Prop Bet Deep Dive: Tyreek Hill in Super Bowl LIV
One of the best ways to evaluate player props is to compare them to stat projections built for fantasy, like the FantasyPros consensus projections. The over/under for Tyreek Hill’s receiving yards in the Super Bowl is 77.5. He’s projected for 87 receiving yards, so we should take the over, right? It’s not that simple.
This article is not intended to find an amazing bet (spoiler alert: it’s OK, but nothing special), but rather to provide a comprehensive explanation of how we use projections and probability theory to evaluate player props. If you just want to see the best play props for the Super Bowl, check out my article from yesterday.
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What do Projections Really Mean?
Using projections to evaluate the bet requires that we dig down into what projections really mean, and how accurate they are. If our projections were time-traveling sports almanac-perfect and Hill was guaranteed to record 87 yards, then, of course, this would be a good bet. In reality, we don’t have that level of information. The goal of projections is to predict the average of a range of possible outcomes. If we were able to rewind time a-la Doctor Strange and watch the Super Bowl a million times, Hill’s average receiving yards across those million games should be 87. So we have the mean of Hill’s range of possible outcomes, but how do we know how big that range is? Is he guaranteed to land between 82 and 92, or could he score anywhere from 37 to 137? It is, of course, possible that he does nothing or goes crazy for 200 yards, but not all possibilities are equally likely. This is where we need a probability distribution.
Modeling Performance With a Probability Distribution
A probability distribution is a mathematical model that describes the range of outcomes for a random or semi-random event like a performance in sports. They come with several tools, including a cumulative distribution function, or CDF, which is useful for our purposes. Once we have a probability distribution, the CDF allows us to choose a bar, and calculate the probability that a number generated by that distribution clears that bar. See where I’m going with this? The line – 77.5 receiving yards for Hill – is the bar we want to clear. Once we have a distribution that models Hill’s performance, we just need to feed the line into it’s CDF, and that will give us our probability of success. (Technically it will give us the odds of hitting the under or pushing, when pushing is possible, but we can subtract that probability from 100% to get the chance of hitting the over.)
How do we decide which probability distribution to use? There are some cases where it’s easy – for stats that happen one at a time, like touchdowns or home runs, there’s a strong theoretical argument for using a Poisson distribution, where the projected mean is the only piece of information we need. For receiving yards, a normal distribution is appropriate (as long as the projection isn’t too close to zero). Unlike Poisson, we need two parameters to determine a normal distribution – the mean and standard deviation. We already have the mean – that’s our projection. The standard deviation is a measure of how wide our range of possible outcomes is, and estimating it requires us to analyze the past accuracy of our projections.
Using Past Projection Accuracy
For the Super Bowl, the FantasyPros consensus is made up of projections from three sources: CBS Sports, numberFire and FFToday. To figure out the standard deviation for a receiving performance with a mean of 87, we should look at all the times players have been projected for a similar number of points in the past. Using consensus projections of the same three sources, there were 45 times in the 2019 season that a wide receiver was projected for between 84 and 90 receiving yards. If we calculate the errors (projected yards – actual yards) for all 45 of those data points, the average is 5.9 and the standard deviation is 50.5.
We were looking for the standard deviation, but found something equally important in the average – these projections over-project receiving yards for players in this range by almost 6 yards. We’ll want to correct for that with our statistical model and use a mean of 87-6 = 81, rather than the actual projection of 87.
Putting it All Together
We finally have a probability distribution to describe Tyreek Hill’s receiving performance – a normal distribution with a mean of 81 and a standard deviation of 50.5. Now we can feed the line of 77.5 into the cumulative distribution function to find our chance of success. The formula for the normal CDF is a little tedious and calculus-y, but there are plenty of online calculators we can use, and it’s built into Excel with the norm.dist function. Plugging those numbers in gives us a 47.2% chance Hill will score below the line, and therefore at 52.8% chance of hitting the over.
Now we can incorporate the juice to calculate the expected value of this bet. DraftKings lists the over at +105, and the under at -130. This means if we bet 1 unit on the over, we will profit 1.05 units by winning. With a 52.8% chance of profiting 1.05 units and a 47.2% chance of losing our 1-unit bet, our expected return is +0.08 units or 8% of our bet. (For comparison, the under has an expected loss of 0.16 units.) While technically profitable, that’s very close to even. While this bet might make sense for someone who bets frequently to grind out a profit from small edges like this, and is obviously fun if you want to root for Hill, it’s not a home run by any stretch.
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Jacob Herlin is a Senior Data Analyst for FantasyPros. For more from Jacob, follow him @jacoblawherlin.