Example Math Projects in Basketball
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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 Dougstats.com NBA.com Basketball-Reference.com 82games.com
Internet
Ask me
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What Data Look Like
Who?
When?
Player or player type Ref Team Franchise League
Career Season Game Quarter Possession
High school College Minor league International NBA
What?
What level?
Traditional stats Calculated stats Collect-your-own stats Physical attributes Financial data
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Analysis
Come up with questions
Cast things in terms of concepts
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?) What statistics reflect winning? Seasonal and boxscore data readily available Make estimates Track own data Set up equalities, inequalities Set up time frame How to convince a non-math person? Room for soft things, not measured
Gather data
Do analyses
Report in concrete terms
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Example 1: Checking Data
Player allen,malik chandler,tyson deng,luol duhon,chris gordon,ben harrington,othel hinrich,kirk nocioni,andres pargo,jannero piatkowski,eric schenscher,luke sweetney,mike
Data from Dougstats.com
Team chi chi chi chi chi chi chi chi chi chi chi chi PS GP Min FGM FGA 3M 3A FTM FTA OR TR AS ST TO BK PF DQ PTS TC EJ FF Sta PF 6 116 14 30 0 0 0 1 5 18 7 2 10 6 16 0 28 0 0 0 6 C 6 104 4 6 0 0 3 10 8 27 3 2 6 2 29 1 11 0 0 0 0 SF 6 182 24 56 1 5 12 21 8 29 3 5 5 4 13 0 61 0 0 0 0 PG 6 131 9 25 7 16 5 6 1 16 13 2 5 0 13 0 30 0 0 0 0 SG 6 246 43 106 15 41 25 37 5 20 18 6 17 0 12 0 126 0 0 0 6 PF 3 14 0 3 0 0 0 0 0 2 0 1 0 0 2 0 0 0 0 0 0 PG 6 234 39 94 9 26 36 42 0 20 46 8 24 2 22 1 123 0 0 0 6 SF 6 230 47 84 10 21 30 35 5 53 9 5 14 2 21 0 134 1 0 0 6 PG 5 19 5 12 3 5 4 5 1 6 3 0 3 0 0 0 17 0 0 0 0 SG 6 27 3 6 2 5 2 2 1 5 1 0 0 1 1 0 10 0 0 0 0 C 3 18 2 2 0 0 3 4 3 7 0 0 1 0 2 0 7 0 0 0 0 PF 6 121 14 34 0 0 15 19 16 33 7 3 7 6 24 1 43 0 0 0 6
team ChicagoBulls Opponents
won lost min fgm fga 3m 3a ftm fta or tr as st to bk pf pts tc ej ff 2 4 1442 204 458 47 119 135 182 53 236 110 34 92 23 155 590 1 0 0 4 2 1444 219 472 47 139 123 177 67 259 116 41 95 32 157 608 5 0 0
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Example 1: Checking Data
Minutes Team = Minutes Opponents
Sum of Individuals = Team?
1442 ≠ 1444
Sum of Games Started/5 = Games?
Minutes: 116+…+ 121 = 1142
(6+6+6+6+6)/5 = 6
Minutes/5/Games = 48 if no overtime?
Points = 2*FGM + FG3M + FTM Team FGA – FGM >= Team OREB + Opp DREB
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1442/30 = 48.066667 ≠ 48
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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
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Example 2: Basic Analysis
Offense or defense?
Possessions = FGA – OR + 0.4*FTA + TOV
Average estimates to get 570.3 Offense: 590/570.3*100 = 103.5 Defense: 608/570.3*100 = 106.6 Playoff Avg: 107.4
Rating: Pts/Poss*100
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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?
Player anderson,derek anderson,shandon doleac,michael haslem,udonis mourning,alonzo o'neal,shaquille payton,gary posey,james simien,wayne wade,dwyane walker,antoine williams,jason Shots 12 5 11 28 5 84 34 41 2 116 85 49 eFG% 58% 20% 55% 54% 80% 61% 54% 66% 0% 45% 45% 45%
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Example 2: Basic Analysis
What was wrong with the Bulls?
Player chandler,tyson schenscher,luke allen,malik harrington,othel sweetney,mike duhon,chris hinrich,kirk pargo,jannero deng,luol nocioni,andres gordon,ben piatkowski,eric Shots 6 2 30 3 34 25 94 12 56 84 106 6 eFG% 67% 100% 47% 0% 41% 50% 46% 54% 44% 62% 48% 67%
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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 = 0.30*420 = 126 Dreb = 420 – 126 = 294
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Example 3: Rebound Estimation
More detailed:
From Chicago example, we see breakdown by position:
Pos C PF SF SG PG oreb 11 21 13 6 2 treb 34 53 82 25 42 %age 32% 40% 16% 24% 5%
Use PG info:
Oreb = 0.05*420 = 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 => x = 61.75 ~ 62 Dreb = 209 – x Percentage = 61.75/209 = 29.5%
OREB in 2002 = 0.295*211 = 62 DREB in 2002 = 211-62 = 149
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Assume that percentage
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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 >= Team OREB + Opp DREB Arizona: 1878-868 >= 334 + 750?
1010 < 1084
1143 >=1032
Opp: (1723-764)*31/26 >= 321 + 711?
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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 Per Per Per Per Per
Game 48 minutes 40 minutes Minute Team Possession 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
Doesn’t 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/TmMin*5*Min – Ast) FGM by teammates = (TmFGM/TmMin*5*Min – 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
AST TMAST AST i q5 1.14 TmFGM i n FGM k
=0.472 (Actual 47%)
k i
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?
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