Golf-Probability Question

[burthoovis]

[ QUOTE ]
STINKYPETE:
there would be lots of pga pros playing a higher variance game in their quest to win. some of them will be well back of the cut line with the final 9 holes (or whatever number) left to play. if they still want to win and not save face, they'll have to increase variance even more. a lot of their scores will suck. it's hard to quantify, but i'd say 150th would be at least +30 on average.

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I'm not sure how you are referring to 'the cut' here. The cut in a PGA event not only refers to who gets the money and who doesn't, it also refers to who gets to continue to play after 36 holes.

I don't think a golfer who is on the bubble for making the cut would necessarily alter his game greatly in order to make up strokes to the leader. A more reasonalbe approach would be to play your best game, make the cut, and then try and win the tournament over the next 36 holes.

You might have someone minimize risks to make the cut, but in almost all cases that's going to be a tactic to win and not a tactic for survival-sake. ( noting that there may be some limited cases where a making the cut for a new player or an open qualifying player will be their goal)

The players that would be playing a wild game might be those who were outside of the cut by a great number of strokes. And by great number of strokes I would assume more than 1 stroke per remaining hole. Even then, how many more risks can a player take than he is already taking ?

The opportunity to take high risk shots in golf is limited if you are really trying to score well. Perhaps carrying a water hazzard with your second shot on a par 5...or playing to a tight pin placement over a bunker...but I think the situations you're talking about already exist in golf.

Players on the bubble play two tournaments currently. One to make the cut, where they have nothing to lose. And then the second is to win the overall. In the second instance, you might get a player who minimizes risk to get a check, but in the first 36 holes I think you have everyone playing in an attempt to post their best score.

And for the purposes of the wager, as it's posed, only the first 36 holes count.

[stinkypete]

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I'm not sure how you are referring to 'the cut' here. The cut in a PGA event not only refers to who gets the money and who doesn't, it also refers to who gets to continue to play after 36 holes.

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i'm referring to the cut as the cut. everyone who follows golf at all knows what the cut is. i don't see the problem.

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I don't think a golfer who is on the bubble for making the cut would necessarily alter his game greatly in order to make up strokes to the leader. A more reasonalbe approach would be to play your best game, make the cut, and then try and win the tournament over the next 36 holes.


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someone on the "bubble" should play a fairly high variance game until the last few holes of the second round. he's going to be so far back of the leader (probably 10+ strokes) that he needs to get something going to win the tournament. remember david said that these players are trying their best to win. they don't care about making the cut or cashing small. making the cut is only important because it gives the players a chance to win, but if they're right on the cut line that chance is very small anyway.
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You might have someone minimize risks to make the cut, but in almost all cases that's going to be a tactic to win and not a tactic for survival-sake. ( noting that there may be some limited cases where a making the cut for a new player or an open qualifying player will be their goal)

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playing conservatively to make the cut only makes sense the last few holes of the second round, as i mentioned.

nobody is going to have the goal of making the cut, because david specified that that's not the case in this hypothetical.

[burthoovis]

Thank you to Troll_inc for helping me hash this out.

So I went and sampled a number of PGA tour courses and
came up with this average.

For Championship Tournament Conditions

Average Rating: 75.68
Average Slope: 141.83

Average score to finish 140th in tournaments on those
courses: 152.33 over 36 holes.

So our golfer would have to shoot 76.165 on average on
that average course.

Now we plug in our conditions for handicap

(76.165 - 75.68) * (113/141.83) =
.485 * 0.796 = .386

The handicap represents 96% of a
golfers average score for the best ten of his last 20 rounds so we divide by .96

to get a handicap of .4

Using the USGA handicap distribution chart and doing a
simple math we can conclude that .808% of the USGA
golfers have a handicap of .4 or better.

Since no numbers are available to distinguish between
male, female, senior or junior golfers, we'll just
lump them all together. And say that of the 840,000
members ( note that we're not using the 10 million originally posed, as the 840,000 is probably a better sampling of avid golfers)

6787 of them could finish 140th or better half the
time.

[stinkypete]

[ QUOTE ]

The handicap represents 96% of a
golfers average score for the best ten of his last 20 rounds so we divide by .96

to get a handicap of .4


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as you said, the handicap is an average of the 10 best scores, which you didn't consider. i don't know what the variance in results is like for the average scratch golfer, but i think you'd be looking at something like a +2 handicap based on those stats.

however, you didn't adjust for the fact that everyone is trying to win rather than going for a decent cash or just trying to make the cut, and that's probably the hardest part to estimate since that situation never occurs in reality.

[stinkypete]

btw, where are you getting these ratings and slopes?

