Model Talk
Who cares about ties? Part I
In match-up betting the tie is often the forgotten outcome. The main reason for this is that most bookmakers offer match-ups with ties resulting in a void bet (i.e. your stake is returned), in which case ties are literally forgotten. When a tie is offered as an outcome to bet on, it is rarely bet because 1) the odds are usually set such that they cannot possibly offer positive value, and 2) who wants to root for a tie? However, predicting the probability of a tie between golfers still plays an important role in match-up betting, and this is true whether ties are void or offered as a separate bet. In this post I focus on the case of a separate tie bet being offered.

For two average PGA Tour golfers on a typical PGA Tour course, the probability of a tie in a single-round match is about 10%, and in a 72-hole match it's about 4.5%. These probabilities will both be slightly higher (lower) if the match is played on a lower (higher)-variance course. The 72-hole match tie probability is also affected by the quality of the field (which affects how hard it is to make the cut) and by whether there is a cut at all. However most significantly, as the skill difference between the two golfers grows, the probability of a tie declines.

This is interesting, but if I'm never betting on the tie why does this matter? It matters because bookmakers tend to offer the same odds on a tie regardless of the characteristics of the match. For example, Bet365 almost always offers odds of 8.5 on the tie in single-round match-ups, while PointsBet typically offers odds between 8.5 and 9.0. Further, the sum of the implied probabilities on the 3 possible outcomes (golfer 1 winning, golfer 2 winning, tie) is roughly constant across bets (within each book). Therefore it follows that the lower is the true probability of a tie, the less juice there will be on the outright win odds offered for the two golfers. Put differently, when a tie bet is offered, blindly betting on match-ups between unevenly-matched golfers will yield a higher return than blindly betting on evenly-matched golfers.

Two example bets offered by PointsBet in the first round of this week's AT&T Pebble Beach Pro-Am help illustrate this point:

Despite the fact that the first bet offers lopsided win odds for the two golfers while the second match offers roughly even ones, fairly similar odds are offered on both tie bets. This implies that the sum of the book's offered outright win odds will also be roughly similar for the two bets. Because the true tie probability (I'm assuming our tie probabilities are approximately correct — it's not rocket science that the likelihood of a tie declines as the skill gap increases) is substantially lower in the Power / Murphy match, you get to bet against a much lower margin.

Here are the calculations that show this: using our tie probability as truth, the probability of one of Power or Murphy winning outright is equal to 92.2%. Given that PointsBet's offered win odds add up to 96.1%, betting randomly on Merrick or NeSmith (with a couple assumptions) should yield a return of just -4.1% (0.922/0.961 - 1). In the second bet, the probability of Todd or Knox winning outright is just 89.5%. With offered win odds that add up to 95.5%, a random betting strategy has an expected return of -6.3%. By simply betting on lopsided match-ups like this at Pointsbet, you would expect to improve your returns by ~2%!

Pointsbet tends to keep the sum of their implied probabilities constant across all match-ups, and vary their tie probabilites slightly. Fanduel, on the other hand, keeps their tie probabilities constant while tending to decrease the total margin on bets between unevenly-matched golfers. This makes it especially advantageous to seek out lopsided match-ups at Fanduel; here are 2 examples from the 2nd Round match-ups this week:

The returns to betting randomly on one of the two golfers in each these three match-ups are -8.2%, -3.8%, and -3.7%, respectively. That's a ~4.5% improvement in returns without any work required! (However, match-ups with a heavy favorite are hard to come by.)

An intuitive way to frame what's happening here is to think of these match-ups as 3-Ball matches where "Tie" is the 3rd golfer. When Golfers 1 and 2 have very different skill levels, bookmakers tend to overestimate Tie's win probability, which increases the value from betting on Golfers 1 or 2.