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Forecasting a Tennis Match at the Australian Open. Tristan Barnett Stephen Clarke Alan Brown. Introduction. Match Predictions Markov Chain Model Collecting Data Exponential Smoothing Combining Player Statistics Real Time Predictions Combining Sheets from Markov Chain Model

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Forecasting a Tennis Match at the Australian Open


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Forecasting a Tennis Match at the Australian Open

Tristan Barnett

Stephen Clarke

Alan Brown

introduction
Introduction
  • Match Predictions

Markov Chain Model

Collecting Data

Exponential Smoothing

Combining Player Statistics

  • Real Time Predictions

Combining Sheets from Markov Chain Model

Bayesian Updating Rule

Excel Computer Demonstration

markov chain model
Markov Chain Model
  • Modelling a game of tennis

Recurrence Formula: P(a,b) = pP(a+1,b) + (1-p)P(a,b+1)

Boundary Conditions: P(a,b) = 1if a=4, b ≤ 2

P(a,b) = 0if b=4, a ≤ 2

where for player A:

p = probability of winning a point on serve

P(a,b) = conditional probability of winning the game when the score is (a,b)

markov chain model1
Markov Chain Model

Table 1:The conditional probabilities of player A winning the game from various score lines for p = 0.6

  • Similarly

sheet for player B serving

sheets for a set (from sheets of a game)

sheet for a match (from sheets of a set)

collecting data
Collecting Data

The ATP tour matchfacts:

http://www.atptennis.com/en/media/rankings/matchfacts.pdf

collecting data1
Collecting Data

fi = ai bi + (1 - ai ) ci

gi = aav di + ( 1 - aav ) ei

where the percentage for player i :

fi = points won on serve

gi = points won on return

ai = 1st serves in play

bi = points won on 1st serve

ci = points won on 2nd serve

di = points won on return of 1st serve

ei = points won on return of 2nd serve

where the percentage for average player on the ATP tour:

aav = 1st serves in play= 58.7%

exponential smoothing
Exponential Smoothing

Fit = Fit-1 + [ 1 - ( 1 – α)n ][ fit - Fit-1 ]

Git = Git-1 + [ 1 - ( 1 – α)n ] [ git - Git-1 ]

where:

For player i at period t

Fit = smoothed average of the percentage of points won on serve after observing fitGit= smoothed average of the percentage of points won on return of serve after observing git

Initialised for average ATP tour player

Fi0 = the ATP average of percentage of points won on serve

Gi0 = the ATP average of percentage of points won on return of serve

n = number of matches played since period t-1

α =smoothing constant

  • When n=1, [1-(1-α)n] = α, as expected
  • When n becomes large, [1-(1-α)n] → 1, as expected
combining player statistics
Combining Player Statistics

fij = ft + ( fi - fav ) - ( gj - gav )

  • gji = gt + ( gj - gav ) - ( fi - fav )
  • where:
  • For thecombined player statistics
  • fij= percentage of points won on serve for player i against player j
  • gji =percentage points won on return for player j against player I
  • For thetournament averages
  • ft = percentage of points won on serve
  • gt = percentage of points won on return of serve
  • For theATP tour averages
  • fav = percentage of points won on serve
  • gav = percentage of points won on return of serve
  • Since ft + gt = 1, fij + gji = 1 for all i,j as required
combining sheets
Combining Sheets

The equation for theprobability of player A winning a best-of-5 set match from (e,f) in sets, (c,d) in games, (a,b) in points, player A serving.

P''(a,b:c,d:e,f ) = P(a,b) P'B(c+1,d) P''(e+1,f ) +

P(a,b) [1-P'B(c+1,d)] P''(e,f+1) +

[1-P(a,b)] P'B(c,d+1) P''(e+1,f ) +

[1-P(a,b)] [1-P'B(c,d+1)] P''(e,f+1)

where for player A :

P''(a,b:c,d:e,f ) = probability of winning the match from (a,b:c,d:e,f )

P'B(c,d) = probability of winning the set from (c,d) when player B is serving

P''(e,f ) = probability of winning the match from (e,f )

bayesian updating rule
Bayesian Updating Rule

where:

θti= updated percentage of points won on serve at time t for player i

μi =initial percentage of points won on serve for player i

φti= actual percentage of points won on serve at time t for player i

n = number of points played

M = expected points to be played

When n=0, θ0i= μi as expected

When M →0,θti→ φti

computer demonstration isf3 xls
Computer Demonstration ISF3.XLS

2003 Australian Open Quarter Final

El Aynaoui versus Roddick

computer demonstration isf4 xls
Computer Demonstration ISF4.XLS

End of 1st set

where: = game to El Aynaoui

= game to Roddick

= set to El Aynaoui

computer demonstration
Computer Demonstration

End of match

where: = game to El Aynaoui by breaking serve

= game to Roddick by breaking serve

= set to El Aynaoui

= set to Roddick