Does Poisson Distribution and Expected Goal Totals (xG ) Suck as a Tool for Pricing Games of Football in Play ?
Ever wondered how to calculate live odds for soccer betting? A Poisson calculation can be used so you can determine if the market accurately reflects on field events. Find out more.
A side’s chances of a particular outcome change the moment a match starts. The longer a game remains goalless, the more likely a draw becomes. There are a number of game incidents that can alter live odds such as yellow & red cards, but it is goals that produce the most dramatic alterations for live bettors.
From a betting perspective, knowledge of the current match odds is essential for those trading in play, and by calculating these they can identify if actual in-game odds are accurate. This is where a Poisson approach provides a basic framework. Every game can be evaluated in terms of the average number of goals each team will score at a particular venue.
Calculating live odds for soccer betting
Let’s use West Ham vs. Man City in Week 9 of the 2014 Premier League as an example. The Hammers – even with home field advantage – were still rated well below last year’s champions, Manchester City, based on the long-term achievements of both teams.
West Ham were expected to average 0.85 goals to Manchester City’s 1.90 goals. A Poisson approach would see City winning around 62% of such games, West Ham 15%, with 23% ending in a draw. These probabilities were consistent with the odds available prior to kick off.
Bettors should be aware that goal scoring tends to accelerate as time elapses
Bettors should be aware that goal scoring tends to accelerate as time elapses, as players become fatigued and risks more readily taken as managers go in search of the elusive goal. This is highlighted by 45% of goals being scored before half-time compared to 55% scored after the interval.
A more general fit for calculating the goal expectation of a side at a particular point in the match can be done with the following equation derived from actual Premier League scoring data.
Remaining Goal Expectation = Initial Expectation * Proportion of Time Remaining ^ 0.85
So as an example, if a side has an initial goal expectation of 1 for the entire game, when half of the match has elapsed, the remaining average goal expectation is given by:
1*(0.5^0.85) = 0.55
Therefore, 55% of the side’s initial goal expectation remains in the second half, in keeping with the observed data. We can of course use this equation to calculate the remaining goal expectation at any time during the match, something very useful for live soccer bettors.
Just prior to West Ham’s opening goal after 21 minutes, when 78% of a typical game remained and the match was still level, the respective goal expectations for each side had fallen from an initial 0.85 and 1.9 to 0.69 and 1.54 goals, respectively.
If we input these two revised figures for West Ham and Manchester City into a Poisson we can generate score lines and their associated probabilities that lead to either a home win, away win or a draw.
Impact of a goal on live soccer betting
21 minutes of scoreless soccer had seen the probability of a draw extend from 0.23 to 0.26, City’s chance of winning fell from 0.62 to 0.58 and the Hammer’s chances remain broadly similar at 0.16.
These figures then changed dramatically when Morgan Amalfitano scored to put West Ham ahead. If we ignore the effect of the new game state in this initial overview, the probabilities for each individual score line occurring in the remainder of the game will remain the same as calculated above.
However, should West Ham only “draw” the remaining 70+ minutes, they will win the match, because they now hold a one goal lead.
So at 1-0, with 21 minutes elapsed, a Poisson calculation – using decayed initial goal expectations for each side – gave the home team a 42% chance of victory, up from around 16% immediately prior to the opening goal. This shows the impact a goal has on game outcomes.
In general 45% of goals are scored before half-time compared to 55% after
This in running win probability is made up from the 16% chance that the Hammers “win” the final 74 minutes of football – increasing their winning margin – and the 26% likelihood that they “draw” it and maintain their current overall advantage.
Therefore, each live scenario depends on the initial strengths of each team, the time remaining and the current score, along with additional factors, such as red cards.
Like City who went 2-0 down, a side trailing by two goals needs to “win” the remaining part of the match by exactly two goals to claim a point or by a margin of three or more to claim all three. A Poisson – with the appropriately decayed goal expectations – can be used to quantify the likelihood of that happening.
Despite David Silva’s goal in the 77th minute making the score 2-1, so little remained meaning that West Ham still had around a 70% chance of a winning immediately after the goal.
Although the closeness of the prize may have made the tension feel more pronounced for their fans, compared to over an hour previously when their team had opened the scoring and held the same advantage on the scoreboard.
A team specific, Poisson approach to in running odds estimation is an improvement on using generic outcomes.
For example on average, a home team wins around 70% of the matches where they score the opening goal after 21 minutes. A pure Poisson approach gave West Ham only a 42% winning chance at that point, reflecting the differing perceived abilities of the respective sides.
Actual betting data from the day gave the Hammers around a 35% chance of winning immediately following the first goal. Perhaps indicating an expectation that trailing sides are likely to attempt to increase their scoring rate whilst behind and also accounting for West Ham’s early yellow card that may have compromised them later in the game.
