Recency or availability bias, for example, is the case where an occurrence from the recent past (such as a side scoring over three goals) is considered to be far more likely than what it actually is. Or confirmation bias, where isolated examples are sought to support a pre-conceived notion, such as a red-carded team winning despite having one fewer player.
Examining comebacks in the Premier League
From a single recent Premier League season, 132 of the 380 matches at one point reached the stage where one team held a 2-1 lead.
On 74 of those occasions it was the home team who led, whilst 58 times it was the visitor - 89 times the third goal broke a 1-1 deadlock and in 43 matches the third goal was scored by a side that was trailing 2-0.
Out of 132 matches that reached 2-1 in a Premier League sample, 101 of the leaders eventually won the match, 25 drew and 6 lost.
16 minutes was the quickest it took to reach a 2-1, while the fourth minute of injury time was the latest arrival of the same scoreline. The average time when the score became 2-1 was a shade over 60 minutes.
The average abilities of the leading or trailing sides were broadly similar across the 132 matches.
The commonest method used to model the outcome of a game or the remainder of a match is based on the Poisson distribution.
A goal-based assessment is made about the relative abilities of the competing teams and the probabilities of subsequent results can then be made by estimating the likelihood that each team will score or concede a particular number of goals.
Putting the 2-1 scoreline to the test
We can model the remaining minutes of all 132 games from the point at which 2-1 was achieved and compare the resultant probabilities to those available in running to see if there is a broad agreement between model and layer.
However, a less labour-intensive approach which would yield similarly informative results would be useful in comparing a Poisson generated estimate, using the average time and relative qualities of the teams when they reached 2-1, in relation to the average outcomes across a season from the perspective of the side who led.
If we use the Poisson model to determine the final outcome of a slightly superior team - in order to allow for the slight preponderance of home teams who lead 2-1 after an hours play - we predict that the leading side wins 75% of the time, draws 20% and their lead is ultimately overturned in the remaining 5% of occasions.
By comparison, out of the 132 matches that reached 2-1 in my Premier League sample, 101 of the leaders eventually won the match, 25 drew and just 6 lost.
These convert to win, draw and loss percentages respectively of 76%, 19% and 5%, very nearly a perfect match to the modelled percentages.
This strongly suggests that tempting though it may be to intuitively see a 2-1 lead as very vulnerable - particularly in view of the still often quoted but now discredited reputation afforded to the 2-0 scoreline - it is very likely that any market inefficiencies associated with this particular scoreline will be rare.
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