They need to win so they’re more likely to………or are they?

So far the Premier League season has been quite exciting. While Arsenal, Chelsea and Manchester City are beginning to open a slight gap over fourth placed Liverpool, at the very least that trio have realistic aspirations of title success. The battle for survival looks even more open, only 6 points separate bottom team Cardiff from Swansea who currently lie just inside the top half in 10th position. As such we may be treated to a succession of very important matches over the next few weeks. “Six pointers”, “must win” games, relegation “dog fights”. The superlatives and headlines write themselves.

One phrase I’m sure you will all hear many times before the end of the season is “I fancy <insert team name> as they need to win”. Many people think just because a club needs to win they are more likely to do so. It sounds perfectly plausible. I bet most people reckon they could summon an extra burst of speed if they were being chased by a gang of rabid dogs rather than merely jogging to the shops to pick up the Sunday papers. Not only do we have a nice marker indicating this to be true, the prices bookmakers offer on these “must win” games will be completely different to the prices if the teams were to meet on less nail biting terms. For example, as Wigan ran onto the field to face Swansea last season, knowing anything but a win would condemn them to The Championship, you could lay Wigan at 1.82 with bookmakers. Using data from 1995 to the end of the 2012-13 Premier League season, I estimate (albeit crudely) that for 1.82 to be a fair price on a home Premier League team then they are about 8.4 points superior to the away team over the course of a season. Yet Swansea finished 10 points ahead of Wigan last year. Using the same data I estimate that a fair price for the home team when playing a team 10 points superior is in the region of 2.78. 2.78 in a non “must win” game but 1.82 in a “must win” game? Even allowing for my crude model I’m sceptical to say the least………………

Crunching the numbers:

Inspired by some analysis Kevin Pullein (The Racingpost’s colossus of football betting) carried out in the 2004 book “The Definitive Guide to Betting on Sports” I used his hypothesis. If teams challenging for the title/battling relegation are more likely to win the more important the game then the average number of points per game they achieve should be higher in the later months of the season when these “six pointers” crop up.

Examining all completed Premier League Seasons since 1995-96 (when the Premier League reduced its numbers to 20 teams) the average number of points the top 3 teams have gained per match is 2.09. If we look at month by month total they won’t all be exactly 2.09, they will move around a bit due to random variation. However, unless the “must win” mantra is true, they will remain reasonably close to this figure of 2.09.

So let’s look at some actual figures. In the following graphs:

– the broken blue line is the average number of points per game over the entire season, in this first example 2.09

– the solid purple line is the average number of points per game achieved by the teams finishing top 3 each month

– the broken pink line is what’s called in statistics a “confidence interval”. In lay mans terms as long as the purple line is within these bounds we are reasonably comfortable that the difference from the broken blue line is not significant, and merely due to random fluctuation:

Figure 1: Average number of points per game achieved by teams finishing in the top 3 of the Premier League since 1995-96 season

Figure 1 Average number of points per game

While the averages do move around slightly, none are outside our “confidence interval”.  This suggests that the average number of points per game a top 3 side achieves is not significantly different month to month i.e. “must win” game or not their performance does not improve as we approach the business end of the season.

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