It’s Not Straightforward: Profiting From Nonlinear Correlation

Most people have a good understanding of what correlation is. In simple terms, correlation is a way of describing the relationship between two things. Most people likely covered the basic mathematics of correlation in their schooling.

Correlation is usually presented with simple, contrived examples. For instance, temperature being positively correlated with ice cream sales. The graphs below summarize how correlation is generally taught. These show various directions and types of correlation along with the associated Pearson correlation coefficient which most people learn in school.

Correlation is one of the strongest tools a bettor has at their disposal. Identifying situations where the market doesn’t capture correlated outcomes can be extremely valuable.

Correlation in sports betting is a well discussed topic. For example, bettors have discussed correlated parlays for decades. Similarly, correlation in DFS is a well-discussed topic as even most recreational players are very aware of it.

This article is about moving away from linear correlation. It’s about starting to think about how to profit from nonlinear correlation. In real life, and especially in sports, correlation rarely follows a straight line. This creates opportunities for bettors and DFS players.

Not Everything Moves in a Straight Line

There are many different types of correlation coefficients and methods to measure correlation. However, 99% of the time you hear someone quoting a correlation coefficient or measure, they will be using Pearson’s correlation coefficient. This method requires several assumptions. Most important, the underlying relationship between the two variables must be linear.

Let’s consider an example. You have two variables with the following relationship:

If you calculate the standard correlation coefficient on this data, you will conclude that the two variables are not correlated. This extreme example shows the challenge of using simple methods in the real world. There is clearly a relationship between the two variables. It just doesn’t move in a straight line, like the more contrived simple examples above.

Let’s discuss a couple illustrative examples to show how this phenomenon can apply to sports.

Two Wide Receivers on the Same Team

Most simple correlation matrices will show that wide receivers on the same team are positively correlated. This means the probability of one WR doing well increases if the other WR does well. This makes intuitive sense. If one WR is doing well, that generally means more first downs and opportunities for everyone on the offense. This includes the other WR. However, that correlation can be very different at different points on the distributions.

Let’s say you know that Deebo Samuel is going to go over his receiving total by 15 yards. Does this mean that George Kittle is more or less likely to go over his receiving total? Most data would suggest it would increase the probability of Kittle going over. It could be a positive game script, playing from behind, or more favorable weather conditions than expected. Two pass catchers are positively correlated around the medians for a host of reasons.

However, now let’s assume we know that Deebo went over his receiving total by 100 yards. Is Kittle more or less likely to go over given this fact? Because Deebo had such a high number of yards, it may become less likely that Kittle will surpass his total.

Deebo and Kittle can exhibit different correlations at different parts of their distributions. This is the type of phenomena that isn’t captured in simple correlation coefficients.

Passing Touchdowns and Kicking Points

Here’s another simple example: a QB’s passing touchdowns and the kicker’s total points. Like the prior example, near the medians, these two metrics are positively correlated. Most passing touchdowns lead to a PAT.

However, consider only the outcomes where the kicker had 15 points. Do you think the quarterback is more or less likely to go over their passing touchdowns? In this example, the QB likely had fewer passing touchdowns as we know many drives ended in field goals. Here again, at different points on their distributions, two variables can correlate differently.

There are many more examples of this in sports. This is the fundamental problem with any analysis that uses simple correlation coefficients.

Why It Matters?

This topic is likely old news for anyone playing traditional salary cap DFS. Yet, it is worth mentioning that this is a big reason why having good DFS simulations is important. Those who rely on static projections, with or without an optimizer, are at a big disadvantage. Being able to simulate sporting events and capture correlations is a huge advantage. Players correlate differently with others based on their position on their probability distribution. Simulations are some of the best ways to capture this. Simple correlation rules don’t account for field size and payout structure. Many of these considerations also apply to the new peer-to-peer Pick’Em games albeit in a simpler manner.

For sports betting, nonlinear correlation presents various opportunities as well. Same Game Parlays (SGPs) are extremely popular. DFS Pick’Em sites continue to grow. This popularity and growth provide many opportunities to apply nonlinear correlation. Many of the SGP engines are still crude. They may rely on simple estimates of correlation between events. However, the true correlation may not be as straightforward as it’s priced.

Here are a couple more examples to get you thinking:

  • 1.      Are two running backs on the same team priced as they are positively or negatively correlated? Are there game states where the correlation changes? Is that correlation always applied uniformly? Whether you’re betting the RBs over their standard total or 20+ yards over their total?
  • 2.      How are passing yards for a team correlated to the winning margin? If you knew that team had 3 turnovers would that change your answer? What if you knew that team had multiple defensive touchdowns?

Nonlinear correlations are everywhere in sports. You just have to look around to find opportunities to apply them.

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