So far the Premier League season has been quite exciting. While Arsenal, Chelsea & Man 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 Aston Villa 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 team X 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 on Betfair. 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
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
To double check I looked at the strength of opposition that they played in each month. If we take all games that teams inside the top 3 play we get the following:
· the average finishing position (or “rank”) of teams playing the champions is 11
· the average rank of teams playing the runners up is 10.95
· the average rank of teams playing the 3rd place team is 10.89
· The average rank of teams all the top 3 teams will face is 10.95
Looking at the graph above we see that the lowest number of points per game achieved by the top 3 teams was in November. While this figure is less than the overall average of 2.09 it is still within the “confidence interval”.
However if we look at the average ranks of teams played each month we see the strength of opposition in November was also slightly higher (an average rank of 10.41, versus the overall average of 10.95). Likewise the highest points figure was in March, but the average rank of the opposition was slightly weaker than average.
The following table compares the average number of points per month with the average rank of opposition. We see that the months where points tallies per game were lowest (when compared to the average of 2.09) were the months where the opposition faced was slightly stronger (as indicated by a slightly higher average finishing position).
Figure 2: Average number of points per game achieved by teams finishing in the top 3 of the Premier League since 1995-96 season compared with strength of opposition
So to summarise:
· the number of points the top 3 achieve month to month appears reasonably constant
· the 2 months were performance was weakest (but still within the bounds of random variation) coincided with them playing slightly stronger opposition
· There is quite a strong correlation between average number of points and strength of opposition (measured by end of season positions)
Next I looked at the performance of the teams who were relegated to see if they really do buck up their performance for those “relegation six pointers”. The analysis was identical to that outlined above for the top 3
Figure 3: Average number of points per game achieved by teams finishing in the bottom 3 of the Premier League since 1995-96 season
Again we see that, apart from one outlier in September, performance does not materially change month to month. There is certainly very little evidence that performance improves later in the season. While the correlation between performance and strength of opposition is not as strong as in the first example, neither is the level of variation in performance month on month
Figure 4: Average number of points per game achieved by teams finishing in the bottom 3 of the Premier League since 1995-96 season compared with strength of opposition
Lastly I looked at the performance of the teams finishing in mid table positions, namely 8th to 12th. These teams would have been relatively “safe” heading into the final stages of a season. As such general consensus would have you believe that these teams (like Swansea versus Wigan, mentioned above) have “nothing to play for”.
The obvious inference being that they aren’t trying as hard and as a result will not pick up as many points. Again I am struggling to find evidence to support this
Figure 5: Average number of points per game achieved by teams finishing between 8th and 12th in the Premier League since 1995-96 season
Yet again performance does not materially change month to month. While performance does appear to drop off in May note:
· this variation is comfortably within the bounds of our “confidence interval”
· The strength of opposition faced in May is quite a bit higher (average rank of May opposition is 9.82 versus a season long average of 10.50)
There is again reasonably strong correlation between performance and strength of opposition
Figure 6: Average number of points per game achieved by teams finishing between 8th and 12th in the Premier League since 1995-96 season compared with strength of opposition
So what are bookmakers playing at?
Looking again at the example of Wigan at home to Swansea last season, you may ask how the hell were Wigan as short as 1.82? As previously stated I crudely estimate that a price of 1.82 suggests the home team are approximately 8.4 points superior over the course of a season.
It is arguable Wigan should not have been 1.82 at home to any Premier League team in 2012-13, let alone a solid mid table outfit like Swansea. Whether Wigan won or not is irrelevant (for what it’s worth they didn’t). Anyone taking 1.82 is destined for the poor house.
So are bookmakers stupid? Unfortunately not! To be successful a bookmaker should possess at least the following two skills:
· they should be able to estimate, with reasonable certainty, the likelihood of various sporting events. In the case of a football match the likelihood of a home win, away win or draw
· they should have a reasonable idea of what their clients will do when presented with various situations and prices
Based on past experience they will know that a huge, huge number of bettors will be lining up to back the team needing to win no matter what the price. I mean why give a punter 2.78 when they’re willing to part with the same amount of cash (if not more) at 1.82?
This is why the analysis above is interesting, if the “must win” team are too short (and I can find zero evidence that if they need to win they’re more likely to) then either the prices available on the other team, the draw (or indeed both) may well be too big. Also the advent of betting exchanges allows a bettor to lay the “must win” team at prices far shorter than they should be.
A pro punter once told me that this was especially the case with teams threatened by relegation. So again I did some investigation. Using historic odds I looked at how one would have fared backing certain teams blind over the course of the season. I looked at return on investment (ROI) from placing a €1 bet at best odds (according to data on the excellent website http://www.football-data.co.uk/). ROI is defined as:
The results are summarised in the table below (note while points analysis was based on data from 1995-96 historic odds were only available from the 2000-01 season onwards):
Figure 7: ROI based on €1 level stakes at best price available as per football-data.co.uk
Looking at the above the figures are quite striking for the bottom 3. Backing them blind over the course of the season results in horrific losses; but we see that the losses increase in the last 3 months of the season. This is indicating to me that the market is (irrationally) pricing them up far too short as the threat of relegation looms and the number of “must win” games increases.
With respect to the mid table teams they do perform slightly worse in the last 3 months but interestingly they achieve their highest ROI (a whooping +11.5%) in the month of May when as stated above they meet, on average, stronger opposition. This could be evidence that the market discards their chances on the basis that they don’t have anything meaningful to play for.
The ROI on the top 3 is positive over all periods looked at. While the ROI is highest in the period March to May this is skewed somewhat by a huge ROI figure of +20.5% in March, when the opposition they face is only slightly weaker than average. I must hold my hand up and admit I’m struggling to explain this, while the average number of points gained per game was higher than average the opposition was slightly weaker (as we saw in the first section above). The ROI for the period April to May is a more modest +2.5%.
Based on the above, if you are sitting down to watch your team play a “must win” game towards the end of the season I’ve some good news and bad news. The bad news is I cannot find a shred of evidence to suggest they’re more likely to achieve those vital 3 points than at any other time of the season. The good news however is that bookmakers may well present you with opportunities to profit from the large number of people who believe they are, and back up their belief with cash.
by Eamon Howlin