It’s the 30th of August 2014. Manchester City are looking to defend their title after winning the 2013/2014 season and have an opportunity to win an easy three points against Stoke City at the Etihad. The bookmakers had priced Manchester City to win the match at 1.18 (1/5 in old money), which means the betting public thought the home side had almost an 85% chance of winning the match.
City did indeed dominate. Here’s a look at the match stats:
Despite having a total shots ratio of 0.696 (they took 69.6% of shots in the game) their accuracy was atrocious, only managing to hit the target twice. Things went from bad to bat-shit crazy in the 58th minute when Mame Diouf did this:
Stoke City managed to hang on and win the game 1-0, despite only being given odds of winning the match of 18.00 (17/1).!!
So wouldn’t it be great if we could find a method to show the teams that are most likely to provide shock-results? (both good and bad). Well thankfully there is one!
The Brier Score is a rating system used to test how accurate weather predictions are, but it has been adapted since then to a myriad of different areas where prediction and outcome are involved – for example sports betting.
Bookmakers are really good at probability. Add on top of that the weight of public opinion which is reflected in match odds and you have a very efficient market. So we can use the Brier Score to test whether teams played to their probability or if they over/under achieved, and over time we can see if their chance at winning is being over or under estimated.
So let’s use this game from August 2014 as our example. Bet365 set the odds as follows:
Manchester City – 1.18 (84.74%)
Draw – 8.00 (12.5%)
Stoke City – 18.00 (5.55%)
Bookies make their money by manipulating prices slightly to guarantee profit. In a fair market, those probabilities would add up to 100%, but here Bet365 set their overround at 102.8%. So first of all we need to adjust this to a true (100%) market.
Manchester City – 84.74/102.8 – 82.43%
Draw – 12.5/102.8 – 12.15%
Stoke City – 5.55/102.8 – 5.40%
Next we need to know the actual result of the match. If the home team wins we take their true probability away from 100%, and keep the values for a draw and away win as they are. If the match ends in a draw, we take the true probability of a draw away from 100% and keep the values for a home win and away win.
Stoke City (the away team) won 1-0, so we keep Manchester City’s probability at 82.43%, the draw at 12.15%, and for Stoke City we take their original probability away from 100% – 100 – 5.40 = 94.80%
Next step is to square each of the values we just calculated:
0.843² = 0.7128
0.1215² = 0.0147
0.9480² = 0.8987
We add these three numbers together and get the Brier Score for the match of 1.626.
So what does that mean? The Brier Score ranges from 0-2. The closer the score is to zero, the better the prediction was. Any score below 0.600 is considered “good”, meaning teams are playing to market expectation. Anything above this is an indication that a team has over or under performed. With a score of 1.626 here we can say with full confidence that this was a shock result for both sides.
Leicester City are a good case to look at. Throughout most of the 2015/2016 season they were consistently under-estimated by betting companies, or they played far better than their actual abilities. I believe a combination of the latter and under-performances from the big 6 was the cause.
Leicester City managed to win the EPL with an average price of 2.91 (almost 2/1). Just look at all that red in their Brier Score and the odds they were being given for each game right until the end of the season. For the betting public this kind of data is invaluable. With it a punter can see which teams are being over or under valued and find an edge in an industry where most of the angles have been smoothed down.
Here’s a look at this season’s Brier Score for the EPL:
Some points of note here. We can see that Liverpool and City have a very low score at home, indicating that they are playing to expectation in front of their own fans. Liverpool’s away score, however is one of the highest in the league. This shows us that they haven’t been playing to expectation (They lost 2-0 to Burnley away and beat Chelsea 2-1). I’ve included each team’s average odds for comparison’s sake and have highlighted the shortest and largest prices. The fact that City have such a low score at home with average odds of just 1.32 underpins just how strong they are this season. The same can be said for Burnley’s away score – they have the lowest Brier score in the league for their away games and the highest odds, so they are playing away from as expected – relegation candidates.
All scores are up to date as of 17th October, as Liverpool and United are playing tonight, their figures will have changed when I post about this again tomorrow.