Last week I wrote a primer on NFL totals for 2021. The intent was to provide another tool in your toolbox for the wagers you make this season on the NFL. Here, my aim is identical in purpose, but the subject matter is variance as it applies to key numbers and favorites.
An Observation on Key Numbers
I am sure that anyone reading this site is very familiar with key numbers on an NFL spread. These numbers represent the most frequent margins of victory in NFL games. Key numbers include 3, 7, 6, 10, 14, and 4.
The following table demonstrates that point conclusively:
If you are on a favorite, you would like to be just below these key numbers. If you are on a dog, you would like to be just over those numbers.
The chart indicates that the two most frequent margins of victory are 3 and 7. That makes inherent sense giving the NFL’s scoring method. Those two key numbers occur in 15.07% and 9.44% of the games. Those two numbers combined represent the final margin of victory in 24.51% of NFL games.
The chart tells us something else as well. The NFL is a blowout league despite the primacy of three and seven. What strikes me is that if we combine all margins of victory that are 17 points and greater, those results account for the final margin of victory in 26.99% of NFL games. Those margins outpace the frequency of the two most common key numbers combined by 2.49%. These results remain essentially consistent through any reasonable sample size you choose to examine, including the previous 20 years.
I wanted to write about this for two reasons. First, I think it is important to remember when assessing lines: it is likely that the number of games with a margin of victory equal to 17 or more points this season is slightly higher than the number of games decided by three and seven points combined.
Second, I wanted to use this data to emphasize that the NFL is a high variance sport. We understand that intuitively. A 17 game season is short by professional sport standards and leads to painfully small sample sizes. A single-elimination playoff format also creates high variance. While our intuition is correct, it also vastly underestimates the role of variance.
The Primacy of Variance in the NFL
Fans view the spectrum as a high-variance single-elimination tournament in the NFL or March Madness on one end and a low-variance best of a seven-game tournament on the other end. Our spectrum is not broad enough. The truth is, even leagues with a best of seven playoff format are subject to ridiculously high variance. Understanding this point brings into focus the enormity of variance in single-elimination tournaments.
For example, assume that teams A and B are playing a best of seven series for the NBA Championship. Assume also that we have perfect math on the teams. We know with certainty that team A is 10% better than team B and should win 55% of the games. Team B would only be a 2.16 – 1 underdog in a seven-game series. Team B would win the series 31.6% of the time. A seven-game series is laughably too short for us to assert that the better team would win the series with any degree of confidence. We would need the teams to play a best of 27 game series in this scenario.
I want to illustrate this through an additional example. If you flip a fair coin ten times, you will not be shocked if you get seven heads, 70%. You will only get five heads and five tails 24% of the time. If you flipped that same coin a million times, you would question its fairness if you ended with 700,000 heads, even though that is the same 70% result from above. It makes sense. Outcomes over an infinite number of trials will converge on their underlying probabilities, this is the Law of Large Numbers. There is not a Law of Small Numbers. The outcomes in small sample sizes, think the NFL season, are subject to nearly incomprehensible variance.
Hopefully, I have convinced you that we overvalue expected results in high variance situations. Now the sportsbook enters the equation. Books know that most people prefer to bet on favorites and overs. People are front runners. So the book shades their numbers even further than the math would suggest and alters the vig to ensure profitability.
The impact of this can be explained by returning to our fictitious NBA Championship series between teams A and B. We established that team A is 10% better, and team B is a 2.16 to 1 dog to win the series. A 2.16 to 1 dog should have a series moneyline of + 216. This is how it would play out in a book. The book will shade the favorite. Team A will open not as 10% better than team B, but 15% better. Team B will go on the board as a 2.46 to 1 dog, or +246.
This creates an outsized opportunity for the value bettor. Anyone that backs team B receives 30 cents of value and a 2.75% edge. The value bettor does not care if he wins a particular bet (a single trial). He cares only that he wins “x” percent of all such similar bets over an infinite number of trials.
This is part of the logic that steers most successful sports bettors to take the value of underdogs and unders more frequently than they back the favorite and overs. The value bettor has turned variance and book bias to his advantage to create a long-term positive expectation. The unavoidable takeaway is that when variance is high, unexpected results are more common than expected results.
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