Analyzing the Theory of Hot and Cold Streaks

You hear it all the time. "This pitcher is really locked in right now" or "this hitter is just seeing the ball so well recently." Looking for patterns and explanations is part of human nature. This manifests itself in sports by people picking up on hot and cold streaks and making quite a big deal about them.

This especially happens in fantasy. If a guy is coming off a four-homer week, fantasy managers will rush to grab them off the waiver wire. If a pitcher gives up six runs a couple of games in a row, managers will be likely to bench them for their next start. But is this justified?

As it turns out, this is not too hard to test. Let's run through a test on hitters and pitchers and see what the numbers tell us.

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Hitter Streaks

I looked at every single box score from the 2019 season and calculated each hitter's DraftKings point totals for each game of the year. I used DraftKings points because it is a pretty good way to put one number on a hitter's performance, which is important to do for this test.

What I was curious to see was whether or not predicting a hitter's next fantasy score could be aided by looking at the hitter's last five games. This encapsulates the "hot streak" theory. The theory would be that if a hitter is "hot", he is more likely than normal to perform well in his next game.  To test this, I took each player (that played at least 120 games in 2019) one-by-one and did the following:

1. Found the hitter's average DraftKings points score for the year
2. For each game they played, I found their average score from their last five games (not using values that came after long lay-offs like time on the IL).
3. Found their score for their very next game played.
4. Subtracted their last five-game average from their season average and subtracted their next game from their season average and put all values in two lists that I could use to compare.

For example, let's look at Jose Abreu. Here's the plot of his average score from the last five games vs. his individual DraftKings scores for each day of the 2019 season.

The blue line follows the orange line with some slight lag. After you see a big spike in the orange line, you will see the blue line slowly creep up as well as that spike game raises the average for the next five games he's played.

In the 159 games above, Abreu averaged 8.5 DraftKings points per game. From April 22nd to April 28th, he averaged 18.8 DraftKings points, his best five-game stretch of the year. That was 10.3 points above his average. In his next game, on April 29th, he scored eight DraftKings points, which was 0.5 points below his average. These two values (10.3 and 0.5) go into the list for comparison, since we are checking whether or not the 10.3 was predictive of the 0.5.

Doing this in one-off examples wouldn't prove anything, of course, but after we do this for every single fantasy score for every hitter that met our criteria, we get lists that are 23,637 rows in length. If it were true that having a higher than average score in your last five games meant you were more likely to see your next game score also be higher than average, these lists would be correlated. When I run the correlation on the lists, they show absolutely no correlation (with a coefficient of -0.00064, showing complete and utter randomness).

When I compare the list of each player's full-season average against what they do in their next game, the correlation balloons way up to 0.20. This is still a pretty weak correlation, because it is simply just not possible to predict an individual game from a hitter, but how much higher the number is there is striking.

This is strong evidence against the theory that a hitter can be "hot" or "cold" with an eye on the future. A player's recent performance has no predictive power on their next game. Their overall average is a better predictor of their next game than their most recent games.

 

Pitching

I did the same exact thing with pitchers as I did with hitters. I used only pitchers that made at least 20 starts. Here's the same plot from above but using Marco Gonzales:

For the year, Gonzales averaged 14.0 DraftKings points per start. His best five-start stretch was from April 2nd to April 25th where he averaged 20.4 points. In his next start after that hot stretch, he got shelled and score -3 points. You can see that on the line above. After that shellacking, his average fell quickly as you can see by the blue line.

When I did the same thing as above and compare the two lists, I get a correlation coefficient of -0.04, suggesting again complete randomness. If you have outscored your eventual season average in the last five games, you are no more likely to do it again in your next game, and vice versa.

 

Exceptions

There are some situations where there is an injury present and that changes things. If a player is playing hurt, he will often underperform and that will lead to cold streaks actually being predictive since the player just isn't their normal self. The problem is that it's almost impossible to tell when decreased short-term production is because of injury or not. There are some situations where you can kinda tell that a player is playing hurt and you can avoid him for those reasons, but those are the exception rather than the rule.

 

Conclusion

How do we apply this? A few ways.

1. When playing DFS, if a player's salary has come down because of a bad recent stretch (this happens quite often), it's advantageous to take the discount because there is no reason to expect continued bad performance.
2. Sell high on "hot" hitters, buy low on "cold" hitters.
3. Don't pick up players off of waivers just because they've had a good week or two. Ignore the recent games and focus on the bigger picture.

Good luck in 2021!

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