NOTE: Lines move in real time, so the exact numbers I’m using in this article may be out of date by the time you read it. The general strategies should hold up regardless.

I first became interested in NFL season win total betting a year ago when I listened to this podcast with Drew, Andy and Fabian. To give credit where credit is due, most of the content I’m going to share here is a regurgitation (maybe with a bit more mathematical rigor) of concepts that they discussed. Each of these things individually can get you +EV bets; putting all three together can easily take your EV percentage into the double digits.

There’s not much to explain in terms of how the bet works – it’s a simple over/under on a given team’s number of regular season wins. Ties count as 0 wins, and the team must play 16 regular season games for the bet to have action. With all the Covid-related uncertainty this year, there’s a decent chance all these bets will get voided and you will end up giving the book an interest-free loan for a few months…so make sure you’re ok with that possibility before you bet any of these, and do your homework on your book’s stability because a shortened or cancelled NFL season could be financially devastating to them and nobody wants to get stiffed.

Ok? Let’s do this. Here are two easy ways (and one fun way) to find +EV bets on NFL season win totals:

#1: Line Shopping

This is not unique to NFL or regular season totals, and it’s been covered extensively in a million other places…my personal favourite is Ed Miller and Matt Davidow’s book The Logic of Sports Betting where they introduce the concept of “Synthetic Hold”. Taking the best available line for each of your bets from a menu of multiple books will give you a higher EV than using the same book for every bet – it’s as simple as that.

As I write this, Cincinnati is 5.5 -156/+129 at CRIS and 5.5 -120/+100 at Circa. You could pick up a few pennies by taking an arbitrage of under 5.5 at CRIS and over 5.5 at Circa, but there’s not much fun in that. It’s a mathematical certainty that AT LEAST one of those two bets is +EV, so how do we figure out which one is better?

What we’re really looking for is an efficient line; that is, the most accurate possible representation of the true underlying probabilities. The theory of market efficiency says that market prices perfectly reflect all available information, but what if different markets have different prices for the same bet? We could average the market prices together, putting more weight on the ones that are more likely to be efficient. Nate Silver has made a career for himself out of doing essentially this. If we’re going to weight different books’ lines by how efficient they are, we should give more weight for books that allow market forces to work to remove any inefficiencies; that is, books that:

• Accept sharp action
• Have high limits
• Price their lines to a low theoretical hold (i.e. charge low vig)
• Are open and easily accessible to bettors around the world

With these considerations in mind, I have formed a “market consensus” using the following books:

• Pinnacle (37.5% weight)
• CRIS (25% weight)
• Circa (25% weight)
• 5Dimes (12.5% weight)

If you can find any of these at a number better than this, you’re in good shape!

#2: Over Bias

Look at the “expected wins – market consensus” numbers in the chart above. Notice anything strange? Of course you don’t. Now try adding them up. I’ll save you the time: they add up to 262.01 total expected wins. One small problem with that…there are 256 games in a full regular season. Assuming a tie happens approximately once every two years (maybe even more with the shortened overtime), that means there are 255.5 total wins to go around. The books are pricing in six and a half wins too many. Divided among 32 teams over a 16 game season, that’s a pretty substantial amount.

So what’s going on here? Two things, that share the same underlying cause…the general public likes to bet overs on these things much more than they like to bet unders. Whether it stems from a cognitive bias or fans simply wanting a rooting interest…the reason doesn’t really matter. The books aren’t stupid, so the first consequence is that they shade the lines expecting more action on overs than unders. The second consequence has to do with how the lines move on action. Suppose a book posts a Patriots win total of 8.5 -130/+110 and decides to move the line after taking a lot of over action. They might move it to 8.5 -140/+120. As the Patriots implied win total goes up, what should happen at the same time is that all of the Patriots’ opponents’ implied win totals should go down – especially the Bills, Dolphins and Jets who each play the Patriots twice. From my observations, this doesn’t seem to happen – the books’ line movements don’t seem to account for the relationship the teams’ win totals have with each other. Wins aren’t a zero-sum game, but they are at most a 256-sum game!

You should have a much easier time finding lines that better than these. In fact, you could blindly take any (or every) under at Pinnacle and enjoy an EV of approximately +2%.

#3. Probability Distributions and Parameter Uncertainty

What we’ve discussed so far has been useful but basic…and let’s face it, dear reader, you did not come here for basic. Time to go deep.

Using the above chart as a starting point, we’re going to build out a full probability distribution for every team, of every possible win total from 0 to 16. This will allow us to:

• Quantify the value of each win, e.g. over 7 -115 is equivalent to over 7.5 at what odds?
• Price alternate win totals
• Price “team to win division” bets
• Price exotic props like “will any team go 16-0?”

Each team has 16 attempts, each of which result in either a 1 (win) or a 0 (loss or tie). At first glance, this seems like a good candidate for the binomial distribution. Arizona is expected to win 7.41 games, 7.41/16 = 0.463 so can’t we model the probability distribution for the Cardinals win total by 16 spins of this spinner?

If we’re working in the center of the distribution (mean and median), sure we can. But there is a fundamental difference between the Arizona Cardinals and this spinner that has a bigger and bigger impact. s we move out into the “left tail” (probabilities of winning a small number of games) and the “right tail” (probabilities of winning a large number of games). With the spinner, the underlying probabilities are known. With the Cardinals, the underlying probabilities are estimated. We think they’re a 7.41 win team, but we don’t have the same level of certainty that we have by looking at the spinner. What if, instead of being certain that the Cardinals are a 7.41 win team, we’re 50% confident that they’re a 5.41 win team and 50% confident that they’re a 9.41 win team? Because those estimates are still centered around 7.41, the analysis above that puts their fair line at 7.5 +107/-107 would still be valid. The difference is that we’d now expect larger deviations, both on the high side and on the low side, between the actual outcome and the mean of 7.41.

