Predicting PredictionsThe Progression of the in Play Bet Prices is

Practically Predetermined

A study of the total goal markets (and some recent additions.)

Avishalom Shalit, Moshe Levy, Sorin Solomon.The Hebrew University , September 2008

avishalom@gmail.com

The object of study The Betfair in-play, soccer, total goals market

Scope and source of study

Data from Betfair.com (through fracsoft) 28 Soccer games (> 10,000 data points each) In each game, a study of 4 over/under markets

(over/under: 1.5 , 2.5 , 3.5 & 4.5 goals) Also the “no goal” option for the “Next Goal”

market. Total of 252 price lines, (9 x 28)

English Soccer – The Championship26 February - Stoke v Barnsley04 March - Birmingham v Cardiff05 March - Preston v Southampton11 August - Wolves v Watford13 August - C Palace v Leeds18 August - Stoke v Charlton25 August - Sheff Utd v West Brom26 August - Ipswich v C Palace01 September - Sheff Wed v Bristol C03 September - Blackpool v Hull16 September - Watford v Southampton22 September - Cardiff v Preston

21 October - Southampton v Cardiff22 October - Hull v Barnsley27 October - Burnley v Southampton27 October - Charlton v QPR03 November - Colchester v Leicester -04 November - Norwich v Ipswich05 November - Barnsley v Blackpool10 November - Stoke v Sheff Utd12 November - Coventry v West Brom24 November - Preston v Charlton26 November - Leicester v Cardiff03 December - Scunthorpe v Blackpool

English Soccer - Coca Cola Leagues

20 April - Derby v Luton 22 April - Wolves v Birmingham 23 April - Burnley v West Brom 29 April - C Palace v Derby

Example Coca Cola 23rd of April 2007Burnley (3) * Gray 15, * Gray 48, * McCann 87

West Brom (2) * Koumas 6, * Ellington 8

Thousands of transactions, differently motivated

Burnley- West Brom: Under 4.5 goals

Minutes since start of game

Impl

ied

Pro

babi

lity

And now for something different

The Model – what if it were random? Constant goal probability per unit of time.

(goals are mutually independent)g= probability for a goal per minute (<#>/90).N=number of minutes left to play

Binomialdistribution

P nomore goals= g0

1⋅1−g N−0

P 1 more goal = g1

2!⋅1−g N−1

P 2 more goals= g2

3!⋅1−g N−2

...

P k more goals= gk

k !⋅1−g N−k

The Model , continuous time

λ is the expectation value of the number of goals in the remaining time

P k∣=k

k !⋅e−

=g⋅T

The model - continued.

Backing “under 2.5 goals” => 0 or 1 or 2 goals.

But after a goal is scored, only 0 or 1 are good So, if we allow at most Γ goals, we get

sP Win=∑K=0

2

P k∣T ,=∑K=0

2k

k !⋅e−

sP 0. .=∑K=0

P k∣T ,=∑K=0

k

k !⋅e−

What does it look like

How well does it fit

Average RMSE < 0.015 Remember that the granularity of the bets is

~0.01

Pic

And the no goal (next goal market)

so....

Thousands of bets Thousands of bettors , differently motivated. All of them make up a “human computer” to

calculate a closed form function

Γ= number of goals to win the “under” betT= time remaining to playg= expected goal rate, per unit time

Price ∣T =∑k=0

T⋅g k

k !⋅e−T⋅g

Summary

Closed form function With a single constant parameter That can be calculated at the start of the game

I$ thi$ exploitable

The projected endgame according to the end of the curve is a ~minute in the future.

The model assumes a random process, and its fit implies that this is the case. (is it ? )

The time to new equilibrium after a goal

Thank you

Avishalom Shalit Sorin Solomon Shiki Levi