Mental models in DFS: Part 4, Regression to the Mean

A RotoGrinders post. 

A recap

So far we’ve focussed on:

  • The availability heuristic – the inability to extract information past the last event that occurred, leading to a biased view of performance.
  • The bias from liking – an inherent & natural bias in all of us to place undue value on something or someone simply because we like it.
  • The gambler’s fallacy – a misunderstanding of the concept of probability.

Time to develop the gambler’s fallacy into it’s more sophisticated cousin, the law of the regression to the mean.

What is “Regression to the mean”?

When Eden Hazard scored 3 goals against Newcastle in 2014, the tendency is either to: think he outworked himself & is going to crash in the next game or that he’ll score another hat-trick. The reality is that in the next game he’ll still play well, just likely not 3-goals well. He’ll regress back to his mean performance.

This is the concept of regression to the mean, that in any situation where there’s many variables & chance is involved, extreme outcomes tend to be followed by more moderate ones. This shouldn’t be confused with the fallacious law of averages, where an unusual amount of successes (or wins, goals etc) should be balanced by losses.

Rather, it’s that good teams or good players will continue on average to perform well, just not as well as their last exceptional performance which was most likely due to an extra bit of luck.

Let’s put it another way. The above chart plots the correlation between weight & height, clearly showing a weak to moderate correlation. What this means is that while height is generally a good predictor of weight, there are lots of other factors at hand that push results above & below the mean. Therefore, when the correlation between two things is less than perfect then we must be wary of regression to the mean.

Whenever the correlation between two scores is imperfect, there will be regression to the mean.

Regression to the mean in DFS

Clearly then, this concept should be of use to DFS players looking to extract value out of DFS games with a salary cap / budget functionality. If an expensive player like Hazard performs consistently well during the season, then it’s no use trying to be overly contrarian & not drafting him because he had a suspiciously good last game.

Rather, you should understand that regularly drafting Hazard over the course of a season is likely to bring you on average a higher return on your investment than other players, because the “mean” that his scores regress to is higher than other players.

Another important point to understand is that just because an unusual player is top projected right now, or has scored 5 times in a row against the next opposition he’s playing against, doesn’t mean he will stay top or score again. There is good fortune involved, so when their performances regress to the mean they’ll be overtaken.

If I could sum up the key takeaway it’s this: remember the importance of track records rather than one-time success stories. When you look at the graphic below of Eden Hazard’s track record in the Premier League the stats don’t lie. Out of 174 EPL games, his goals per game stands at 0.33. Even if next game he scores 5 goals, that’s hardly going to move that average significantly up or down. That’s the beauty of sample sizes.

Another perfect example of this is Leicester winning the Premier League, which many argue arose from a combination of chance factors (not discrediting their achievement here.) Rating Leicester as likely of winning the league again going forward simply isn’t sustainable.

Don’t be fooled by one time events, always respect the regression to the mean.