B.R.E.A.M.: NFL Home Field Advantage in 2020

Estimating NFL Home Field Advantage Without Fans

While there is absolutely no certainty at this point about any of this, let’s suppose that the NFL regular season begins on schedule but without fans in the seats. What, then, is the value of home field advantage?

It could be diminished without the encouragement provided by a screaming crowd, and/or if the crowd reaction subliminally influences calls by officials.

On the other hand, I’ve heard the argument made that it could actually be increased as the COVID-19 pandemic severely increases the level of inconvenience and stress that comes with travel.

The truth is, nobody knows. We’re dealing with a situation that has never happened before, at least not in the NFL. From my informal Twitter research, the experts’ consensus for home field advantage in 2020 seems to be around 1.75 points. In the absence of any information, that seems like a reasonable estimate going into week 1.

Hopefully there will come a time when week 1 is in the books and we’ll get a chance to take a second look at our estimate for home field advantage going into week 2. Same going into week 3, and then week 4, and so on. We’ll be receiving a stream of new information as we observe how home teams actually perform. Whatever this new information says, the real challenge is to figure out what it means. How much of it is signal that we can learn from, and how much of it is pure random noise that influences game to game results? How do we react without overreacting or underreacting?

This is a perfect application of Bayesian Inference. Bayesian Inference is the science of how we learn – how we update our beliefs as new information emerges. In both my day job as an actuary and my hobby as a gambler, Bayes rules everything around me, B.R.E.A.M. (No not him – cool mustache though.)

Setting a Bayesian Prior for Home Field Advantage

Anyway, let’s get to it. The first thing we need is a “prior distribution” that describes what we think the value of home field advantage could be, going into Week 1. Let’s synthesize the information above into a few assumptions:

• It’s likely that 2020 HFA will be less than the historical average of between 2.5 and 3 points;
• It’s unlikely, but not impossible, that 2020 HFA will be more than the historical average;
• Our point estimate – that is, the average of the prior distribution – is 1.75 points;
• It’s impossible that 2020 HFA will be less than zero.

Based on this, I’m going to select what’s called a “uniform distribution” between 0 and 3.5 for our prior, which is a fancy statistician way of saying what normal people express with an emoji: ¯\_(ツ)_/¯. It means that all possible values between 0 and 3.5 have equal probability, and everything less than 0 or greater than 3.5 has zero probability. If we had to distill our prior estimate into a single number, we’d take the expected value of this distribution; for the uniform, this is simply the mid-point, 1.75.

Updating the Estimate with Weekly Results

So if week 1 data implies a HFA above 1.75, our week 2 estimate will go up. If it implies a HFA below 1.75, our week 2 estimate will go down. But how do we measure the HFA implied by a week’s results? You could just take the average margin of victory among all home teams, and this would work great when looking at an entire season – but in any given week you won’t necessarily get a balance of good and bad teams playing at home. To evaluate this, I’m going to look at each week’s schedule using the team power ratings derived by my friends at the Deep Dive Podcast:

Visual aid for this week’s pod… pic.twitter.com/NAVO6TI0L9

— Drew Dinsick (@whale_capper) July 1, 2020

One small problem – these ratings don’t add up to zero. Whale tells me it’s due to rounding and he’s a pretty sharp guy so I’ll give him the benefit of the doubt. However, I need perfect balance so I’m going to adjust Detroit from -3.5 to -3.

Week-by-Week Home Field Advantage Charts

Now let’s look week by week to see what the combined point spread of all home teams would be, in the absence of any HFA:

In week 1, the relative strength of all home teams is such that they would be expected to lose by a total of 4 points in the absence of any HFA. If we use our starting point of 1.75 points of HFA times 16 games, this adds up to 28 total points of HFA. So, if the total point differential for home teams in week 1 is 28 – 4 = +24, we should not move in either direction and should keep our estimate of 1.75 going into week 2.

But what if the week 1 differential is more or less than +24? How much should we move our HFA estimate? We’re going to assume that individual game score differentials follow a Normal distribution (they don’t in reality because of “key numbers” but that is irrelevant to our HFA analysis) with a standard deviation of 13.37 based on an analysis of historical game deviations between the point spread and the actual result. If you don’t understand what I’m talking about or it reads like this, just ignore this paragraph and keep reading.

With a little Excel magic, we can use this method to build a chart where we look up the total home team point differential for week 1 to find our updated HFA estimate going into week 2:

For example, if the total week 1 home team point differential turns out to be -20, we’ll update our HFA estimate to 1.5. If it turns out to be +120, we’ll update our HFA estimate to 2.25.

We can do the same exercise after week 2, using the cumulative home team point differential for weeks 1 and 2.

A total home team point differential of -100 through weeks 1-2 would lead us to adjust our HFA estimate to 1.0 point going into week 3. A differential of +100 would lead us to adjust our HFA estimate to 2.0 points going into week 3.

Through week 3:

Through week 4: (Note that I adjusted the scale on the graph because there’s a wider range of possibilities through this many games)

Through week 5: (Note the shift – it’s because week 5 home teams would be favoured by a total of 47.5 on a neutral field. Week 5 includes such gems as CIN @ BAL, LV @ KC and JAX @ HOU.)

Through week 6:

Through week 7:

Through week 8: (Adjusted the scale again)

Through week 9:

Through week 10:

Through week 11:

Through week 12:

Through week 13:

Through week 14:

Through week 15:

Through week 16:

Through week 17, heading into playoffs: (Adjusted the scale one last time)

You can come back to these charts after each week to see how the model updates its HFA estimate as data emerges.

All this of course, assuming there is a season. Please, Americans, don’t ruin this for me…

Learn Bayesian Thinking for Sports Betting

This article is a practical example of Bayesian thinking in sports betting: start with a prior belief, observe new data, separate signal from noise, and update your estimate without overreacting to small samples. If you want to build the probability and Bayesian modeling foundation behind this approach, start with Art of Sports Betting Analytics. If you want to connect these ideas to market efficiency, CLV, backtesting, bankroll management, and model-based betting decisions, continue with Science of Sports Betting.