The graph above compares the Poisson calculation for all game outcomes and the implied probability of a West Ham win as a reflection of the live Pinnacle odds.
This analysis highlights that bettors can use a Poisson approach to calculate live match odds during a soccer game, and can therefore judge for themselves if the market accurately reflects on field events, most notably when a goal is scored, to identify profitable opportunities.
Sat 25/10/14 PRL West Ham United
2 – 1
Manchester City View events More info
M. Amalfitano 21′
1 – 0
D. Sakho 75′
2 – 0
2 – 1
77′ David Silva
501/100 > West Ham Price at KO
341/100 > draw price at KO
11/20 > Man City Price at KO
Manchester City last away win in the league when losing 1-0 half time was 1992 > hang on > City have spent loads of money in the last few seasons > look below because in this profile in the Premier League an away win is a rare event but the market at half time in the West Ham game did not to factor the effect of the game state ( current score ) added to the effect of the time of the opening goal < West Ham last 15 home games in the Premier League when winning 1-0 Half Time game state > 13-2-0 < lost 0%
E0 1617 2017-04-30 Middlesbrough Man City 1-0 2-2
E0 1617 2017-01-15 Everton Man City 1-0 4-0
E0 1617 2016-12-31 Liverpool Man City 1-0 1-0
E0 1415 2015-04-06 Crystal Palace Man City 1-0 2-1
E0 1415 2014-10-25 West Ham Man City 1-0 2-1
E0 1314 2013-11-10 Sunderland Man City 1-0 1-0
E0 1314 2013-10-27 Chelsea Man City 1-0 2-1
E0 1213 2013-03-16 Everton Man City 1-0 2-0
E0 1213 2012-08-26 Liverpool Man City 1-0 2-2
E0 1011 2011-02-12 Man United Man City 1-0 2-1
E0 1011 2011-01-22 Aston Villa Man City 1-0 1-0
E0 0910 2010-03-14 Sunderland Man City 1-0 1-1
E0 0910 2010-02-06 Hull Man City 1-0 2-1
E0 0910 2009-12-16 Tottenham Man City 1-0 3-0
E0 0910 2009-10-18 Wigan Man City 1-0 1-1
E0 0910 2009-10-05 Aston Villa Man City 1-0 1-1
E0 0809 2009-05-16 Tottenham Man City 1-0 2-1
E0 0809 2009-04-04 Arsenal Man City 1-0 2-0
E0 0809 2009-03-15 Chelsea Man City 1-0 1-0
E0 0809 2009-01-31 Stoke Man City 1-0 1-0
E0 0809 2008-12-28 Blackburn Man City 1-0 2-2
Premier League last 5 completed seasons where the home team opened the scoring in 21-30 time band and still 1-0 with 31 minutes elapsed
and 1-0 on
You are welcome to think that Manchester City were the perceived stronger team so naturally the betting industry algorithm should consider the individual goal totals before a game start but if you look at the game between West Ham and Manchester City from 31 minutes to half time < the actual expectation of a Man City win via the time of the opening goal and the game state ( game state analysis ) was in the range of 2%-7% > in effect the betting industry had much higher expectation of Manchester City fighting back then they should have .
“each live scenario depends on the initial strengths of each team, the time remaining and the current score, along with additional factors, such as red cards.” < the additional factor(s) that the betting industry algorithm has never used is the effect of the time of the opening goal on accuracy for the rest of the game.
Full Time Summary
The betting industry at 1-0 on 21 minutes priced West Ham at 15/8 when given the time of the opening goal there was 70% + expectation that the Hammers would hold onto their advantage.
“Perhaps indicating an expectation that trailing sides are likely to attempt to increase their scoring rate ” the betting industry did not understand that it was West Ham that were more likely to go to 2-0 pathway then > 1-1 < the academics that have looked at survival analysis > the ability of a team to hold their opening goal advantage < have not looked at the effect of the time of the opening goal in individual leagues . The Effect of 1-0 HALF TIME to the Home Team with the goal in 21-30 minutes time band in the Premier League: Under/Over 2.5 goals
Posted on: December 11th, 2016 by Jonny Grossmark
1-0 to the home team in the Premier League added to the goal in the 21-30 minutes time band and in general LOW expectation of the away team fighting back and winning and also lowered expectation of goal(s) production in the second half with the caveat that if there is a fight back goal by the away team ( 1-1 ) with a goal in the 46-70 minutes time band then this could result in expectation of further goal(s).
In the 102 games in the table below the total shot on target production to the away team in the second half was 239 and they scored 59 second half goals > 59/239 = only 24.69% of the shots on target were converted which is lower then the average for the Premier League over a season which in general will be around 30% conversion.
The home teams in the 102 games total shot on target production in the second half was 232 and they scored 65 second half goals > 65/232 = 28% > expectation that in this profile of game that the home team will be more accurate then the away team in the second half but still below average accuracy.