It is possible to calculate the likely number of goals that will be scored in a football match using Poisson Distribution with historical data. In fact, a probability for every possible match outcome can be established.
If we wanted to calculate the possible outcomes for a match, we’d first need to calculate a value for each team’s “Attack” and “Defence Strength” before you can use Poisson Distribution to calculate the likely number of goals in a game.
Using Newcastle vs. Tottenham in the 2012/13 Premier League opener as an example, we’d need to collect relevant data to give an indication of what this season’s performance could be like. We used data from the previous season, as the 38 games provide a good sample size to average-out freak results or what are called outliers.
To calculate Attack Strength, first work out the number of Premier League goals scored at home (604) and away (462) in 2011/12. To get the average attack strength, average the number of goals scored per team, per game, per season. In mathematical terms, that’s:
In 2011/12, that was 604/20/19 at home and 462/20/19 away, equalling an average of 1.589 goals per game at home and 1.216 away. The difference from this average is what constitutes a team’s “Attack Strength”.
Poisson Distribution Betting – Attack Strength vs. Defence Strength
We can now use the numbers above to calculate the Attack and Defence Strength of both Newcastle and Tottenham for their match on August 18th, 2012.
To calculate the Attack Strength:
1. Take the number of goals scored at home last season by the home team (Newcastle: 29) and divide by the number of home games (29/19): 1.526
2. Divide this value by the season’s average home goals scored per game (1.526/1.589), to get the “Attack Strength”: 0.960. This shows that Newcastle scored 4% less goals at home than a hypothetical “average” Premier League side.
To calculate the Defence Strength:
1. Take the number of goals conceded away last season by the away team (Tottenham: 27) and divide by the number of away games (27/19): 1.263.
2. Divide this by the season’s average goals conceded by an away team per game (1.263/19) to get the “Defence Strength”: 0.795. Tottenham conceded 20.5% less goals than an “average” Premier League side on the road.
We can now use the following formula to calculate the likely number of goals the attacking team might score:
In this case, that’s 0.960* 0.795 * 1.611 (the average number of home goals scored last season), which equates to Newcastle scoring 1.213 goals.
We now need to work out how many goals Tottenham are likely to score. We use the same method as above, but use the number of goals Tottenham have scored on away from home (making an Attack Strength of 0.856) and the number of goals Newcastle have conceded at home (making their Defence Strength 1.359).
Putting that into the above formula, we calculated that Tottenham are likely to score 1.415 goals.
Poisson Distribution Betting – Predicting Multiple Match Outcomes
Of course, no games end 1.213 vs. 1.415 – this is simply the average. Poisson Distribution, a formula created by French mathematician Simeon Denis Poisson, allows us to use these figures to distribute 100% of probability across a range of goal outcomes for each side. The results are shown in the table below:
The formula itself looks like this: P(x; μ) = (e-μ) (μx) / x!, however, we can use online tools such as this Poisson Distribution Calculator to do most of the equation for us.
All we need to do is enter the different goals outcomes (0-5) in the Random Variable (x) category, and the likelihood of a team scoring (for instance, Tottenham at 1.415) in the average rate of success, and the calculator will output the probability of that score.
This example shows that there is a 0.243 chance that Tottenham won’t score at all, but the side is equally as likely to get two goals. Newcastle, on the other hand, are mostly likely to score once (0.361), but are also more likely to score none (0.297) than put two past Tottenham (0.219).
Hoping for a five-nil drubbing? The probability is 0.34% if Tottenham are the scorers, or 0.16% for Newcastle to do it.
As both scores are independent (mathematically-speaking), you can see that both teams are most likely to score one goal. If you multiply the two probabilities together, you’ll get the probability of the 1-1 outcome – 0.153 or 12.4%.
Now you know how to calculate outcomes, you should compare your result to a bookmaker’s odds to help see how they differentiate.
For example, taking into account all possible draw combinations (0-0, 1-1, 2-2, 3-3, 4-4 and 5-5), this method gives a probability of 0.261 or 26.1% – which translates to odds of 2.855. Pinnacle Sports’ odds are 3.560 (a 28% probability).
Therefore if last season’s form was a perfect indicator of this season’s results betting on a draw would be a good bet, but unfortunately it isn’t as simple as that, which is why pure Poisson analysis has limitations.
Poisson Distribution Betting – The Limits of Poisson Distribution
Poisson Distribution is a simple predictive model that doesn’t allow for a lot of factors. Situational factors – such club circumstances, game status etc. – and subjective evaluation of the change of each team during the transfer window are completely ignored. In this case, it means the huge x-factor of André Villas-Boas’ first Premier League game in charge of Tottenham is entirely ignored.
Correlations are also ignored, such as the widely recognised pitch effect that shows that matches have some tendency to be either high or low scoring.
The system is of greatest benefit over a long period of time – using it for a whole season’s worth of games, rather than one-off matches.
These are particularly important areas in minor league games, which can gives punters an edge against bookmakers that is hard to achieve in major leagues, given the expertise that modern bookmakers like Pinnacle Sports possess.
One issue is for sure you want to beat the bookmakers at their own game, along with getting an edge – from Poisson or other modelling – it is crucially important to ensure you get the best odds available, which will usually be found at Pinnacle Sports.
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