A convex betting system for soccer matches
I am a big fan of sports statistics, even sometimes they don’t provide really useful information or they even provide false clues. For instance, I remember a remark from the great Spanish basketball coach Aito Garcia Reneses where he claimed that basketball matches were usually won by the team who gets more offensive rebounds, which is probably true, but then there is still the question of how and why winner teams are able to get those rebounds. What I am implying is that sports stats usually give you incomplete information.
I am also a big fan of Nassim Nicholas Taleb ideas, that apply to probability and risk. This post is not a total application of those ideas, but it got influenced by them. He applies his ideas into real sh** scenarios, I choose instead to focus in a very naive scenario: football (soccer) matches. Sports events are boxed, which means that they are limited in time and possible outcomes (you will never get a 100–0 soccer result, a match that lasts 3 hours or a championship that ends after more than a whole year), which is also convenient for playing with the data and comparing different series (seasons, teams, etc…).
I decided to taking advantage of an unusual situation in a very specific sport competition: Spanish La Liga. In Spanish football championship, there are two worldwide teams, Real Madrid and Barcelona, that usually win 90% or more of the championships. That’s a trend that started long time ago, from the beginning of the competition, but seems have been reinforced during last decades. From time to time, there are other teams that dispute that domain, like happened with Deportivo or Valencia at the beginning of the 2000s or Atletico de Madrid during late 2010s. But if you are reading this now there are huge chances that one of those clubs is in top of the table, closely followed by the other one.
So, how that situation can be exploited for a profit in, let’s say, a betting scenario? The victory of those clubs is usually paid really low, close 1 to 1 most of the time with a few exceptions. And most of their defeats, because they are so scarce in normal circumstances, are paid really high, usually more than 7 to 1, which means that for every single penny you bet, you’ll get 7 in case you win. Those are the Black Swans, extremely unexpected events, and those are the ones we are looking for.
But hold on!… Isn’t it the chance of winning one those matches lower than the betting odds? I mean, you can expect, i.e., that Osasuna wins one of every ten matches against Real Madrid, which is a 10% success chance, but the betting odds are like 7 to 1, which means you would only recover 70% of your investment, the house wins again and you are wasting your money like a drunkard gambler in Las Vegas Casino. And that’s absolutely right. And that’s where we can use the Martingale betting system.
In case you haven’t read the Wikipedia article, Martingales are old betting systems where you basically cover your losses gradually increasing your bet amount in every new bet for covering your losses. When I read it first time, I thought it was simply genius and unbeatable. Then I read it again, and saw the reasons in real world it doesn’t work that well, specially with probabilities closer to 50%, and when you have to pay a cut of your earnings to the house (and we even haven’t talk about taxes).
Martingales usually don’t work but maybe they do in some cases. I decided to try that approach for betting against the two big asses of the Spanish soccer championship. My approach starts betting a minimal amount (1 unit, could be euro, dollar or pound…), then increasing it when the possible earning doesn’t cover the already spent amount. Doing this way, you will lose a bit every single bet, but you will be exposed to a great win that should compensate previous loses. That’s called a convex or barbell strategy (please, don’t try this at home with real money).
Here you have some results using a lower bound of 7 (minimum odd is 1 to 7 against the main team), excluding draws:
- Real Madrid 2018/2019: 13.00 spent 53.49 earned 13/29 games
- Real Madrid 2017/2018 27.00 spent 49.79 earned 27/38 games
- Real Madrid 2016/2017 34.00 spent 0.00 earned 28/38 games
- Barcelona 2018/2019 19.00 spent 26.12 earned19/29 games
- Barcelona 2017/2018 37.00 spent 10.46 earned 29/38 games
- Barcelona 2016/2017 32.00 spent 64.11 earned 32/38 games
Turns out that the strategy seems to be only valid in a long enough run, as there are some seasons (Barcelona 2017–2018, Real Madrid 2016–2017) where the outcome is clearly negative, and they are compensated with the positive earning ones in other seasons. I did the calculations based on whole seasons, but a combination of mid-season and multiple seasons should also be valid. It’s also noticeable that the same strategy could work for other teams in other leagues where the top teams are always the same (i.e. Scotland), and also could stop working in Spain, as another Black Swan could happen to one of the big teams, similar to the one got Juventus demoted in Italy due cheating, a few years ago.
You can try those results in a web app I developed and deployed in http://martingale.manel.pro . You can try it, but remember that is only an experiment, and I still haven’t discounted the betting exchange commission ;) It’s only the beginning when exploring the marvellous world of statistics in sports.
