golf question

5 random thirteen-handicap golfers play a round of golf at Bethpage black. 5 scratch golfers also play. What is the probability that the person with the fewest putts for the day is one of the high handicappers? Assume that none of the golfers are purposely trying to miss greens in order to lower the number of putts.

[BruceZ]

I'm assuming a golf handicap is just determined by how many strokes over par a golfer is on average. In that case, we don't have enough information. We would need to know how consistent the golfers are (standard deviation). The more consistent, the less likely it is for the high handicapper to beat the low one.

Bruce, You're assumption about handicapping is close enough for this question. Even closer, assume the handicap is derived by taking the best 10 of 20 rounds, averaging those 10 scores, and the scratch golfers ave. 72. The thirteen handicappers ave. 85.
These golfers are random, so you can only assume how consistent they might be. But I believe that the MORE consistent the hi handicappers are, the BETTER their chance of having fewer putts.
Thanks for your response.

THis question is absolutely impossible to answer. Not a chance that you could come up with an answer which is correct in any real , useful way. Some 10 handicappers are better putters than scratch markers, and vice versa. Handicap does not reflect putting ability, and in the case of 5 handicap v scratch, their putting ability is very close anyway, so every 5 handicapper could be better than the scratch handicappers. I would say that the chances are approx 45%, but like i say, that answer is purely intuition, no formula could do it.

[lorinda]

The trouble being that a 13 handicap might be a guy who always shoots 85, every round, day after day.
Or it might be a nutcase who shoots 98 sometimes and beats course records on other occasions.
We need far more data Im afraid,
Even the best and worst rounds these guys have shot would be a start.

[Mike Haven]

can you not make and state assumptions - like the good guys two putt and the bad guys 2.75 putt most of the time?

[Ray Zee]

the higher handicappers will always have less putts. unless they are really bad players. but i think 13 is about okay for this thing here.
what the trick is that worse players dont hit the greens in two as do the good players, who then tend to have long putts. the weaker players are near the green in two and then chip up close for one or two putt greens.
if you are going to count the number of cows in a field count the heads rather than the feet and divide by four.

Okay, this talk of "handicap does not reflect putting ability" is obviously pretty silly. Somebody mentioned that a ten handicapper may be a better putter than a scratch handicap. This would be very, very rare. Scratch handicaps might complain about their putting, but they can't be that bad, or they wouldn't be scratch. It is the very rare 10 handicap that is better.
Also, someone mentioned that we need to know the consistency, as a 13 handicap might shoot 95 one day, then break course records the next. This is pretty much impossible. No one has that kind of variability in golf. Bottom line is, I'll take the 5 handicappers at even money, no question. ( Assuming randomly picked golfers of the required handicaps). I'll go even more extreme - if the greens are PGA tour pace, the scratches are almost a lock. On "regular" greens, I'll go with the scratches at maybe 1:15.

Go Ole Miss!
(Watched the SEC women last year, it made me wonder why I'm such a hack, they make it look so easy)

Anonymous,
There is a correlation with handicap and putting ability. Like many problems, you may not be able to give an exact answer, but that doesn't make any educated guess useless. Also, the question regarded 13 handicap golfers against scratch golfers, not 5 vs. scratch. Intuition is allowed, although formulas may be helpful. Thanks for your response.
OleMissGolf

You are allowed to make your own assumptions- in fact, making an accurate answer depends on making proper assumptions.

Ray Zee,
Lower handicap golfers generally average fewer putts per round than higher handicap golfers. You are right that hi hdcp golfers miss more greens, but they are also poor chippers and putters.

Joey,
15:1 might be a bit much, but you are at least in the right ball park. That's the reason I mentioned Bethpage Black, to emphasize the difference in putting ability. Better players will separate themselves more in more difficult environments. (Hence the impossibility of Tigerproofing golf courses). Thanks for your response, and good luck with your game.
Olemissgolf

[Ray Zee]

yes but the scratch golfer still cant compete with putt numbers against a player that shoots in the 80,s. he will just be much closer to the pin when its his time to putt. even if he chips poorly dont you think he will be closer than someone who just hit a four iron to the green or even a sand wedge from 50 yards out.
or what about the old men golfers that never get to the green until about four shots then chip up close and one putt.

Sorry Ray, you're off on this one. Scratch golfers have fewer putts, by a long shot, when compared to 13 handicappers. They putt better, they chip & pitch WAY better. At a difficult course such as Bethpage Black, it's even more extreme as the scratches will be missing a lot of greens themselves, and chipping up. 30.43 is dead last on the PGA tour this year for average putts per round. This is a dream average for the vast majority of 13 handicaps. (Of course PGA players are a lot better than scratch, but this should give some perspective).

[Ray Zee]

okay say the average 13 hits an average green in three. thats 54 strokes. plus 30 putts. thats 84. around a 13 handicap i guess. few scratch golfers will do 30 putts unless the couse is long and they are chipping all the time. but i will defer to your guess.

this is imperfect
how is handisap determined for this 90 or 80 %
what assumptions are we making concerning putting vs scoring
correlations

We do not know the actual probability of course, it would be impossible to figure out, even if we had tonnes more information. But, the probability does exist. The question is legitimate, and has an answer out there in the ether. We were simply taking guesses as to what this probability would be.