NBA Prop of the Day
Jake Silverman
We often think of variance as the enemy of projections in sports. When a player has a surprising game, was the projection bad, or was the result just a product of variance? Golf is no different. Players shock us all the time with how well or how poorly they play. However, if we can reliably estimate a player’s volatility, we can harness this “randomness” in a powerful way that actually improves projections.
Consider this – most of the time in sports, we’re trying to project the most likely outcome. Who will win Game 7 between the Red Sox and Yankees, will LeBron James go over or under his 25 point player prop, who should you start at QB in your fantasy football playoffs? All of these questions are close to the odds of a coin flip, and the degree to which a projection is correct is usually moot — after all, you don’t make extra money if the team you bet on covers by 20 points instead of by two.
So, what makes golf so different? The ultimate question in golf is “Who will win the tournament?”, but for every player (possibly excluding Tiger Woods in his prime), a win is an unlikely outcome, often as low as a 1% chance. We’re no longer dealing with a coin-flip, we’re dealing with the roll of a hundred-sided die. As we get further and further from 50/50, the less the median outcome matters and the more variance matters.
Why Variance Matters
Imagine two players of equal baseline skill (equal average strokes gained per event), but one is enormously volatile and the other is consistent. To win a tournament, the more volatile player may only need to achieve a 75th percentile outcome for himself, while the more consistent player may need a 90th percentile outcome to lift the trophy.
This is one of the dangers and shortcomings of evaluating player talent by wins alone. It often tells us more about how volatile a player is, not how good he is. Sam Burns won three times in 2022, averaging 1.6 strokes gained per round. Patrick Cantlay won twice, averaging 2.1 strokes gained per round. Who had the better season, or more importantly, who did you expect to have the better 2023?
Sidenote – this is also why I consider Tiger Woods’ 142 consecutive cuts made record to be as impressive as any of his 15 Major championships. To win as often as he has without any reliance on volatility is pure insanity.
The Different Measures of Volatility
There are two ways to measure variance in golf:
- Round-to-round standard deviation
- Event-to-event standard deviation
As it turns out, the first is rather useless. A player’s standard deviation (in strokes gained) from one round to the next is entirely unstable year to year. In other words, we can have no confidence that a player with a high round-to-round standard deviation will continue to have a high round-to-round standard deviation in the future.
One explanation for this is best illustrated with the following hypothetical example consisting of two hypothetical tournaments:
In the first tournament, Player A is all over the place, great in two rounds and bad in the others. Player B is consistently bad. In the second tournament, Player A is once again all over the place, but Player B is consistently good. Despite Player B’s consistency, he has the same round-to-round standard deviation as Player A. Essentially, round-to-round standard deviation fails because it has difficulty separating round-to-round numbers from event-to-event ones.
To that note, event-to-event standard deviation is stable from one year to the next and incredibly powerful. One interpretation of this fact is that certain players tend to continue to play well when they start hot more so than others. I don’t think I have to sell you on the potential implications of such a finding in the betting and DFS worlds.
How to Use Variance to Your Advantage
The popularity of Monte Carlo simulations has exploded in the DFS industry this year, but it’s long been a wonderful tool in the betting world. Our entire betting model is powered by a Monte Carlo simulation that requires only two inputs – our expected strokes gained projection and our estimated event-to-event standard deviation for each player.
For the less scientifically motivated, you can think about variance intuitively. For example, Scottie Scheffler can win any event at any time because he doesn’t need a ceiling outcome to contend – he just needs to be Scottie Scheffler. On the other hand, if you’re searching for your favorite 100-1 outright bet of the week, or your favorite cheap and contrarian DFS play, chances are you should be looking for a player with a high event to event standard deviation, perhaps even more so than someone who projects well in that range. This makes sense mathematically, but a player’s variance is also less likely to be taken into account by a sportsbook/the DFS field than his skill-level.
Lastly, make sure you’re looking at event-to-event standard deviation instead of round-to-round standard deviation, as only the former has real utility. We will post our volatility estimates each week along with the rest of our projections and projected odds.
The Power of Counterintuitive Results
When I decided to look into the utility of round-to-round vs. event-to-event standard deviation, I expected to find that each played a useful role. However, I love that the finding is counterintuitive, at least at first thought. To be clear, I do think that the concept of round-to-round standard deviation is a good one and potentially quite useful, but the way it’s measured needs to account for its current flaw. And until it does, round-to-round standard deviation’s surprising lack of any utility whatsoever, paired with event-to-event standard deviation’s importance, opens the door for a major edge in the PGA space.
