The Fish has Spoken ... and the title is heading to Dundalk!

There is a mathematical probability distribution called the Poisson distribution.  It turns out that the Poisson model can be successful at predicting arrival rates, for example the number of cars arriving per red light cycle, number of customers arriving at a store per hour, number of claims received at an insurance company per day or number of goals scored by a football team per match.  All you need to know is the average, and from that you can calculate the probability.

 The formula has been around for centuries and is tried and tested.  Even the bookie's place some weight on it (you can read about Pinnacle Sports version of the Poisson here).

 There is some significance in the Dundalk vs Cork City match in Oriel Park this Friday.  Lets calculate the home win/draw/away win probabilities for that match.

 The trick is in finding the average home goals and away goals to use in the formula.  We know that home field advantage plays a big part in football.  So for our averages we will look at the average goals scored and conceded by Dundalk at home.  We will also look at the average goals scored and conceded by Cork away.  I will base the average on this season, you could pick a shorter period (more relevant) or a longer period (less susceptible to outlying results).  Using the season to date will be perfectly fine for this example.

 The chart below shows Dundalk have averaged 2.82 goals per game at home, but Cork have only conceded on average 0.80 goals on the road.  These two figures actually give us two different estimates for the same thing (home goals scored = away goals conceded).  So we average both figures to give us a single expected home goals scored of 1.81 specifically for this match.  This figure gives us a good estimate of the likely home goal tally taking into account both Dundalk's high scoring home record and Cork's tight defensive record.  The same process is carried out for away goals scored.

This is where the Poisson Formula fits in.  Given the average (which we now have) the Poisson Formula can calculate an accurate probability that Dundalk will get 0 goals, or 1 goal, 2 goals, etc.  And similar for Cork.
The equation is: 
\!f(k; \lambda)= \Pr(X=k)= \frac{\lambda^k e^{-\lambda}}{k!},
which looks complicated but we now know all the variables so its just a case of keying it in to a calculator and churning out the probabilities.  The table left shows the probabilities already calculated.  It shows that Dundalk have a 29% chance of scoring exactly one goal and a 26% chance of scoring exactly 2 goals etc, Cork have a 35% chance of scoring exactly no goals and a 36% chance of scoring exactly 1 goal etc.

 After that its just a number crunching exercise to calculate the probability for every home/away score combination.  Then sum up the probabilities for each combination that makes a home win, draw and away win.

 The final result is good news for Dundalk - remember they need to win.  Cork will lift the trophy with a draw.  It looks like a 55.7% chance the title is heading to Dundalk.  Leaving Cork with a 44.3% chance.


OutcomeProbabilityRough Odds
Dundalk
55.7%
4/5
Draw
23.0%
10/3
Cork City
21.3%
15/4

These estimated odds are not far from those published by Paddy Power.

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