What’s wrong with Rory?

Rory McIlroy missed his second cut in a row this week at the Scottish Open. A flurry of news articles and social media posts are likely to follow in the next couple days wondering what’s wrong with Rory. “Where has the lad’s game gone?!” cries a devoted Rory fan — “You can cross him off the list of potential contenders next week.”  tweets a Golf Channel pundit — “It’s simple, really. The deadlifts have finally done him in; this is causing Rory to slump a bit through impact, losing the angle, missing right.” analyzes Brandel.

In my opinion, however, there is nothing wrong with Rory. My argument is simple: golf scores are really random. Below is a density plot of Rory’s scores over the last 2 years.

This is how I like to think of a golfer’s performance; Rory’s score each day (no matter what course he’s on!) is a draw from the above distribution which has mean 2.3, and standard deviation 2.7. Better golfers will have distributions with higher means, and more consistent golfers will have distributions with smaller standard deviations. So, when Rory shoots 2 shots worse than the field, I don’t panic; this isn’t that unlikely (it should happen about 6% of the time).

So, back to Rory’s MC-MC performance over the last 2 weeks. How often should that happen for a player of Rory’s caliber? Well, my sample of data contains the last 2 years, in which Rory played 38 events (I think). I simulate these 38 events 10,000 times (doing exactly what I said above; each round is a draw from the above distribution). I deem Rory to have missed a cut if the sum of his first 2 rounds is less than 0 (so he lost to the field, which should, roughly speaking, result in a missed cut). In 35% of the simulations, Rory had back-to-back MCs at some point in the 38 event sequence.

This is Rory’s first stretch of consecutive missed cuts since May 2015. So, in the 2 year sample I’ve considered, Rory has missed back-to-back cuts on exactly one occasion. This is not unexpected at all, given our simulation exercise above.

Humans love to find patterns in small stretches of data when really there are none. Rory’s poor performance of late is not inconsistent with him still being the same player he’s been for the last few years. That is, he may still be pulling from the same distribution, with mean ~2.3 and sd ~2.7; maybe Rory just had a couple bad draws the last 2 weeks.

Or, maybe he has actually lost it (his putting does look awful). The point is that these last 2 weeks don’t tell us very much about which opinion is the correct one.

 

 

Benchmarking the model’s betting performance through 17 weeks

Using our predictive model we have been betting on the outcomes of PGA Tour events for 17 weeks (starting with the Genesis Open, and only skipping the team event in New Orleans and opposite fields events since). Other than a few bets at the start, we have focused on Top 20 bets. Our total return to-date is 151%! Here are some graphs that summarize how we are doing relative to some useful benchmarks.

This first graph shows 300 simulations of the profit path for 17 weeks (and 147 bets) using the adjusted implied probabilities as *truth* for each simulation. By adjusted implied probabilities, I mean the probabilities you obtain by normalizing the implied (or, “breakeven”) probabilities to 1. In a simple example of picking one of two teams (A and B) to win, if A has implied odds of 64%, and B has implied odds of 40%, then the adjusted implied odds will be 61.5% for A and 38.5% for B.

Continuing with this example, to simulate I let A win with probability 61.5% (in practice, this is achieved by drawing a number between 0 and 1 at random, and if it is less than 0.615, A wins) and I use the listed payouts to calculate simulated profit. Here is the graph:

The returns are compounded each week. I have also included our realized return on the graph. (Note: for the following numbers, I performed 4000 simulations – I didn’t plot 4000 because it gets messy). Only 0.8% of the simulations performed better than our current returns in the 17 week period. Because the bookie takes a cut (the “juice”) the average return is about -25% in these simulations. This indicates that it is unlikely that our current returns could have arisen in a world where the bookies probabilities are correct on the bets we have taken.

The next graph shows 300 simulations of the profit path through 17 weeks using the model probabilities as *truth* for each simulation:

Here we see that our realized return is slightly above the average return in the simulations, indicating that, if the model is correct, we have been getting a bit lucky. (Again, the following numbers are based off 4000 simulations). The mean return in the simulations was 131%, and, interestingly, about 15% of the simulations had negative profits. This speaks to the wide variance in returns that are possible when making the types of bets we do (i.e. fairly low implied probabilities) and to the fact that 147 bets is still not a huge sample size.

Finally, here is a graph plotting the player-specific returns and investment sizes:

The model has loved Streb all year, unfortunately for us Streb has yet to finish in the Top 20 since we’ve started betting. Kevin Na’s large total return is mainly due to his Top 5 finish (our first and only Top 5 bet win) in the Genesis Open – our first betting week!