Saturday 5 April 2014

Crystal Balls And The Perfect Model

Hejik left a comment on my Zero-Inflation adjustment to the Poisson distribution pointing out that the implied assumption that Poisson is an effective tool in modelling football matches is debatable, and indeed it is certainly a valid topic for debate.   
There seems to have been much debate about Poisson on various forums of late and the danger would appear to be the perfectly natural beginners obsession with building the perfect model.
Such a thing does not exist as you'll well be aware and 'best guess' is a reasonably fair assessment of what professional bettors are doing.
As long as your 'guess' is extremely well educated you have half a chance at the books who are also, apparently surprisingly to some, employing 'best guess' pricing models, not psychic witches with crystal balls.
For what it's worth, I think it's important that we question how efficiently Poisson fits to football and observation would suggest it's far from perfect.

However, even without that information it's easy enough to arrive at the same conclusion when we consider that some of the biggest bookmakers in the world are actively promoting it as a method of beating them. I'm not sure they'd be so inclined to do that were it even near as effective as they suggest.
Going through the comment in point order, the impossible perfect model that Hejik speaks of does not and cannot exist, and as I have commented on before, the perfect is the enemy of the good. A football match has far too many random variables for any model to get anywhere near to perfection, but that shouldn't be a reason to give up on creating a model that predicts outcomes more favourably than the available odds imply.

The beauty of football betting is that there is no shortage of matches to apply your model to, although there does seem to be a tendency for people to start shouting about their ROIs before they have even a few hundred matches under their belts. Compare this sport to the NFL, with its 256 regular season games a year.

As for Hejik's point about the bookmakers promoting Poisson, there is an article from last August that Pinnacle Sports are promoting, but interestingly there is no mention of the zero-inflation issue which, given the frequency of team scores being binary is a rather key omission. Fortunately you have me to help you out here! I suspect that there is a good reason why the topic was omitted. The cynic in me suggests one reason, but it may be as simple as that the mention of the added and significant complexity to calculations would be beyond many of their readers who prefer the 'weatherman' approach to putting in any real effort.

One well-known and understood issue with using Posisson for football matches is that Poisson assumes the totals to be independent, but everyone knows that goals beget goals. Studies from 2006 have shown that this is truer in lower levels of football than the top levels, but it is true nonetheless.

If you are trading a match in-play, then understanding how goal expectancy is increased after a goal is critical, but if you are pricing up a match for a punt, you take your best guesstimate, and if there's a first minute red card, penalty and a goal, maybe it works for you and maybe it doesn't. Random fluctuations of probability will happen, but that doesn't mean your model is flawed. The thickness of a coat of goal-post paint can make the difference between a win and a draw, an over or an under, but such happenings need to be 'brushed' off.

A second (sort of related) comment was from my new best friend Danny:
Cardiff 0 Crystal Palace 3 was a Poisson buster alright!
It certainly was. It was in October 1997 when Palace last scored three goals in a Premier League away game (3:1 v Sheffield Wednesday) and with a total of 6 in 15 trips this season, the likelihood of 3 in one game was remote. I had 0:3 priced at 70.2, and as XX Draws and More subscribers will know, a +0.3 rating to Cardiff City meant this was an XX Draw selection. Some draw losses hurt more than others though! Palace finished the 1997-98 season in last place, and while I am not celebrating yet, to say that Palace have exceeded my wildest expectations this season after a promotion that was in many ways almost accidental last season, would be an understatement.

1 comment:

Unknown said...

Poisson on its own is a sufficiently good enough model - the difficult bit (as with any model) is evaluating the inputs for each match.

From what i've seen, for pure poisson, the Dixon & Coles adjustment is the way to go. Inflation will make a small difference; and you can even combine both. But the real issue is the inputs.