Golf-Probability Question

[David Sklansky]

Agreed. So what is your answer to the question I asked?

[stinkypete]

[ QUOTE ]
Agreed. So what is your answer to the question I asked?

[/ QUOTE ]

well, the 151st player would have to suck.

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.

to have a 50/50 chance of finishing +30 or better, i think you're looking at something like a 6-8 handicap. i don't know the numbers but there's at least tens of thousands of golfers who are better than this.

140th, i'd assume something like +18. again, this is a rough estimate, it's way too hard to quantify results based on everyone "trying their best to win". i'm sure most pga tour professionals wouldn't even understand how to maximize their chances of winning without a bit of coaching on the subject. you're probably looking at about a 1 handicap here. i have no idea how many golfers that is.

EDIT: i answered two questions here, the first being what you discussed in the other thread.

[stinkypete]

it's very difficult to quantify what trying your best to win actually means when you're several strokes back of the cut line. you have to increase your variance, but increasing variance in golf is really costly in terms of stroke EV. when you're a few strokes back with lots of players behind you, its hard to determine whether you should just do your best to lower your score or hope that the winds pick up and ruin the scores of the players behind you.

once you're so far back that your chances of making the cut are zero, you can basically just give up and play the standard low variance game, so scores shouldn't really blow up too huge.

but the cut line is going to be a lot higher than it normally would, if everyone is just trying to win. the entire field, with the exception of maybe tiger woods, should be trying to increase their variance significantly in the first 2 rounds. this might mean a cut line 5-10 strokes above the normal expectation.

what it seems to come down to is where that cut line is expected to be with everyone playing a higher variance game, and how far above that cut line a player can be before his chances are reduced to zero. plus a few strokes for variance.

quantifying this is hard.

[pete fabrizio]

[ QUOTE ]
I alluded to this on another thread. In order to answer it accurately, one would have to have a pretty good idea about both the subject of golf and the subject of probability and statistics. The answer will get screwed up if you don't understand both. JUST LIKE SO MANY OTHER THINGS. AND GETTING THAT THROUGH ALL YOUR THICK SKULLS IS WHY I HAVE BEEN PUT ON THIS EARTH.

Where was I? Oh yeah, golf. Assume American golfers only. Rank them from one to ten million. Now assume a typical PGA men's tournament comprised of the top 150 golfers, all healthy, playing their best and trying to win. Not trying to get a minor check. 72 holes.

You are given the opportunity to nominate a golfer to be the 151st player. You are asked to pick someone who is pretty steady in his performance. Not someone whos scores are all over the place. You are also asked to pick someone who is at least 50-50 in your mind to come in at least 140th. Say you have to bet on it. In order to have a good bet, the golfer you pick should be no worse than the xth best golfer in the country. What, approximately is x?

[/ QUOTE ]

Ok, I get the intuition that it would have to be pretty low, but too much math for me. To figure this out wouldn't we need a good estimate of the variance in golf? I mean, if the game were Go it would be something like the 160th guy. If it were Poker, it would be something like the millionth guy or lower (actually pretty much undefined, b/c you could just fold yourself into 140th in basically any tournament).

[southerndog]

David, I have often thought about variance in regards to golfers, and also how your horse racing gizmo could be easily applied to golf as well.

Now, the thing that makes this hard to answer, is that in a lot of ways, golf is about consistency. But, on the other hand, its a lot like tournament poker... You're better off finishing first one week, and then missing the cut the next 7 times. If a golfer wins one tournament a year, over the course of his career, he would have a VERY successful career.. Much like a tourney pro would do very well to win one 10k buyin event, and then miss the money in the rest.

So, some golfers may have very low averages each week, and do very well that way, but some golfers may be totally eratic, have a high average but have everything click right once or twice a year.

[burthoovis]

There are a couple of considerations that haven't been mentioned.

1) The cut. I don't know of any PGA tourney that allows 140 players to finish. Any statistical work that you do should account for variance over 36 holes because that's as far as your 151st golfer is going to get to play typically. Anyone making the cut will always finish above 140...usually the cut is something like top 75 and ties.

