Tuesday, 21 May 2013

How Important Are "Six Pointers"?

Imagine an alternative end of the season. Wigan and Aston Villa find themselves locked on 40 points going into week 38, trailing a host of teams, each with 42 points. So there is an anxious final 90 minutes in store, not only for Wigan and Villa in the fight to avoid the Premiership's final relegation spot, but also for the raft of sides two points in advance of them.

Except because of the vagaries of the fixture list only Villa and Wigan are at risk of relegation. Villa visit Wigan on the final Sunday and so everyone else is perfectly safe because the two lowly rivals cannot both get three more points to overhaul the pack.One of the two final day rivals is guaranteed to finish the season in the final relegation spot.

Such considerations quickly become major factors when simulating potential points totals for various teams or scenarios. The fixture list is thoroughly entwined and if Stoke defeat Arsenal at the Britannia in one particular simulation, the result for Arsenal on their travels to the Potteries for this particular iteration must also reflect this.

The hypothetical Wigan/Villa scenario boils down to a winner (or draw) takes all, but the importance of so called "six pointers", where teams who are likely to be locked together in the final table, has long been recognized. The most eagerly dissected head to head confrontation this season involved long term rivals Arsenal and Tottenham and with all title hopes extinguished by January, their fight for fourth place and Champions League football in 2013/14.

With all due respect to Everton, who found themselves sandwiched between the two London sides at the end of January, I am going to merely simulate the post transfer window campaign from the perspective of Arsenal and Spurs, taking particular account of the effect on the simulation of the result of the North London derby played on March 3rd at White Hart Lane. A true "six pointer", with Arsenal still trailing Spurs by 4 points at the time.

Once the window shut in January both sides had 14 games left. Arsenal, it would transpire had the easier run in. The median position of their opponents at the time of each match during the final third of the season was 12th compared to a more elevated 9.5 for Tottenham. That advantage was partially counter balanced by the use Spurs had already made from a less onerous set of fixtures. They led Arsenal at the start of February by three points after each side had played 24 games.

The race for fourth, therefore appeared very tight and so it proved. In the simulations, which account for strength of schedule and simulate matches played from February onwards, Spurs won 51% of the races where there was a clear league points winner. However, 6% of the races ended with both sides tied on league points and Arsenal's already superior goal difference at the start of February would make them much more likely to win the majority of these simulated contests on the tie breaker. If we take this best case scenario, Arsenal now grab fourth spot in 52% of the simulations.

So how pivotal in the simulations was the head to head encounter in March? In simulations where Spurs beat Arsenal, their share of the Champions League winning spoils rose from around 50% of the simulations to nearly 70%, with almost the absolute reverse being the case on the occasions where the Gunners triumphed. A drawn game saw Tottenham and Arsenal winning virtually identical percentages of the trials.

Bale's opening strike in the North London derby would ordinarily have led to Champions League football.
So in simulations, a head to head result from a near level break in January appears to give a large boost to the winning side. Spurs did in reality beat Arsenal in March, but they still came up short in May. Arsenal were always likely to gather more points than Spurs during the post January run in, they did so in 73% of the simulations, but Spurs' win at White Hart Lane would, more often than not have been decisive. Expensive, post Europa losses to the likes of Fulham may fuel another debate and combined with Arsenal's impressively fine run in, the Gunners can look forward to high quality European action next term.

I'll flesh out the numbers in a later post, but more good stuff based around the race for 4th spot can be found here from Simon Gleave , here from James Grayson and here from Zach Slaton.

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