Probability of winning a golf tournament off a double eagle (2 on a par 5)

white paper by: Prabuddha Bansal

One of the rarest shots in golf is an albatross or a double eagle, a 3 below par on a hole, a 2 on a par 5. Executing this is extremely difficult, and doing it to win a tournament has far fewer odds. In this white paper, I will show you how to calculate the odds of hitting an albatross to win a tournament off the last shot. While there is some data on professional golfers, there is very little data on tournaments for amateur golfers. To that end, I interviewed three single-digit handicap golfers whom I know personally; their handicaps ranged from 3 to 6. I myself am a 13-handicap golfer, so I know a thing or two about golf and golf courses. Additionally, we will look at the odds of hitting an albatross and the odds of hitting that off the last shot separately. I will combine all that, along with the odds of being 2 or 3 shots behind the lead. Using data from various sources, like Arccos, PGA tour, and driving distances, we will compute the odds of making a double eagle.

To get started, let me lay out some basic definitions that will help you get grounded. What are odds and probability? Odds represent the likelihood of an event occurring versus not occurring. For example, the odds of the Bengals reaching the Super Bowl this year maybe 5 to 1. This means that the experts predict that the likelihood of the Bengals reaching the Super Bowl is 1/5th of them NOT reaching the Super Bowl. Alternatively, this means that if this season were played out an infinite number of times with the same conditions, then 5 out of 6 times, the Bengals would not reach the super bowl. When it comes to probability, you can state that the probability of the Bengals reaching the Super Bowl is 1/6. So both probability and odds are related and represent the same thing, though they are written differently. Probability is a more fundamental number from a mathematics and statistics standpoint.

Now, with the math definition out of the way, let us get back to golf and take a shot at the albatross odds (no pun intended). While the odds for a professional golfer are somewhat calculated and documented by The Double Eagle Club, it is more complex for amateurs. For the record, for a PGA tour golfer, the odds of hitting an albatross on a par 5 are 72,000 to 1. Recalculated and reworded, this is approximately 1 million to 14. I asked three golfers (handicap 3 to 6) the following questions:

1. When going for the green on par 5’s in two shots, what is your success rate in hitting the green?

Answers: 5%, 10%, 20%

1. How long have you been playing golf?

Answers: 20 years, 25 years, 34 years

1. Have you ever come close to hitting an albatross (par 5 or par 4)?

Answers: no, no, once to within 3 feet (on a short par 5)

1. Is your game better in a tournament or on a relaxed weekend with friends?

Answers: weekend round, weekend round, in a tournament

We will use the above data provided in their responses along with some basic probability aspects to come up with an albatross odds. The area of a golf hole is about 0.1 square feet, and that of an average green is 5000 square feet. If there was not enough sharpness in the aim for the flag from, say, 250 yards out on a par five, then the odds of holing out are about 5000 to 0.1 or 50,000 to 1. However, an amateur golfer will only sometimes hit the green on a par 5. Not all par 5’s are reachable, and not all the time will the golfer reach the green even when going for it (as shown in the questions answered). Whether a par five is reachable or not in two shots is very subjective to course conditions and the player, but in general, approximately 3 out of 4 par fives are reachable in two shots. Remember that to even get to the green, a golfer has to hit two good shots. An average par 5 is about 500 yards for the amateur, so you have to hit a 260 yards plus drive, and then 230-240 yards 3 wood or a club with that distance. Looking at data from Arccos, only 8% hit more than 260 yards, and by extension a fairway wood about 230/240 yards. Accuracy is also important as one must hit the fairway to get a good lie for a good second shot. The accuracy of fairway hitting with drivers is about 50% for amateurs (Button Link). Combining all of those numbers – 8% 260 yards plus likelihood of hitting the fairway, accuracy of a 230/240 yards fairway wood, only 75% par 5 reachable, success rate of reaching the green when going for it, and the fact that the hole size is only a tiny fraction of the green area, we can compute the odds of hitting a double eagle for an amateur to be about 60% of 6 million to 1 (or 6 million to 0.6). This is a little less than what you might have read in some of the online articles.

Now let us come to tournament day. To win a tournament of the last shot being a double eagle, being 2 or 3 behind needs a few conditions to be met. So let us compute those odds. The odds of a course finishing with a par 5 are about 10 to 3 (35% probability to be precise – 15 out of 43 most challenging PGA tour courses in 2022/23 ended in par 5’s Button Link). In addition, the golfer must be 2 or 3 shots off the lead while on the 18th tee on Sunday. The odds of these can be computed by looking at how some top golfers finish relative to the field in a PGA tournament or a major. Even the best of all time, Tiger Woods, won only 5% of the tournaments he played in, so in 95%, he was second or lower, and maybe more than 2 shots off the lead. This tells us that the odds of a golfer being precisely 2 or 3 shots off the lead are much lower than 5%. Let us say that is a conservative 5%, then factoring in the 35% likelihood of a golf course ending in a par 5, the odds of winning a tournament with a double eagle are approximately 600 million to 1. 

References:

Button Link

Button Link