STATISTICS IN SPORT

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STATISTICS IN SPORT

• David Forrest
• University of Salford

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A WIDE RANGE OF APPLICATIONS

• Professional sport is of relatively trivial
  importance to the economy
• But it is a focus of the passion of millions
• And it is an excellent laboratory for testing
  theories of human behaviour, for example capacity
  to act rationally or degree of responsiveness to
  incentives
• Illustrations-
• Randomness in left right decisions when
  serving in tennis or taking penalties in football
• Times in marathons related to structure of
  prizes

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ON THE FIELD

• Measurement of Performance eg the McHale-Scarf
  ACTIM Index
• Devising Scoring Systems eg Duckworth-Lewis
  method to determine the winner of a cricket
  match
• Testing for Bias by Officials eg injury time in
  football, nationalistic bias in ice skating
  competitions
• Testing of Strategies many studies flawed because
  of selection bias

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FORECASTING SPORT

• Building of Probabilistic forecasting models
• ISSUES-
• How reliable are world rankings? Not very
• How important is recent performance compared with
  long-run reputation? In golf, very (McHale and
  Forrest, 2005)
• Do tipsters possess extra knowledge? In baseball
  and football, tips fail to add power to a
  forecasting model
• Can models beat the bookie? Using just odds to
  forecast outcomes does at least as well as the
  very richest statistical models- but one tip is
  that odds understate importance of match
  significance at the end of the football season

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SPORTS AS BUSINESS

• Should a failing business sack the manager?
• How do crowds vary according to the time of week
  at which a match takes place?
• Is it true that fans crave outcome uncertainty
  (and how can this be measured anyway)?

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Modelling Attendance(with Babatunde Buraimo and
Robert Simmons)

• Dozens of studies football, cricket, rugby
  league, US sports
• All use the fixed effects estimator
• ATTit f(club dummies, time of week, home team
  form, visiting team quality, whether on tv, etc)
• THE FE ESTIMATOR ESSENTIALLY ALLOWS EACH CLUB TO
  HAVE ITS OWN INTERCEPT TERM
• RESULTS OF SUCH MODELS ALWAYS SHOW THAT MOST OF
  THE VARIATION IN ATTENDANCE IS ATTRIBUTABLE TO
  CLUB FIXED EFFECTS

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UNLOCKING THE BLACK BOX

• HAUSMAN-TAYLOR ESTIMATOR
• Divides variables into four categories according
  to whether they are
• (a) endogenous or exogenous and
• (b) time invariant or time varying

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VARIABLES AFFECTING CROWD SIZE

• Home Club History and Geography (population,
  overlap, age of club)
• Away Support (distance, population, overlap, age
  of club)
• Scheduling (month, day, holiday)
• Quality (home and away wages, home and away form,
  derby)
• Television (on terrestial or satellite tv,
  competition with big games on tv)

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Overlap Example 1 Leicester City FC
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Overlap Example 2 Preston North End
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HAUSMAN-TAYLOR RESULTS2,884 matches, 1997-2004
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MORE
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More
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TOSS AND WEATHER IN CRICKET (with Ron Dorsey)

• Luck plays a part in all sport- bad referee
  calls, injuries, etc
• But cricket has two distinct forces that may
  distort Championship outcomes
• -The Weather- games not replayed, so opportunity
  to win points just lost
• -The Toss- games last four days, conditions
  change, so potentially who can choose the batting
  order of the teams is decisive

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VALUING THE TOSS AND TIME LOST

• Ordinary Least Squares Regression Results
• Dependent variable Championship points won in a
  season
• Coefficient Robust
• Estimate Standard p-value
• Error
• Probability odds 150.984 33.996 0.000
• Sessions lost -0.877 0.304 0.004
• Tosses won 3.682 1.345 0.007
• 1996-1998 points regime 6.993 8.701 0.422
• 1999 points regime -17.592 8.723 0.045
• 2000-2002 points regime -22.435 7.689 0.004
• 2003-2004 points regime 20.545 7.264 0.005
• Constant 176.381 18.175 0.000
• R2 .24

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REVISED LEAGUE TABLE
(mean8)
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IMAS 2007

• Major international conference on mathematical
  modelling in sport
• The Lowry Centre, June 24-26
• IMA will publish a book of contributions and a
  special issue of its Journal of Management
  Mathematics
• Let me know if you want to be on the mailing list
  for this conference