Premier League Boxing Day Arbitrage-a-Ganza! Making (Probably Stupid) Value Bets Using ELO

Soccer ELO: The Rebuild, Part 3.

Chelsea fans reacting to current transfer market valuations. Img: Unbet

We’ve made a huge dataset. Now it’s time to embrace our inner Oscar and make some cash money.

Not only can ELO peacefully rock the casual blog reader to sleep with methodology discussions and inspiring lullabies about competitive parity, it can predict match results. And if we can predict matches correctly, there is money to be made.

How does ELO predict match results?

Recall the Expected Result Variable (ex_res for short) from Part 1 is the engine of the whole ELO algorithm:

This takes all the pre-match information (the ratings of the two teams playing and the expected home field advantage) and normalizes it into a standard-logit probability score from 0 (away win) to 1 (home win). Now you might say something like:

Well, that’s fine and fancy, Matt, but this is soccer. Teams draw all the time.

To which I’d say: yes, you’re technically correct (and also kind of a jerk). The result variable controls for this with Draw == 0.5. But ultimately we’re dealing with a continuous ex_res variable that spans the gamut across a categorically binary variable: you can’t necessarily round up or down to get the probability of a draw. But what we can do is make an informed assumption off of a long term average of results. If we fit every ex_res observation from our 21 year, 10 league dataset into 0.5-percent chunks and count the number of results into (home) wins, draws, and losses, we would get the following:

As expected, the incidence of a draw expands to its maximum proportion of results as ex_res approaches 0.5, and then contracts as ex_res approaches 0 and 1, as losses and wins would be much more likely to occur at those points, respectively. Now, let’s isolate each probability (proportion of total results) and see if we can’t find any trends:

We can already see three trends for which we can draw fitted lines:

Probability of a home win: Linear-ish (R² = 0.9661)

Probability of a away win: Linear-ish (R² = 0.9523)

Probability of a draw: calculated as 1 minus sum of the first two probabilities.

Using linear regression, we can estimate the best-fit lines and get the 20-ish year historical average of result probabilities between teams of different skill levels. That formula can be estimated using R or any statistical software, so it will stay in the pocket for now. #sorrynotsorry, but what I can provide are this week’s Boxing Day matches given the current ELO ratings:

Current home field advantage = 71.7 ELO points.

Okay, cool, but how can you bet using the result predictions?

Watford [1467] and Burnley [1445] have some solid coin-flip match-ups that the market is undervaluing. Img: Sky Sports

Good question. Now we need to understand the odds market. I wrote down the Bovada.lv three-way-moneyline odds for the #PremierLeague Boxing Day Extravaganza (otherwise known as Matchday 18):

Bovada odds collected 22 December 2016

For argument’s sake, let’s take the Arsenal-West Brom match, and break down what each of the money-line odds suggests:

• BovH: Home (Arsenal) victory odds. Bet $300 to win $100, or 1/3odds. The betting win includes the amount of the original bet.
• BovA: Away (West Brom) victory odds. Bet $100 to win $750, or 15/2 odds.
• BovD: Odds of a draw. Bet $100 to win $425, or 17/4 odds.

While we could translate the odds into probabilities, it may be more useful to translate the ELO probabilities into odds using the following formula:

We’re putting everything in terms of a home result here just to make things easy.

So now that we have that, let’s convert everything into odds and put them up against Bovada to see where the best value bets are:

Thank you, Chelsea and Bournemouth, for throwing off the significant digits function and making my table ugly.

I’ve highlighted what I think are the strongest value bets, where the market odds pay out much higher than the ELO odds. Of those bets, however, only two of those bets are anything close to a coin flip (Watford over Palace, Burnley over Boro). However, two other conclusions definitely present themselves.

1. The market overvalues favorites and well-known teams. Well-known teams like House Manchester and Chelsea will likely always be overvalued by the markets, as these are well-known quantities in a global market. Especially in cupcake matchups against the bottom of the table, teams like
2. Value bets are sucker bets unless they are spread against risk. Of course, that doesn’t necessarily mean that every European unknown is significantly undervalued, or, of course, that betting the underdog is a good bet. Betting houses regularly jack up the odds for underdogs to entice betting, otherwise known as “sucker bets.” Recently guilty of making such an assumption:

Bayern [1611] was up 2-nil at 27’ and Leipzig [1605] got a red card at 28'. #CoinFlipOrMassacre

Remember that this particular ELO prediction method is based on historical averages. Despite the many traditional powerhouses that exist in European soccer, one must remember that soccer is a hyper-realistic reflection of our ever-changing culture. Results unlikely years ago may be much more likely now; results likely today may be much less likely years ago. Understanding this autocorrelation would be a definite and solid tweak to this model.

In other words, putting all your money on plucky-but-very-bad Hull City to beat the Manchester City Money Machine is both stupid and unsmart, even if the market odds are in your favor.

If you are going to take my (unqualified) advice and bet undervalued underdogs, do so wisely and spread your risk across multiple matches. For instance, I would place small bets on all of the highlighted matches instead of a larger bet on a Watford to beat Pard-OUTed Crystal Palace, the match in which I was the most confident (Sorry, Big Sam). Optimizing this portfolio accordingly seems like another fun project for another time.

But, for now, know that ELO can be a predictive baseline to judge how probable or improbable certain results are. In fact, it would be sad days for football if I were actually able to make it rain using this particular measure, as it would also mean soccer has become predictable, disparity has become the norm, and Tony Pulis has become TIME Man of the Year.

But, just for fun, let’s see what we can do.