Bayesian sports betting: using statistical or empirical Inference and Bayes Theorem to crush the markets

Here's one for the bayes.... would you rather be a high stakes sports bettor who struggles to get on and keep accounts, playing to an EV of around 2-3%? Or would you prefer to be a smaller stakes player with live accounts for the most part, juicing away at a big edge in terms of ROI, with a high volume of bets?

Well I'm in the latter camp and I've never really wanted to change that. I've been doing this for many years and have had over 50 betting accounts in that time. That might seem like a lot of accounts to plenty of you but it's really not if you're talking about betting seriously. In terms of staking it's more a hobby for me, but in terms of very long term ROI across all my portfolios, it's right up there. My approach is all about Bayesian reasoning and probability theory. I love having bets and I love watching them play out so I couldn't do without betting accounts. Even if I am factored down to a few schuid, I'd rather keep my sports betting accounts than have no access without lots of effort with burners and agents etc.

It's never been about money for me - I just absolutely love the game and the constant test of trying to stay ahead of the ever changing sports betting markets. In fact, because it's never been about money, maybe that's the reason I've lasted so long in the game. That and the fact I've nothing else to do. I learned to manage risk and about how variance works almost sub consciously while never staking amounts of any real significance to my personal life. This is the very same for me both in sports betting and poker. 

In the earlier poker days I was never really tempted to move up through to high stakes - I was perfectly happy absolutely crushing the online small to mid stakes SNGs and STTs. I was one of the few to have the little shark's fin beside my name on Sharkscope! I learned game theory and optimal bet sizing empirically through trial and error, over hundreds of thousands of hands and multiple tables at a time. The odds and probabilities were second nature. 

My real edge came from my somewhat unique ability to deviate from game theory for situational circumstances and technical analysis - essentially using Bayesian Inference and conditional probability. I could change my strategy from GTO vs certain players or in certain situations. 

For example: I could narrow down the range of hands my opponents might have by considering their bet sizing or the time it took them to make a bet, and adjust. Along with concepts such as independent chip model (ICM), I had a big edge vs even the other top players, who used a more frequentist style probability approach.

Introduction to probability theory in sports betting

A good way to describe me is a probability aficionado, a "visual mathematician" according to my aptitude tests. I was always this way. I've never really put content out like this before as I was a bit secretive in this area but I feel this is the way forward. I love it. Maths was the easiest thing I ever did in school. I was naturally a probabilistic thinker and questioned everything. 

Sometimes I felt class was so slow that I used to skip to the examples at the end of the chapters and reverse engineer and figure it out for myself. I studied probability theory in college doing Engineering. It was pish easy. I found I could estimate most answers accurately before actually using the formulas (most of which I don't even remember fully right now). The actual math part of it isn't really needed in sports betting. Conditional probability theory is what's needed to exploit the market odds, which are more of a frequentist approach to modelling, just like my poker rivals - a load of old heuristics if you ask me!

Applying probability theory to sports betting market dynamics

This is my approach to beating the sports betting markets - I apply probability theory to the dynamics of the betting markets which are not near as efficient as even the mushroods think they are, even the highly liquid markets at close. I mean who controls the markets? How shrewd are the big players and syndicates really? Can they predict the future? No. I talk about the Efficient Market Hypothesis in my upcoming book Hypnotised By Numbers

Big syndicates use the first approach I alluded to in paragraph 1 going through brokers and agents and exchanges and wherever will take their sharp action. Some will have deals in place. There are not many "probability masters" in the world, never mind the world of sports betting. Most top class odds originators will be small players no one knows about and they'll use Bayesian reasoning and or empirical evidence based bayesian type models. I'm talking about the best of the best - the small few. It's the same in poker - the Big Time Charlies or most of the high stakes players you see on TV are not the best players. The best players are often incognito, basement boys that no one has heard of.

What is the Bayes Theorem?

The Bayes Theorem is a mathematical formula for determining conditional probability. Conditional probability is the likelihood of an outcome occurring, based on a previous outcome occurring. This is key to finding an edge in the sports betting markets.  In English for dummies, it means changing probabilities based on new information. Estimating that is obviously the hard part:

P(A|B) = P(B|A)*P(A) / P(B)

The Bayes Formula takes it 1 step further than conditional probability by constantly adding in new information to update the probabilities. When floods of money come in to the betting markets essentially changing the odds, this is actually Bayesian Inference in disguise, as explained brilliantly in the article.

Consider this:

Denzel Dumfries was on the team sheet for the Dutch as a right back for the Euro 2021 matches. He was priced up (using whatever the key stats said about him) at around 10/1 to score anytime which is about right for an attacking full back you might estimate or infer if your domain knowledge is up to scratch. What happens though if he actually plays more as a winger come forward on the flank and gets himself into plenty of great positions and even scores a goal? Well nothing happens apparently. He did score and he was priced up the same for matchday 2. The same thing happened again - he actually got man of the match in both games aswell as scoring in each. Now if you watched that first match, using bayesian reasoning you could have deduced that his fair odds to score anytime were plenty less than 10s. You don't actually need a large sample to know this.

Again, my upcoming book "Hypnotised By Numbers" is all about this kind of thing with loads of examples. If you refer to my course fit model for the golf that many will be familiar with, basically that's a bayesian model where I've estimated probabilites for the parameters using empirical inference over many years. I've also turned the outputs into expected strokes gained numbers in a way that probably no one else could do as precisely. This model has already been taken on board by some of the big data players.

Bayesian Sports Betting Summary

It is very possible to estimate parameters and probability distributions very accurately using bayesian reasoning in small samples. Frequentists might dispute this, and that I understand, as they haven't experienced it for themselves as their brains are not wired that way. Some people could for example watch maybe 50 horse races in different conditions with around 150 or so different horses involved in total. Then they could price up a race with any 10 of those horses on a random track more efficiently than any model could, even if it had the data of finishing positions adjusted for track type. The fact that you won't find many people like this is what means the betting industry will always be exploitable so happy punting.....

Bryan Nicholson has not 1 but 2 books coming out (hopefully both in 2022) which covers so much he has learned in the last 20 years. Having seen plenty of the content, we can suggest if you get both of these books you won't need to look anywhere else ever again in your quest to become a better bettor. The 1st of these (early 2022) is Hypnotised By Numbers

This article: Bayesian Sports Betting: Using statistical or empirical Inference and Bayes Theorem to crush the markets was written by probability expert and small fry professional bettor Bryan Nicholson 


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