How To Use Distributions in NFL Betting
Spread values are not the same thing as average scoring differential.
One of the most common questions we received after our NFL launch is some confusion around the numbers we show on our NFL odds page. Specifically, there appears to be some discrepancy around our projected margin of victory for each home team and the point spreads from which they are derived. Take this week’s upcoming Lions/Patriots game for example, where the Patriots are favored by 3 points, and yet their projected average scoring differential is 2.2:
How can this be possible? In order to understand what’s going on, we need to dive a little deep into one of our favorite subjects, distributions.
What does a spread of -3 points imply? It does not, as you might first guess, imply that the favored team will win by 3 points on average. It actually implies that the total number of times the scoring differential is more than 3 points is the same number of times the scoring differential is less than 3 points. You might think that the scoring evens out on both sides and it should still average out to 3 points, but this is famously not the case with the NFL. Scoring differentials land more often on what are called key numbers, where teams win by specific margins more often (3 points for winning by a field goal, 7 points for winning by a touchdown, etc.) In fact, here’s what the average actual scoring distribution looks like for games where the home team is favored by 3 points:
In visual terms: a spread of -3 points says the sum of the bars to the left of the red line is equal to the sum of the bars to the right of the red line. (And for good measure, the final home scoring differential ends in exactly 3 points roughly 8% of the time, representing a push on a spread bet.) As you can see, the scoring is not evenly distributed on both sides, and it does in fact land disproportionately on some key numbers like 3, 7, and 10. This throws a wrench into the assumption that scoring differentials even out on both sides of the red line. In order to get the true average home scoring differential, we need to multiply each bar (the odds of that exact scoring difference) by the value of the bar (the number on the X-axis) and add all of those numbers up to get the average scoring difference. You can do the math yourself, but you can also trust me that it adds up to 2.2, which is different than the actual value of 3 you might have guessed. This math gets especially important in prop bets as well for other sports, but the scoring quirks of the NFL make it equally important a concept to utilize.
One way to capitalize on this concept is to use projected scoring differentials to evaluate both spread and moneyline bets. My friend Ed Feng, who runs the analytics site The Power Rank, projects scoring differentials using his Markov chain-based approach each week. A simple way to use his projections would be to compare projected scoring differentials against spread values, but as we’ve shown above, that approach has some built-in inaccuracies. The more complete way to use these projected scoring differentials would be to convert them into their corresponding distribution, then compare the implied distribution probabilities to every single spread and moneyline bet at every sportsbook and select the best market for you to bet on. If that sounds exhausting to do yourself, that’s because it probably is. Fortunately for you, this is exactly what Betscope does when we run our calculations engine.
As a practical walkthrough, Ed has this same Lions/Patriots game projected at New England winning by 4.2 on average:
We can input his projected scoring differentials and totals into Betscope and click “Update Stats”, and Betscope will generate an updated distribution, as well as new distributions for all other correlated outcomes:
After the new distributions for all fields are generated, we run those new distributions against every spread, total, and moneyline bet we can find in the market, and return the recommended bets along with their estimated ROI, outlining which sportsbooks have good enough prices for you to bet those numbers at:
This bet recommendation list is hitting on some essential components of being a winning sports bettor:
It utilizes distributions for the most accurate possible calculations.
It captures the full set of correlated outcomes associated with those scoring differentials.
It scans the entire market to find the best price possible for every market.
The implied distributions from Ed’s projections show profitable bets at these particular books at these particular prices, outlining exactly where you should be betting these numbers to maximize your profits.
Utilizing distributions is complicated, but we make it easy as possible to do so with Betscope. Understanding how to switch between average projections and implied distributions will give you a complete evaluation of all prices and all sportsbooks, and we’re happy to do that heavy lifting for you. You can give it a try yourself today for free by heading over to our NFL page and trying it yourself.