BASKETBALL ON

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Example Math Projects in Basketball

Dean OliverAuthor, Basketball on Paper

Consultant to the Seattle SupersonicsMath in Sports Symposium

Seattle, WAMay 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

Internet Dougstats.com NBA.com Basketball-Reference.com 82games.com

Ask me

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What Data Look Like Who?

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

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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 Staallen,malik chi PF 6 116 14 30 0 0 0 1 5 18 7 2 10 6 16 0 28 0 0 0 6chandler,tyson chi C 6 104 4 6 0 0 3 10 8 27 3 2 6 2 29 1 11 0 0 0 0deng,luol chi SF 6 182 24 56 1 5 12 21 8 29 3 5 5 4 13 0 61 0 0 0 0duhon,chris chi PG 6 131 9 25 7 16 5 6 1 16 13 2 5 0 13 0 30 0 0 0 0gordon,ben chi SG 6 246 43 106 15 41 25 37 5 20 18 6 17 0 12 0 126 0 0 0 6harrington,othel chi PF 3 14 0 3 0 0 0 0 0 2 0 1 0 0 2 0 0 0 0 0 0hinrich,kirk chi PG 6 234 39 94 9 26 36 42 0 20 46 8 24 2 22 1 123 0 0 0 6nocioni,andres chi SF 6 230 47 84 10 21 30 35 5 53 9 5 14 2 21 0 134 1 0 0 6pargo,jannero chi PG 5 19 5 12 3 5 4 5 1 6 3 0 3 0 0 0 17 0 0 0 0piatkowski,eric chi SG 6 27 3 6 2 5 2 2 1 5 1 0 0 1 1 0 10 0 0 0 0schenscher,luke chi C 3 18 2 2 0 0 3 4 3 7 0 0 1 0 2 0 7 0 0 0 0sweetney,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 ffChicagoBulls 2 4 1442 204 458 47 119 135 182 53 236 110 34 92 23 155 590 1 0 0Opponents 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:

Use PG info: Oreb = 0.05*420 = 21 Dreb = 420-21 = 399

Pos oreb treb %ageC 11 34 32%PF 21 53 40%SF 13 82 16%SG 6 25 24%PG 2 42 5%

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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

=0.472 (Actual 47%) See Basketball on Paper, Appendix 1

TmFGM

ASTTMAST14.1

FGM

AST5

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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?