Predicting Predictions The 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 [email protected]
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Predicting Predictions · Predicting Predictions The Progression of the in Play Bet Prices is Practically Predetermined A study of the total goal markets (and some recent additions.)
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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
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 ? )