Math question for Golf, 'hole in one'.
In a foursome, the odds of 2 golfers getting a hole in one, on the same hole, is 26,000,000 to 1.
Based on this information, or lack thereof, What are the odds of 3 or all 4 golfers ace'ing the same hole?
Thanks!
Assuming the probability of a hole in one on that hole is 1/12,500 (in which case the 1/26,000,000 for two out of four is accurate):
The probability of three = (the probability of one player getting a hole in one) cubed x (the probability that one player does not) x (the number of ways to get three in a foursome)
= (1 / 12,500)3 x (12,499 / 12,500) x 4 = about 1 in 488 billion
The probability of four = (1 / 12,500)4 = about 1 in 24.4 quadrillion
I think the 1 in 12.500 figure is an average for par-3 holes and no figure exists for par 4/5 holes for obvious reasons.Quote: ThatDonGuyFirst of all, I question those numbers, as the first one sounds like it's the probability in general, while the second one applies to a specific hole. The probability of getting a hole in one on a 130-yard par 3 is much greater than on a 500-yard par 5.
The only practical use of the number is probably for these amateur tournaments where you win a car or something if you hit a hole in one on a certain (par 3) hole. The tournament operator will be insured for any potential payout, and the premium calculation will use 1/12,500 for amateurs and 1/2,500 for pros, if any.
Incidentally, if you do a rough estimate of holes played by a pro over his entire career, he will expect several hole-in-ones and it’s quite unlikely to get none.
Quote: Ace2I think the 1 in 12.500 figure is an average for par-3 holes and no figure exists for par 4/5 holes for obvious reasons.
The only practical use of the number is probably for these amateur tournaments where you win a car or something if you hit a hole in one on a certain (par 3) hole. The tournament operator will be insured for any potential payout, and the premium calculation will use 1/12,500 for amateurs and 1/2,500 for pros, if any.
Incidentally, if you do a rough estimate of holes played by a pro over his entire career, he will expect several hole-in-ones and it’s quite unlikely to get none.
Yeah, it's kinda weird. Hole in ones are seemingly "super duper hard" or whatever, but I've seen bets for golf tournaments (or maybe a series of tournaments?) as to whether or not there's going to be a hole in one, and am surprised when I see how likely the casino thinks it is for someone to hit a hole in one. But if you think about it, having 20 or 50 or 100 golfers each playing 18 holes a few times, it's a lot more likely than I'd initially think for someone to hit a hole in one.
Quote: DHass22According to a Golf Digest article, the odds of and average golfer, hitting a hole in one, is 12,500 to 1.
In a foursome, the odds of 2 golfers getting a hole in one, on the same hole, is 26,000,000 to 1.
Based on this information, or lack thereof, What are the odds of 3 or all 4 golfers ace'ing the same hole?
Thanks!
I wonder what the profile of an "average golfer" looks like. There's a very wide variety of players out there, and quite a few of them are simply incapable, whether through a lack of strength, skill, equipment, or a combination of these factors; of hitting the green on a par 3. Assuming an equal distribution of these factors, does this mean there's a clump of players that consistently hit the green and collect aces in double digits each year?
How many par 3 tee-off attempts, and how many holes-in-one were recorded on all the PGA tours last year?
Quote: AyecarumbaI wonder what the profile of an "average golfer" looks like. There's a very wide variety of players out there, and quite a few of them are simply incapable, whether through a lack of strength, skill, equipment, or a combination of these factors; of hitting the green on a par 3. Assuming an equal distribution of these factors, does this mean there's a clump of players that consistently hit the green and collect aces in double digits each year?
How many par 3 tee-off attempts, and how many holes-in-one were recorded on all the PGA tours last year?
There have been 32 holes in one on the men's PGA tour this year.
Some holes I feel I have a decent chance of getting a hole-in-one, others I feel it’s a real miracle. I only include par threes which on a standard course there are only four of. There are some holes that the pin placement makes it relatively easy and others which make it nearly impossible
There are so many factors that make the odds either substantially easier than one in 12,000 or substantially harder than one in 100,000
This whole post was really about me bragging about my most recent hole-in-one!
Quote: DRichThere have been 32 holes in one on the men's PGA tour this year.
Any figures on par-3 tee shots at these events? Assuming 2,500-1 for pros is a good figure, does 80,000 smell right?
Quote: AyecarumbaAny figures on par-3 tee shots at these events? Assuming 2,500-1 for pros is a good figure, does 80,000 smell right?
I would guess around 1500 a week. 125 golfers x 4 par 3's x 2 days + 65 golfers x 4 par 3's x 2 days
I think the PGA tour probably averages close to one hole in one per week.
