,luol          chi    SF  6 182   24  56 1 5 12 21 8 29 3 5 5 4 13 0 61 0 0 0                0
duhon,chris        chi    PG  6 131    9  25 7 16    5  6 1 16 13 2 5 0 13 0 30 0 0 0            0
gordon,ben         chi    SG  6 246   43 106 15 41 25 37 5 20 18 6 17 0 12 0 126 0 0 0           6
harrington,othel   chi    PF  3 14     0   3 0 0     0  0 0 2 0 1 0 0 2 0           0 0 0 0      0
hinrich,kirk       chi    PG  6 234   39  94 9 26 36 42 0 20 46 8 24 2 22 1 123 0 0 0            6
nocioni,andres     chi    SF  6 230   47  84 10 21 30 35 5 53 9 5 14 2 21 0 134 1 0 0            6
pargo,jannero      chi    PG  5 19     5  12 3 5     4  5 1 6 3 0 3 0 0 0 17 0 0 0               0
piatkowski,eric    chi    SG  6 27     3   6 2 5     2  2 1 5 1 0 0 1 1 0 10 0 0 0               0
schenscher,luke    chi    C   3 18     2   2 0 0     3  4 3 7 0 0 1 0 2 0           7 0 0 0      0
sweetney,mike      chi    PF  6 121   14  34 0 0 15 19 16 33 7 3 7 6 24 1 43 0 0 0               6


team                  won lost min fgm fga 3m 3a ftm fta or tr    as st to bk pf pts  tc ej ff
ChicagoBulls            2    4 1442 204 458 47 119 135 182 53 236 110 34 92 23 155 590 1 0 0
Opponents               4    2 1444 219 472 47 139 123 177 67 259 116 41 95 32 157 608 5 0 0



                                                    Dean Oliver
              BASKETBALL ON PAPER                deano@rawbw.com                                 6
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
BASKETBALL ON PAPER     deano@rawbw.com    7
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
BASKETBALL ON PAPER     deano@rawbw.com   8
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
BASKETBALL ON PAPER          deano@rawbw.com    9
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
BASKETBALL ON PAPER         deano@rawbw.com   10
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
BASKETBALL ON PAPER         deano@rawbw.com   11
Example 2: Basic Analysis
   Breaking down eFG%
        Was it Shaq?
        What was wrong with the Bulls?




                          Dean Oliver
BASKETBALL ON PAPER    deano@rawbw.com    12
Example 2: Basic Analysis
   Was it Shaq?
                      Player                 Shots         eFG%
                      anderson,derek           12           58%
                      anderson,shandon         5            20%
                      doleac,michael           11           55%
                      haslem,udonis            28           54%
                      mourning,alonzo          5            80%
                      o'neal,shaquille         84           61%
                      payton,gary              34           54%
                      posey,james              41           66%
                      simien,wayne             2            0%
                      wade,dwyane             116           45%
                      walker,antoine           85           45%
                      williams,jason           49           45%



                                            Dean Oliver
BASKETBALL ON PAPER                      deano@rawbw.com          13
Example 2: Basic Analysis
   What was wrong with the Bulls?
                      Player                  Shots        eFG%
                      chandler,tyson            6           67%
                      schenscher,luke           2          100%
                      allen,malik               30          47%
                      harrington,othel          3           0%
                      sweetney,mike             34          41%
                      duhon,chris               25          50%
                      hinrich,kirk              94          46%
                      pargo,jannero             12          54%
                      deng,luol                 56          44%
                      nocioni,andres            84          62%
                      gordon,ben               106          48%
                      piatkowski,eric           6           67%




                                            Dean Oliver
BASKETBALL ON PAPER                      deano@rawbw.com          14
Example 3: Estimation of
Rebounds
   College data for Dwyane Wade
    (basketball-reference.com)




   How many offensive and defensive
    rebounds?

                         Dean Oliver
BASKETBALL ON PAPER   deano@rawbw.com   15
Example 3: Rebound Estimation
   Basic:
        Offensive rebounds are typically about
         30% of total
        Oreb = 0.30*420 = 126
        Dreb = 420 – 126 = 294




                           Dean Oliver
BASKETBALL ON PAPER     deano@rawbw.com           16
Example 3: Rebound Estimation
   More detailed:
        From Chicago example, we see breakdown by
         position:
                      Pos   oreb      treb     %age
                      C      11        34      32%
                      PF     21        53      40%
                      SF     13        82      16%
                      SG      6        25      24%
                      PG      2        42       5%


   Use PG info:
        Oreb = 0.05*420 = 21
        Dreb = 420-21 = 399
                                Dean Oliver
BASKETBALL ON PAPER          deano@rawbw.com          17
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
BASKETBALL ON PAPER         deano@rawbw.com       18
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
BASKETBALL ON PAPER    deano@rawbw.com          19
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
BASKETBALL ON PAPER           deano@rawbw.com        20
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
BASKETBALL ON PAPER         deano@rawbw.com     21
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
BASKETBALL ON PAPER        deano@rawbw.com   22
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
BASKETBALL ON PAPER    deano@rawbw.com     23
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
BASKETBALL ON PAPER        deano@rawbw.com        24
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
BASKETBALL ON PAPER   deano@rawbw.com          25
Example 6: Percentage of Shots
Assisted
   Better estimate:
        Sum of chances of each player assisting
         others

                     ASTi            TMAST  AST
         q5                1.14 
              i  n  FGM k            TmFGM
                      k i
              =0.472 (Actual 47%)
        See Basketball on Paper, Appendix 1



                                  Dean Oliver
BASKETBALL ON PAPER            deano@rawbw.com     26
Finally…
   Repeated experiments!
   Use the structure of Basketball on Paper
   Are players similar?
   Play games
   Chart games for data
   Other suggestions?


                         Dean Oliver
BASKETBALL ON PAPER   deano@rawbw.com     27

				
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