During a class of the inaugural run of Applied Analytics and Sports Betting, Professors Harry Crane and Phillip Maymin were sharing examples of how they used specific analytic techniques to find profitable betting opportunities in the past. Harry provided the example referenced above describing how he used a Beta-Binomial Distribution to estimate the probability of exact win totals of every NFL team. The process uncovered a significant number of profitable opportunities in the prior season. Amazing, but not replicable. Matt Buchalter (PlusEVAnalytics) had published the work and opportunity before the prior season and many popular sportsbooks had adjusted.

What is the intuition behind the opportunity? 

The over / under bets on NFL season win totals tend to be a deep, liquid market. This implies that they are tough to beat without excellent handicapping skills. However, exact win bets (i.e. Eagles win exactly 10 games) historically had a flaw in how they are priced, which you could exploit with knowing the right way to model the problem. Generally, sportsbooks priced exact win bets with an assumption that the “skill” of a team is constant. The reality is that this “skill” is extremely volatile. Rookies will surpass or fall short of expectations, coaches will be better or worse than expected, QBs will be injured, etc. In summary, some books had taken a shortcut to price exact win totals. This shortcut significantly underestimates how often wild outcomes actually happen. 

John’s Perspective

One evening after work a couple weeks later, I noticed that a popular site had expanded its offerings to include NFL exact season win totals. I reviewed a few teams’ offerings and sure enough the prices seemed to have adjusted to Matt’s discovery the year before. I  checked the other well known sites, but an eyeball test suggested they were fair odds. If anything, it seemed as though they had overcompensated for the year before – a common trend in all walks of life.

I reasoned if an opportunity existed, it would likely be in a sportsbook that:

1)      Has a broad enough offering to potentially include exact win total bets

2)      Less popular nationally, so if they do offer a line with value, it is less likely anyone has bet into it yet and moved the line

3)      Ideally hadn’t offered the market the year before and hence hadn’t learned what the other bookmakers learned from the prior season

I put together a short list, including a sportsbook I recently heard about at a recent VIP appreciation event. The site not only offered the market but also appeared to be at an advantageous price. I spot-checked the Chiefs offerings and immediately saw their odds diverged significantly from the more popular sportsbooks I had seen the day before. 

Using KC as a test case, I began to consolidate the offerings of the new book and one of the market leaders into a spreadsheet and identified the best odds available at each win total between the two sportsbooks as highlighted in green in the chart below. I notice that a 12% risk-free return could be achieved with this strategy, which indicates a massively favorable opportunity.

However, I was not willing to commit the time or energy to build a Beta-Binomial model from scratch at 11 pm on a work night. Limits (due to prior sports bets) on the more popular sites eliminated the possibility of playing the available arbitrage, so I took a few easy-to-identify bets (i.e. KC to win 16 games at 60-1). Just because I don’t have the midnight adrenaline to model it out doesn’t mean someone else doesn’t. I post the following in our classes’ slack channel and enter Tom Quinn:

“For those interested the XXX Sportsbook is pricing way too much concentration around the mean and have way too narrow tails as discussed in class for NFL season win totals. SB A & B are pretty close to each other. I just bet Chiefs to win 16 games at 60-1, it was best value I saw for the Chiefs on XXX. SB A is offering 17-2 for comparison.”

Tom’s Perspective

I love nothing more than betting on mispriced tail events, so I jumped on the opportunity John presented and spot-check the site, I focused on the Cardinals as a team I viewed to have a wide range of outcomes for the season. It was obvious to me that the sportsbook that John identified was mispricing the tail outcomes (Higher peak and flatter tails in the chart below). 

A few other members join the discussion and began to bring up additional sportsbooks to check and pointed out the flaws in my many attempted shortcuts to find the most profitable bets. 

I finally decide to build the model Harry and Phil went over in class. I am a mediocre programmer, so I would have to make it work in Excel. I believed that my approach was very rudimentary and flawed until I enrolled in the Bayesian Sports Betting course and found out that Matt, whose work I was trying to replicate also does most of his work in Excel and the solver functionality offered. 

I won’t bore you with all of the details of the modeling, you will have to take the class to for that. But a brief summary: 

Estimating the Parameters: 

To calculate the probability of an outcome using a Beta-Binomial model, you need 2 inputs (A and B), which can’t be directly calculated (of course). You can however observe A+B, which we had calculated in class to be 18.3 for the 2020 season. We calculated prior seasons as well, but I chose to use the 2020 number due to Covid related issues with player availability being a common factor not accounted for in prior seasons. 

I calculated the market-implied median number of wins for each team using a combination of ‘sharp’ over/under lines (also taught in class). This gave me a specific data point to target (what values of A and B would 50% of forecasted outcomes fall below the median estimate, while A+B=18.3). To solve this, I used the Excel solver and a statistical add-in to excel, which calculated the beta binomial function. (Vose Risk software)

Once I had the A and B parameters for each team, it was a straightforward process to calculate the probability of each exact win total. 

Identifying our bets

Using the odds posted on the first book John discovered, we identified 36 bets where the edge was greater than 70% based on our probability estimates. 

Results

Of the 36 bets, Bengals to finish with 10 wins paid 60-1, and Giants to win 4 games paid 40-1. This is a profit of 66 units and an absurd 183% ROI. This was also a historically ‘tame’ NFL season. If you chose to bet 100$ per opportunity, you could have paid for the 2 classes offered on Analytics.bet with enough left over to fly to Vegas for Betbash II. 

In the interest of full disclosure, my personal results were not quite as good as the model indicated. I was actively betting some of the lines John had discovered as he (and others) were arguing the need to build the full model. Patience and discipline proved to win this round. This analysis and discussion was shared on the private class slack for anyone to use prior to the season. We made an open offer to share the bets we had made and many students took us up on it (this was after we placed our bets of course). As Don Barzini says in the Godfather “after all… we are not Communists.”