Quote: DRichI would guess around 1500 a week. 125 golfers x 4 par 3's x 2 days + 65 golfers x 4 par 3's x 2 days
I think the PGA tour probably averages close to one hole in one per week.
Most events I think allow 144 to start, and average over 70 for the last two rounds. Plus there are weeks (majors, and World Golf Championship event weeks) that there are two separate events that count as PGA tour events. Plus nowadays most courses have a par 4 that the pros can reach the green in one shot adding another tiny chance for a hole in one.
My guesstimate for myself is that I've played 6000 par 3 shots, so my two put me on the plus side of variance for sure.
Quote: DRichI would guess around 1500 a week. 125 golfers x 4 par 3's x 2 days + 65 golfers x 4 par 3's x 2 days
I think the PGA tour probably averages close to one hole in one per week.
This is close I'd say. 1 in 1000 seems like close to PGA tour pro odds.
Source: https://www.golfdigest.com/story/want-to-know-your-odds-for-a-hole-in-one-well-here-they-are.
Dog Hand
Two aces but not by the same person. How many golphers per tournament? How many rounds of golf per torunament?Quote: DogHandThe "1 in 73" odds for 2 aces in 1 tournament cannot be right... The author must have left off a "million" or so.
Dog Hand
Quote: DogHandThe "1 in 73" odds for 2 aces in 1 tournament cannot be right... The author must have left off a "million" or so.
Dog Hand
I would have guessed lower if we are talking about professional golfers. There is an average of about one hole in one per week on the PGA tour. There was one yesterday at the British Open and it was the first day.
Quote: DHass22According to a Golf Digest article, the odds of and average golfer, hitting a hole in one, is 12,500 to 1.
In a foursome, the odds of 2 golfers getting a hole in one, on the same hole, is 26,000,000 to 1.
Based on this information, or lack thereof, What are the odds of 3 or all 4 golfers ace'ing the same hole?
Thanks!
Let me reword the statistics from Golf Digest to make their math work:
The odds of an amateur making a hole in one on a specific hole are 1 in 12,000.
The odds of two out of four amateurs making a hole in one on a given hole are 1 in 26,000,000.
Under this line of thought, here are my probabilities for 3 or 4 players acing the same hole in a round:
3 players: 1 in 488,281,250,000
4 players: 1 in 24,414,062,500,000,000
Quote: ThatDonGuyThe probability of three = (the probability of one player getting a hole in one) cubed x (the probability that one player does not) x (the number of ways to get three in a foursome)
= (1 / 12,500)3 x (12,499 / 12,500) x 4 = about 1 in 488 billion
The probability of four = (1 / 12,500)4 = about 1 in 24.4 quadrillion
Glad we agree.
Quote: onenickelmiracleI had a thread mentioning a major hole-in-one insurer which was sued and prosecuted for fraud iirc. What a wonderful business to have.
I recall a similar situation where an insurer for these type of "lightning strike" promotions refused to pay a guy who hit a hockey puck through a small hole in a piece of plywood across the goal mouth. I think they said he stepped over the line that he was supposed to be all the way behind when he made the shot.
Four holes in one, all on the same day, all on the same hole, all within two hours of each other:
https://www.latimes.com/archives/la-xpm-1989-06-17-sp-1636-story.html
Quote: EdCollinsI cut this story out of my local newspaper when I read it while living in Michigan, back in 1989. I saved it because I wanted to discuss it with a buddy of mine who's a big golfer, the next time I saw him.
Four holes in one, all on the same day, all on the same hole, all within two hours of each other:
https://www.latimes.com/archives/la-xpm-1989-06-17-sp-1636-story.html
The odds mentioned in the article were very different from each other. I wonder what happened?
(Hole 16 at Peek N Peek course, where a Korn Ferry event (used to Web.com tour, used to be Nationwide tour) was played.
I play one 230 yard hole that is a par 3. If I've played it 30 times I've only been on the green once. You can put the pin anywhere and 80+% of golfers can't even hit the ball that far.
Let's assume the 1 in 12,500 probability per hole is correct. Let's also assume that all hole-in-ones happen on par 3 holes. Let's also assume that a round has four par-3 holes. That would make the probability on a par 3 equal to 1 in 2,778 per golfer. Let's call that probability p.
Then the probability of a foursome seeing two golfers making a hole-in-one on the same hole would be:
4*combin(4,2)*p^2*(1-p)^2 = 1 in 321,734.
Yes, I know a hole-in-one is possible on a par 4 or 5 and this ignores 3 or all 4 players getting a hole in one. I'm trying to not muddy the waters with those factors, to keep things simple.
Where Golf Digest seems to err is in assuming every hole has the same chance at a hole in one. If I assume that, I get fairly close to their figure with 1 in 1,446,991.
