Why would we want to do this? Because we can then learn the parameters that the odds compilers have in mind when they set the odds for the match. And in the case of a Poisson model (which is standard), this parameter is the expected number of goals.
Hence, we can find out the odds compilers estimate of the expected number of goals to be scored by each team. This is extremely useful information to have when choosing a fantasy team. Picking the top goal scorers from teams that are likely to score goals and defenders from teams that are unlikely to concede them is a sure fire way to score points.
I've gone ahead and done that using the odds for this week in the EPL. Here are the results:
- 2.31 — Manchester United
- 1.72 — Arsenal
- 1.62 — Chelsea
- 1.48 — Bolton
- 1.47 — West Brom
- 1.47 — Liverpool
- 1.38 — Manchester City
- 1.34 — Tottenham
- 1.25 — Fulham
- 1.21 — Blackpool
- 1.05 — West Ham
- 1.00 — Blackburn
- 0.97 — Newcastle
- 0.84 — Birmingham
- 0.78 — Wigan
- 0.75 — Wolves
- 0.70 — Stoke
- 0.70 — Sunderland
- 0.53 — Everton
- 0.53 — Aston Villa
Like any mathematical technique, this one has limitations. So let me point out potential places where this could go wrong:
- The odds compilers might not be assuming a Poisson distribution. This isn't a serious concern, in my opinion, since a Poisson model is very standard and fits these data very well.
- The odds compilers may not be assuming that goals scored by each team are (probabilistically) independent events. I have no reason to think this is not the safest assumption, however.
- The "over-round" may not be distributed evenly between win, lose, and draw. This seems like a potential concern. However, as these odds had an over-round of only 0.075, it won't affect these estimated parameters much in any case.
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