## Thursday, 10 November 2011

### Drawing the Wrong Conclusions.Draws in the EPL.

In a case of extreme Karmic Retribution,Bolton inflicted a 5-0 thrashing on Stoke at the Reebok on Sunday.The result may have gone some way to easing the pain their players and fans suffered at Wembley on a very sunny afternoon in April 2011 when The Potters beat The Trotters by the same scoreline to reach the FA Cup Final.It was also equally noteworthy because it extended Bolton's run of games without a draw to 21 league games,more if you include cup ties.The run of non drawn games is certainly unusual,the next longest current run for teams in all games is 13 shared by Nottingham Forest and Peterborough,but is it so unusual that we have to assume that Bolton have a unique (ish) quality that is leading to definite outcomes in games they play?

 Bolton don't appear to do Draws.

There is much less variation in the likelihood of games in the EPL ending all square compared to games ending with say a win.Even when the very best play the very worst there's still around a 20% chance that the game will end deadlocked and in the vast majority of run of the mill match ups that are played the probability of a draw doesn't move much from 26 or 27%.Therefore,we can fairly easily model an extended sequence of games where the odds of a draw is in the region of 27% and the odds of a non draw is 73%.If you enter =rand() into a spreadsheet the cell will return a number between 0 and 1 and if you designate any return below 0.27 as a draw you have your very own,primitive draw generator.In the run of simulated draws I have just done a sequence of 25 consecutive non draws occurred after just 77 games,the next one appeared 700 games later.

So it would seem that although an extended run of non draws is relatively rare,if you look at enough games one such run is bound to occur.Bolton weren't designated as the team to watch for if you wanted a definite outcome before they started their run of non draws and by monitoring the EPL as a whole over a long enough time scale a team with Bolton's unusual sequence of results was bound to appear by chance.It just happened to be The Trotters.

World famous illusionist,Derren Brown does a trick where he tosses a coin to come up heads ten times in a row.It's shot in realtime with no video editing and it happens just as it appears on film.What isn't shown is the probable hours of coin tossing that preceded the run of ten heads.Shown out of context the ten consecutive heads seem remarkable instead of just uncommon and it's the same with Bolton's current run.It's certainly uncommon,but no so remarkable,in the context of 20 EPL teams constantly playing sequences of games,that we have to look for reasons why Bolton don't do draws.Bolton's 25 games without a draw are indistinguishable from a naturally occurring sequence in a much larger sample of games.

If non drawing teams occur largely at random,what about so called draw specialists.We could repeat the simulation on a team by team and season on season basis to see how common an unusually large number of draws were in the simulation,but instead I've taken so called draw specialists and seen how frequently they drew games in their next season in the top flight.If draws were for example a tactically based,repeatable talent we would expect a lot of teams to be able to retain this trait across seasons.A few do,but again this could just be a continuation of the random process,but most do not.Home teams who recorded the most home draws in season N averaged 8.4 draws per 19 games since 1988,but in season N+1 they only averaged 5.6 draws and just 15% of the teams equalled or bettered their previous draw total.Away draw specialists showed similar figures.The average number of home or away draws in the English top flight over that period was 5.3 draws,so draw specialist are most likely random streaks and the teams on average fall back to earth in subsequent seasons.

Average Number of Draws by Venue for the most Draw Prone Teams in the English Top Flight.1988-2011.

 Draw Prone Team Type. Average Number of Draws per Season. Average Number of Draws Next Season. Home Teams. 8.4 5.6 Away Teams. 8.8 5.6