One thing we've noticed with respect to round matchup and 3-ball bets is our model finds by far the most "value" on Fridays of tournaments. In this brief post, we'll explain why.

Shown in the table below are 2 round matchup bets (ties are void) that a popular bookmaker offered on Thursday and are offering again on Friday. The goal here is to use these odds to back out how much the bookmaker is adjusting each golfer's ability (in strokes per round) in response to their play on Thursday. These matchups were not cherry-picked. It's clear that something similar occurs with 3-balls, but it is a little harder to remove the margin accurately when there are longer odds due to the well-known favourite-longshot bias.

To understand the table, let's walk through the first row as an example. On Thursday, odds of 1.91 were given to both Thomas Pieters and Haotong Li; evidently, this implies that the bookmaker (or, the public if you think the bookmaker is largely responding to public money) thinks that these two players are of equal ability. "0, 0" is the strokes-gained per round estimate for each player implied by these odds.

In Thursday's round Li beat Pieters by 1 stroke. For Friday's round, the odds have changed to 1.86 and 1.95, in favour of Pieters. Now, what ability levels for the golfers are consistent with these odds? First, we remove the bookmaker's margin (assuming that it was applied equally to each golfer), and come up with "fair odds" of 1.95 and 2.05. Then, by assuming the typical variance in golfer performance for each golfer, we can back out that these odds imply Li is 0.1 strokes better per round than Pieters.

Here is the full reverse engineer: a 1 round matchup between two golfers with an ability difference of 0.1 strokes per round has (roughly) outcome probabilities of 46%, 44%, 10% for the better golfer winning, the worse golfer winning, and a tie, respectively. This would then have a margin of ~5% applied to each player, and then we can arrive back at the listed odds. Recall that ties are void here, so we throw them out: e.g. for the better golfer, listed odds = 1 / (1.05 * (0.46/0.90)) = 1.86.

Given that you likely feel slightly nauseous after reading math in paragraph form, here is the main point you should take away from the table: the bookmaker is adjusting player abilities by 0.1 strokes per round for every 1 stroke difference in round 1. In our opinion, this is way too big of an adjustment to be making. Our current model applies about 2% of the most recent round's performance to the prediction of a golfer's skill in their next round. That is, if a golfer performs one stroke better than their predicted skill level in the first round, their skill level for the second round would be increased by about 0.02 strokes per round. In an old blog post we did a rough analysis and found broadly similar conclusions (this analysis indicated slightly more form is carried over – maybe 3%).

In general, it seems that most people believe there is a much stronger correlation between performances within a tournament than across tournaments. That is, much larger adjustments are made in response to round 1 performances for round 2 predictions, than from Sunday performances to a player's next round 1 performance (in the following tournament). We haven't done a rigorous analysis of this, so perhaps it's possible single round performances are slightly more predictive within tournaments. But my guess is that this is not the case (ignoring cases where the golfer has a long layoff). This within-tournament bias is in addition to the general tendency of the market to weight short-term form quite heavily. The result is these large fluctuations in odds we observe for the same matchups from one round to the next.

To take advantage of what seems like a pretty big bias to us, the plan is clearly either to bet on golfers who played well below their expected performance level on Thursday, or bet against golfers who played well above their baseline. In the second round of this week's PGA Championship, this will involve backing golfers like Shane Lowry (+5 on Thursday) and J.T. Poston (+7), and fading golfers like Brooks Koepka (-7) and Danny Lee (-6).