## Predicting the WGC-Dell Match Play Championship

This week we are providing probabilistic forecasts for the only match play event on the PGA Tour schedule, the WGC-Dell Match Play Championship. A few adjustments were made to the model to accommodate the different format.

If you are unfamiliar with our predictive model that we use for stroke play events on the PGA Tour, you can read about it here. From our usual model setup, we obtain each player’s predicted component, and the standard deviation of each player’s random component. With these in hand, we then simulate each player’s scores over a 7 day stretch (the maximum number of rounds a player can play in this week’s tournament). We allow for round-to-round persistence in a player’s performance in the same manner as in our stroke play model.  With these 7 simulated scores in hand, we have the information required to determine the winner of a simulated match play tournament.

Recall that the match play tournament is organized into 16 groups of 4 players apiece. The winner of each group advances to an elimination bracket, which takes 4 knockout rounds to determine a winner.

To determine the outcome of each match, we simply compare the simulated scores of the two players involved. Evidently, it is not always the case in match play that the player with the lowest stroke total wins (as it is about holes won and lost). However, we view this as a very good approximation. You could think this is problematic because certain players are more volatile from hole-to-hole, and as such are more likely to succeed in match play where their big numbers don’t matter as much as stroke play. While this is true, we don’t think this plays a critical role, and, in any case, cannot correct for it because we do not simulate at the hole-level.

To start, within each group we determine the winner of each match by rounding a player’s simulated score to the nearest whole number, to allow for the possibility of halved matches. The player with the lowest simulated score wins. (Note that simulating a match without rounding, so that every match is either won or lost, is basically equivalent to simulating with rounding and randomly assigning a win to one of the players if the match is halved). Match wins are awarded a full point, while halved matches get a half point. The player with the most points advances. If two or more players are tied in point total, I “flip a coin” to determine the winner (i.e. I draw a number from a uniform distribution on the unit interval for each player, and the highest number wins). The winner of each group advances to the round of 16.

The outcomes of the elimination round matches are determined by simply comparing simulated scores for the relevant round (no rounding). For example, simulating the final match is done by comparing the 7th scores in the series of players’ simulated scores for the two players in the final. This easily allows for the determination of a winner.

Perform this simulation many times, and we have our probabilistic forecasts for the match play event.

When we update our predictions after each round, we input the actual scores players shot into each simulation, and then simulate the rest of the tournament from that starting point. Because we don’t actually observe the 18 hole scores for the players in each match, there is some extrapolation involved. Specifically, we obtain players’ scores over their completed holes, divide by the number of holes played, and then multiply that by 18. For example: Rory shoots -8 for 16 holes. We will give him a score of -8 (18/16) = -9. The score is important for the model because we allow persistence in performance from one round to the next. However, we do recognize that a player’s score is an imperfect measure of performance in match play as there is more strategy involved than normal stroke play. As a consequence, the parameter controlling round-to-round persistence is smaller than in the usual stroke play setting.