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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…
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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? 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
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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 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
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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
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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?
(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
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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
Rating: Pts/Poss*100
Offense: 590/570.3*100 = 103.5
Defense: 608/570.3*100 = 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?
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%
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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%
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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 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
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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%
Assume that percentage
OREB in 2002 = 0.295*211 = 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 >= Team OREB + Opp DREB
Arizona: 1878-868 >= 334 + 750?
1010 < 1084
Opp: (1723-764)*31/26 >= 321 + 711?
1143 >=1032
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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
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
ASTi TMAST AST
q5 1.14
i n FGM k TmFGM
k i
=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?
Dean Oliver
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