Thank you to everyone who pointed out that AU covers more scores than just 4-0. I promise you, despite the tripe I often write, I DID know that :-)
So after that little exercise I have a couple of questions, born out of curiosity rather than intent.
Firstly, the same stats are available to all, so a Poisson distribution designed around average home goals, average away goals or average total goals per game will presumably present the same results for everyone trying it. So for it to be of any use some subjective input must be made. How, for example, should we treat the errant results? The stand out errant result so far this season was surely the Man U trouncing of Arsenal by 8 goals to 2. That match skews Man U's home goals too high, and suggests the Gooners are (too) easy to score against. As the season progresses, assuming no more such errant results for either side, these averages willl come down a bit, but I'd be interested to hear how this kind of thing might be addressed.
My second question, of purely academic interest, is how do I get Excel to calculate a PD for any score of 4 or more goals to either side? I'm assuming that you don't need to calculate and aggregate 4-0, 4-1, 4-4 etc to achieve this but I'm blowed if I can work out how to do this! What did occur to me was to calculate the PD for all scores up to 3-3 and subtract the sum of those 16 results from 100. The resulting figure looked about right for some very evenly matched low scoring sides, but put say Man U and Chelsea in there and ... let's just say I'd back AU at the suggested odds!
My toying with this has reinforced in my mind the substantial gulf between the mathematically competent (and despite my self deprecation I am reasonably adept at 'normal' maths) and the statistician!
A zero-inflated Poisson model doesn't work because of the under-estimation of 0 and 1 goals, and thus the draw is significantly underrated. The two keys are modifying this and calculating the goal expectancy in the first place. People have different ideas on this, how many matches to include or weighting them for example. As for calculating the probability of 4 goals or more, simply sum the probabilities of 0, 1, 2 and 3 goals, and subtract this total from 1. Check out my flatfish post today http://green-all-over.blogspot.com/2012/01/flatfish.html
ReplyDeleteHello Gundulf,
ReplyDeleteI'm portuguese and I discover your blog last month. Let me say thank you because I feel I learned a lot with you.
One question if possible:
If it's possible can you please tell me how does the odd 3-0 moves with an early goal? Imagine a favorite with +-1.80.
Thank you very much!