1. 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
There were a lot of things I could talk about in a second talk.
Playing up or down to opponents
Analysis of college players
Chance of winning the game at a given time/score
Roboscout – applying math to interpret what scouts do
The process of optimizing a team through numbers
Ultimately these are long projects, the kind of project I don’t see my 13 year old doing for quite some time.
So I wanted to illustrate some of the more basic things, some algebra that helps just work with data.
These are skills that I don’t necessarily see out of some college kids who have come to work for me.

2. 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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Dean Oliver

3. Where to Get Data Newspaper Books Internet Ask me
Sporting News, NBA Guide, NBA Register
Total Basketball
Internet
Dougstats.com
NBA.com
Basketball-Reference.com
82games.com
Ask me
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Dean Oliver

4. What Data Look Like Who? What? When? What level? 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
Team playing stats are interrelated!
Need team stats!
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Dean Oliver

5. 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?)
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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Dean Oliver

6. Example 1: Checking Data
Data from Dougstats.com
These are the kind of tasks I’d ask for someone to do at an entry level
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Dean Oliver

7. Example 1: Checking Data
Minutes Team = Minutes Opponents
1442 ≠ 1444
Sum of Individuals = Team?
Minutes: 116+…+ 121 = 1142
Sum of Games Started/5 = Games?
( )/5 = 6
Minutes/5/Games = 48 if no overtime?
1442/30 = ≠ 48
Points = 2*FGM + FG3M + FTM
Team FGA – FGM >= Team OREB + Opp DREB
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Dean Oliver

8. 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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Dean Oliver

9. 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:
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Dean Oliver

10. Example 2: Basic Analysis
Four Factor Analysis
eFG%: (FGM * FG3M)/FGA O: D:
Avg:
TOV%: TOV/Poss O: D:
Avg:
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Dean Oliver

11. Example 2: Basic Analysis
Four Factor Analysis (cont.)
OR%: OR/(OR + OppDR) O: D:
Avg:
FTratio: FTM/FGA O: D:
Avg:
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Dean Oliver

12. Example 2: Basic Analysis
Breaking down eFG%
Was it Shaq?
What was wrong with the Bulls?
The biggest focus of coaching analysis
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13. Example 2: Basic Analysis
Was it Shaq?
Was it Shaq in the post?
In transition?
One specific game?
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Dean Oliver

14. Example 2: Basic Analysis
What was wrong with the Bulls?
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15. Example 3: Estimation of Rebounds
College data for Dwyane Wade (basketball-reference.com)
How many offensive and defensive rebounds?
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16. 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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Dean Oliver

17. Example 3: Rebound Estimation
More detailed:
From Chicago example, we see breakdown by position:
Use PG info:
Oreb = 0.05*420 = 21
Dreb = = 399
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Dean Oliver

18. 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 = ~ 62
Dreb = 209 – x
Percentage = 61.75/209 = 29.5%
Assume that percentage
OREB in 2002 = 0.295*211 = 62
DREB in 2002 = = 149
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Dean Oliver

19. 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 from the field
In 26 games, Arizona 2002 opponents had 898 total rebounds and went from the field
What is their opponents’ offensive rebounding percentage?
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Dean Oliver

20. 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: >= ?
1010 < 1084
Opp: ( )*31/26 >= ?
1143 >=1032
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Dean Oliver

21. 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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Dean Oliver

22. 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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Dean Oliver

23. Example 6: Percentage of Shots Assisted
Data from NBA.com or Dougstats.com
Ray Allen FG, 289 AST, 3069 Minutes
Seattle team FG, 1483 AST, Minutes
Multiple factors affect %asstd
Minutes played
Assists by teammates
FGM by teammates
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Dean Oliver

24. 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
=( )/( )*3069
=220
Doesn’t consider FGM by player
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Dean Oliver

25. 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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Dean Oliver

26. 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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Dean Oliver

27. 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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Dean Oliver