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**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.

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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… BASKETBALL ON PAPER Dean Oliver

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**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 BASKETBALL ON PAPER Dean Oliver

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**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! BASKETBALL ON PAPER Dean Oliver

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**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 BASKETBALL ON PAPER Dean Oliver

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**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 BASKETBALL ON PAPER Dean Oliver

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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? ( )/5 = 6 Minutes/5/Games = 48 if no overtime? 1442/30 = ≠ 48 Points = 2*FGM + FG3M + FTM Team FGA – FGM >= Team OREB + Opp DREB BASKETBALL ON PAPER Dean Oliver

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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 BASKETBALL ON PAPER Dean Oliver

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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: BASKETBALL ON PAPER Dean Oliver

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**Example 2: Basic Analysis**

Four Factor Analysis eFG%: (FGM * FG3M)/FGA O: D: Avg: TOV%: TOV/Poss O: D: Avg: BASKETBALL ON PAPER Dean Oliver

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**Example 2: Basic Analysis**

Four Factor Analysis (cont.) OR%: OR/(OR + OppDR) O: D: Avg: FTratio: FTM/FGA O: D: Avg: BASKETBALL ON PAPER Dean Oliver

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**Example 2: Basic Analysis**

Breaking down eFG% Was it Shaq? What was wrong with the Bulls? The biggest focus of coaching analysis BASKETBALL ON PAPER Dean Oliver

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**Example 2: Basic Analysis**

Was it Shaq? Was it Shaq in the post? In transition? One specific game? BASKETBALL ON PAPER Dean Oliver

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**Example 2: Basic Analysis**

What was wrong with the Bulls? BASKETBALL ON PAPER Dean Oliver

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**Example 3: Estimation of Rebounds**

College data for Dwyane Wade (basketball-reference.com) How many offensive and defensive rebounds? BASKETBALL ON PAPER Dean Oliver

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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 BASKETBALL ON PAPER Dean Oliver

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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 = = 399 BASKETBALL ON PAPER Dean Oliver

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

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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 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? BASKETBALL ON PAPER Dean Oliver

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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: >= ? 1010 < 1084 Opp: ( )*31/26 >= ? 1143 >=1032 BASKETBALL ON PAPER Dean Oliver

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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%) BASKETBALL ON PAPER Dean Oliver

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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 BASKETBALL ON PAPER Dean Oliver

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**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 BASKETBALL ON PAPER Dean Oliver

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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 =( )/( )*3069 =220 Doesn’t consider FGM by player BASKETBALL ON PAPER Dean Oliver

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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 BASKETBALL ON PAPER Dean Oliver

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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 BASKETBALL ON PAPER Dean Oliver

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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? BASKETBALL ON PAPER Dean Oliver

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