So let’s build our mathematical model using this concept. Instead of the Binomial distribution, we’re going to use something called the “Beta-Binomial distribution” – it’s just like a regular Binomial, but with an extra dose of variance that comes from “parameter uncertainty” – the fact that our “p” parameter is unknown and has its own variability. We’re going to use the symbol v to represent this extra variance. If v=0, the Beta-Binomial turns into a regular Binomial – with no parameter variance, we’re back to the spinner. For you Beta-Binomial enthusiasts out there, what I’m calling v is 1/(alpha + beta).

To estimate v, we can look at the history of what each team’s regular season win total line was and how much it varied from their actual number of wins. We can find the value of v that fits the best to the observed data:

So we have an estimate that is somewhat stable around v=0.0545. In case you’re wondering, 2017 was the season in which the Browns went 0-16, the Giants went 3-13 and the Rams went 11-5 among other surprises!

We can now put all the pieces together. Based on the market consensus and a Beta-Binomial distribution with v=0.0545, we can calculate the probability of any team achieving any number of wins:

We can use this to answer all kinds of questions. The probability of any team going 0-16? 7.2%. The probability of any team going 16-0? 7.0%. These may seem high based on history, but 2020 has two potential juggernauts in the Chiefs and Ravens, as well as the poor Jags who have a chance to be historically awful.

There are some books, such as 5Dimes, that are kind enough to post a good selection of alternate totals. For example, they have the Cowboys “regular” total of 10 wins -115/-105, but you can get as high as 11.5 wins at +213/-253 and as low as 8.5 wins at -324/+264. How do books price these alternate lines? Are they (incorrectly) using a pure Binomial distribution with v=0? Are they using the same v=0.0545 that I estimated above? The answer appears to be somewhere in between: when I solved for the v that best fit the probabilities implied by the 5Dimes alternate lines, I came up with v=0.0222.

Here is a visual representation, for a team with 8 expected wins, of the difference in distribution between a pure Binomial with v=0, the distribution implied by the alt lines with v=0.0222 and the distribution implied by the historical deviance with v=0.0545:

While all three distributions are symmetrical around the mean of 8, you can see some pretty big differences in their variance. Our distribution has “fatter tails”, i.e. higher probability of more extreme outcomes, than the distribution implied by the odds. This means that you are likely to find value by taking overs on the “alt high” totals like Dallas over 11.5, and/or unders on the “alt low” totals like Dallas under 8.5.

So there you have it: 3 ways to find +EV bets on NFL regular season win totals. If you put all of them together, what does that look like? It looks like taking the under on the “alt low” at a book whose number on this particular team is lower than the market consensus. There are several opportunities of this variety out there in the +10% to +20% EV range as I write this.

Go get ’em!

Wait, one more thing…

BONUS #4: The Clipboard Delta

What if not all teams share the same value of v? What if it’s higher for some teams and lower for some others? If you could pick teams with the highest v and play their alt unders, you could boost your edge even more.

The thing that we’re calling v is an expression of something I’ve written about many times – parameter uncertainty. There are many things that could happen during a season that could cause a team to perform better or worse than their preseason expectation. Good players could get traded for future draft picks. Rookies and free agent signings could show their true potential (or lack thereof). New coaches could fit in well, or poorly. But there is one thing that stands head and shoulders above the rest in terms of the potential to inject chaos into a team’s season…an injury to the starting quarterback. We saw what happened last year when Brees, Roethlisberger and Mahomes went out with injuries – their teams’ lines moved substantially.

I’m not going to try to judge each starting QB’s likelihood of getting injured – that would require a detailed analysis of age, injury history, etc. What is a bit easier is to look at the impact of an injury to each starting QB, defined as the difference in ability between each team’s starting QB and their backup.

There’s no easy mathematical way to do this, so it’s time for some good old fashioned domain knowledge. To bring this cruise ship full circle, I asked the same Drew, Andy and Fabian from the podcast I referenced in the intro (and with whom I’ve now become good friends) to rank the teams according to the difference between their starting and backup quarterbacks, a metric that Andy cleverly called the “clipboard delta”.

Here are the official Deep Dive x Suuma “Clipboard Delta Power Rankings”:

So even though I can’t put a precise number on it, I’m inclined to value Seahawks and Texans alt unders more than Bears and Dolphins, all else equal.

Tout Time!

Stuff I like at current numbers:

• Panthers under 5.5 +126 (Pinnacle)
• Jags under 4.5 +105 (Pinnacle)
• Bengals under 5.5 +130 (CRIS)
• Jaguars under 4.5 +111 (CRIS)
• Washington under 5 +114 (CRIS)
• Cardinals under 8 -125 (5Dimes)
• Cowboys ALT under 8.5 +264 (5Dimes)
• Texans ALT under 5.5 +380 (5Dimes)
• Vikings ALT under 7.5 +236 (5Dimes)
• Steelers ALT under 7.5 +299 (5Dimes)
• Ravens ALT under 10.5 +170 (Circa)
• 49ers ALT under 9.5 +175 (Circa)

I’ll be sure to remind everyone of these picks if they win and pretend they never happened if they lose.

Most of all, let’s hope for a safe, complete and incident-free regular season!

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