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BASKETBALL ON
PAPER
Math & Basketball: Astronomy used to be just watching pretty stars, too
Dean OliverAuthor, Basketball on Paper
Consultant to the Seattle SupersonicsUsing Sports to Teach Math Symposium
Seattle, WAMay 13, 2006
BASKETBALL ON PAPER
Dean [email protected] 2
Some History Every science we have today was
once just “interesting” Chemistry Biology Astronomy Finance and economics Physics
Interesting + math = science Math = Science - Interesting
BASKETBALL ON PAPER
Dean [email protected] 3
Language and logic first… Score a game
5 CHI 23D/ 91-A
4 UTA 32R 12D/ 3 32 12D 14-X
6 CHI 13R 9D/ 33 23 33 13F32(1)X* 6 UTA 12D/ 14 32 3-R 00R 12D 32++B
8 CHI 33D/ 91 23D 33 23++A
8 UTA 12D/ 32++2
8 CHI 33 / 9D 23D-3 13R-L 13F12(1) 23 91 33 9 23D-B
9 UTA 14R 32D 12D/ 3 32DF91(1)X* 8 CHI 33D/ 23D 9 33 23 13 9-Y
11 UTA 3RD / 12 14 32 12++R
BASKETBALL ON PAPER
Dean [email protected] 4
…Then counting… How many lines? How many lines with a score? How many touches? How many post-ups? How many offensive rebounds off
missed free throws?
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Dean [email protected] 5
…And Analysis Same number of possessions…
Equivalence scale on possessions Per available rebound
Basketball on Paper Points per possession Four Factors
Effective shooting percentage Turnovers per possession Offensive rebounding percentage Free throw rate
BASKETBALL ON PAPER
Dean [email protected] 6
Stories to tell Grades
Is ___ the next Michael Jordan? Who should we draft? Is __ a good coach?
Tactics Why so many offensive rebounds? Is offense better when forcing more touches? Should we double team the post? Is it easier to shoot an open jump shot from 3pt
range or a contested one from 2pt range? Financial
Should a team pay more to win? When do players get their big paycheck?
BASKETBALL ON PAPER
Dean [email protected] 7
The Possession Framework Possessions are equal What you do per possession is what
matters Possession ends:
Missed shot rebounded by defense Made field goal, no free throw Turnover Made last free throw
Possession formula: (FGA – FGM – OR) + FGM + TOV + 0.4*FTA
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Dean [email protected] 8
Floor% and Play% Floor%: Percentage of possessions
on which there is a score Scoring Possessions/Possessions
Play%: Percentage of “plays” on which there is a score Scoring Possessions/Plays
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Dean [email protected] 9
Four Factors Effective Field Goal Percentage
(FGM + 0.5 * FG3M)/FGA Turnover Percentage
TOV/Poss Offensive Rebounding Percentage
OR/(OR + OppDR) Free Throw Ratio
FTM/FGA
BASKETBALL ON PAPER
Dean [email protected] 10
Test! Seattle 1998
eFG%: 52.1% FT%: 72% TOV%: 15.7%
LA Lakers 1998 eFG%: 51.9% FT%: 68% TOV%: 16.2%
Better offense?
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Dean [email protected] 11
Answers Lakers had better offense
111.9 pts/100 poss to 111.4 How?
Shot worse from everywhere Rebounded worse Turned ball over more
But… Shot 600 more free throws! More shots of overall higher percentage
shot
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Dean [email protected] 12
More Framework: Estimating Wins Wins come from point difference
(points/possession) Wins ~
A*(points – points allowed) + 0.5 B*(pts/poss – pts allowed/poss) + 0.5 pointsC/(pointsC + points allowedC)
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Dean [email protected] 14
Wins from a Bell CurveFigure 2: Distributions of Home and Road Scores, 2000-2001 and
2001-2002 Seasons
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
<=6061
-65
66-7
0
71-7
5
76-8
0
81-8
5
86-9
0
91-9
5
96-1
00
101-
105
106-
110
111-
115
116-
120
121-
125
126-
130
>130
Score
Per
cen
tag
e o
f G
ames
Road Scores
Home Scores
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Dean [email protected] 15
Bell Curve Principles Consistency matters Playing up or down to opponent
matters Don’t blow teams out by too much Unbiased referees change odds
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Dean [email protected] 16
Player Evaluation What makes a good player?
Almost the same as what makes a good team
Roles/Interactions affect everything Volume of shots Communication Coordination
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Dean [email protected] 17
Decreasing Marginal Returns
Player Skill Curve (Averaged)
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
75 85 95 105 115 125 135
Rating
% T
m P
oss
J. Stackhouse A. Iverson M. Jordan
BASKETBALL ON PAPER
Dean [email protected] 18
Optimize Lakers’ Offense
Player % Tm Poss Off. Rtg.Bryant 26% 119Odom 22% 103Parker 18% 99Brown 16% 98Walton 18% 95Totals 100% 104
Player % Tm Poss Off. Rtg.Bryant 36% 114Odom 19% 111Parker 15% 107Brown 14% 106Walton 16% 101Totals 100% 109
Unbalanced offense
More balanced offense
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Dean [email protected] 19
Overall Player Ratings “Ratings” aren’t objective What are you measuring? Offense, defense, (in)tangibles
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Dean [email protected] 20
Other Projects Best player to step up to help offense What to emphasize on defense How will players develop? How to help
them? What tactics to take against good teams? What tendencies do teams have to take
advantage of? How to predict player performance from
another league?
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Dean [email protected] 21
Work with 82games.com They do research projects
Ahead by 3, foul or defend? Does Steve Nash help his
teammates? What does Kobe Bryant do in the
clutch? How likely is it to make a shot after
making the previous one?