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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

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Some History Every science we have today was

once just “interesting” Chemistry Biology Astronomy Finance and economics Physics

Interesting + math = science Math = Science - Interesting

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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

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…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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…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

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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?

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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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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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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

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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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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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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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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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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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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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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

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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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Overall Player Ratings “Ratings” aren’t objective What are you measuring? Offense, defense, (in)tangibles

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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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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?