[bearly]

i would treat this as a prop bet for an ammount i could afford to bet, say, $100. (i don't think this is the bet you are proposing) i would assume the bet would be for the first offical pga event of 1907 that has a full field (no toc or something like that). i would start w/ the top 125 money winners (americans) from the previous year. then, eliminate all who i know are injured, or will skip the tourney. i would guess i would end up w/ about 100. then take the sponser's exemptions (guys like john daly, etc) and pick thru them. finally , i would fill out the list w/ players who just earned their full-time player status thru q-school.(now , what i think is your bet) as to picking the 151st player exactly--i would have to see that prop bet spelled out. so many people walk on and try to qualify for a 144 man field. so, the bet as written would require that you have a tourney w/ a no-cut field of over 150 players. i don't know of one on the pga tour (especially when you have to eliminate foreign players). maybe i am missing something david. i was a player, not an odds-maker..................b

[burthoovis]

[ QUOTE ]
Poster: stinkypete
Subject: Re: Golf-Probability Question
as you said, the handicap is an average of the 10 best scores, which you didn't consider. [ QUOTE ]


-acutally the handicap is 96% of average of the ten best of the last 20 scores. I factored out the 96%. I'm not sure how to caluculate in variance of discounted scores. I'd make the assumption that the variance for better golfers would be less than for high handicappers. I'd be interested in hearing how someone would calculate this. It would make a good refinement to what we've proposed.

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however, you didn't adjust for the fact that everyone is trying to win rather than going for a decent cash or just trying to make the cut, and that's probably the hardest part to estimate since that situation never occurs in reality.

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I'm going to respectfully disagree with your premise as stated here and previously. I belive that in the first 36 holes all the players are trying to employ their best strategy to win the tournament. I also don't agree with your premise that the players on the cut are 10+ strokes behind and out of contention. Looking at tournaments on www.pgatour.com shows that top 70 and ties tend to be far less than 10 strokes after 36 holes that you suggest. I'm of the opintion that anyone still in the tourney after 36 holes still has a legitimate chance to win. ( unless of course that Tiger is in the tournament...then everyone else has a legitimate chance at second place)

[burthoovis]

> Stinkeypete: btw, where are you getting these ratings and slopes?

I took a random sampling of 6 tournaments. I checked the scores for 2006. I then went to the course websites and looked up the slope and rating from the championship tees.

I could have had a greater sample pool, but I think I've wasted enough time.

BTW what isn't factored into the equation, and what I think is a far bigger factor, is the players nervousness. My brother has played in 4 PGA tour events, open qualifying with a 66 or 67 each time. He's was a collegiate golfer and accomplished regional tournament player in a very competitive section. He's never made a cut.

You could adjust my caluculations for handicap, and you could reduce that pool of 6000+ down to half of that to give me the top 3000 players and I still wouldn't take the bet. The only way that I'd take the bet is if you gave me all the guys who qualify through Q-school...and even then I'd be nervous.

[stinkypete]

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-acutally the handicap is 96% of average of the ten best of the last 20 scores. I factored out the 96%.


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yes, an average. in this case a scaled average. the 4% difference is negligible compared to the best 10 out of 20 thing though.

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I'm going to respectfully disagree with your premise as stated here and previously. I belive that in the first 36 holes all the players are trying to employ their best strategy to win the tournament. I also don't agree with your premise that the players on the cut are 10+ strokes behind and out of contention. Looking at tournaments on www.pgatour.com shows that top 70 and ties tend to be far less than 10 strokes after 36 holes that you suggest. I'm of the opintion that anyone still in the tourney after 36 holes still has a legitimate chance to win. ( unless of course that Tiger is in the tournament...then everyone else has a legitimate chance at second place)

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you're still ignoring the fact that the optimal strategy for this situation isn't how they play in those tournaments. yes, the cut line is often less than 10 strokes from the lead. but that would change with the higher variance play. i might have overestimated the increased variance in my original post, but i don't see how it could be an insignificant factor.

[stinkypete]

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I took a random sampling of 6 tournaments. I checked the scores for 2006. I then went to the course websites and looked up the slope and rating from the championship tees.

I could have had a greater sample pool, but I think I've wasted enough time.


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i'm sure your sample size is fine.

the course as its set up for a pga tour tournament is going to be significantly more difficult than it normally plays from the championship tees though. often the tees will be pushed back even further than where the regular "championship" tees are. the greens will be faster, the roughs longer, fairways narrower, etc. i think you'd have to add about 1-3 strokes to the course rating on average to get an accurate idea of the difficulty. for US open setups the difference would be significantly more.