2) Course slope, rating, difficulty and weather are all significant factors. People here have supposed that 140th is 30 over par.....I haven't found that to be the case at all. The instances where you have players shooting 30 over are for major tournaments where the course set up is significantly more difficult...and you have non-tour players participating through other qualification. In a typical tour event, the 140th place player is around 5 over after 36 holes. But that number has a lot of variance as the west coast swing courses early on have a very easy set-up with the cut being under par...that cut number has a tendency to move up during the season.

3) Then there's the "holy [censored]" factor. Golfers who will be playing in a tour event for the first time will have a tendency to shoot worse than their average due to unfamiliar stressors. Outside of the European tour and, perhaps, the largest of the Nationwide tour events, domestic golfers will not have to deal with crowds, TV cameras, etc. I'm not sure if there's any way to reasonably quantify this factor.

[pvn]

[ QUOTE ]
There are a couple of considerations that haven't been mentioned.

1) The cut. I don't know of any PGA tourney that allows 140 players to finish.

[/ QUOTE ]

Leader David,

Do responses like this make you want to tear your hair out?

[burthoovis]

[ QUOTE ]
Poster: pvn
Subject: Re: Golf-Probability Question


Quote:
--------------------------------------------------------------------------------

There are a couple of considerations that haven't been mentioned.

1) The cut. I don't know of any PGA tourney that allows 140 players to finish.


--------------------------------------------------------------------------------



Leader David,

Do responses like this make you want to tear your hair out?


[/ QUOTE ]

What's that supposed to mean wise-azz ?

Players in PGA tour evens ARE placed down below the cut and listed as far down as 140th place and beyond. Those not making the cut are still placed.

The initial post laid forth a wager that called for a placing above 140th place in a PGA event. How could you NOT factor in the cut for your calculations ?

If you account for variance of scores over 2 round versus 4 rounds, it's possible for someone who could have made the cut in the first two rounds to have been someone who placed outside to top 140 over 4 rounds. But in a real life situation, the guy who makes the cut isn't going to finish worse than the number of people who make the cut.

Conversely, you could have someone who sits in 141st place after two rounds and isn't allowed to continue to play....who may have easily moved up the ranks after four rounds to finish higher than 140.

In fact, taking the cut into account you need only need to compute 36 holes in making your determination.

Unless I'm completely missing the point of your post, you're really not offering anything to the conversation other than your misguided ignorance.

[southerndog]

[ QUOTE ]
David, I have often thought about variance in regards to golfers, and also how your horse racing gizmo could be easily applied to golf as well.

Now, the thing that makes this hard to answer, is that in a lot of ways, golf is about consistency. But, on the other hand, its a lot like tournament poker... You're better off finishing first one week, and then missing the cut the next 7 times. If a golfer wins one tournament a year, over the course of his career, he would have a VERY successful career.. Much like a tourney pro would do very well to win one 10k buyin event, and then miss the money in the rest.

So, some golfers may have very low averages each week, and do very well that way, but some golfers may be totally eratic, have a high average but have everything click right once or twice a year.

[/ QUOTE ]

My point is that, golf rankings don't go by average score, AFAIK, they go based on tourney performances.

[southerndog]

[ QUOTE ]
[ QUOTE ]
Poster: pvn
Subject: Re: Golf-Probability Question


Quote:
--------------------------------------------------------------------------------

There are a couple of considerations that haven't been mentioned.

1) The cut. I don't know of any PGA tourney that allows 140 players to finish.


--------------------------------------------------------------------------------



Leader David,

Do responses like this make you want to tear your hair out?


[/ QUOTE ]

What's that supposed to mean wise-azz ?

Players in PGA tour evens ARE placed down below the cut and listed as far down as 140th place and beyond. Those not making the cut are still placed.

The initial post laid forth a wager that called for a placing above 140th place in a PGA event. How could you NOT factor in the cut for your calculations ?

If you account for variance of scores over 2 round versus 4 rounds, it's possible for someone who could have made the cut in the first two rounds to have been someone who placed outside to top 140 over 4 rounds. But in a real life situation, the guy who makes the cut isn't going to finish worse than the number of people who make the cut.

Conversely, you could have someone who sits in 141st place after two rounds and isn't allowed to continue to play....who may have easily moved up the ranks after four rounds to finish higher than 140.

In fact, taking the cut into account you need only need to compute 36 holes in making your determination.

Unless I'm completely missing the point of your post, you're really not offering anything to the conversation other than your misguided ignorance.

[/ QUOTE ]

Why can't u just ignore the cut?