O.T. Math Question Re: Better Ball Tactics

[Jim_Coleman]

    Since it took me two years to get through geometry, and I never really got through algebra !!, I have no shot at answering this.  But, there must be a math whiz here who can:
     Player A has a 25 ft. birdie putt.  (His partner already has a par.)  Assume his chances of making the putt are one in 25.  Player B has a 20 foot putt on the same line.  Assume Player B's chances of making his putt are one in 20 if he doesn't see the line before putting, and one in 15 if Player A putts first.  Should Player A try to make the putt, or pick up?
     This happened to me in a club championship match.  I (as player A) missed; player B made; and my partner and I lost on the 19th hole.  I thought of the situation today when Villegas sunk a putt on 17 after seeing Donald miss, and Faldo commented, "If these guys know the line, they usually make the putt."
     I find this kind of question fun, but maybe I'm a little pathetic.

[Tim Martin]

    Since it took me two years to get through geometry, and I never really got through algebra !!, I have no shot at answering this.  But, there must be a math whiz here who can:
     Player A has a 25 ft. birdie putt.  (His partner already has a par.)  Assume his chances of making the putt are one in 25.  Player B has a 20 foot putt on the same line.  Assume Player B's chances of making his putt are one in 20 if he doesn't see the line before putting, and one in 15 if Player A putts first.  Should Player A try to make the putt, or pick up?
     This happened to me in a club championship match.  I (as player A) missed; player B made; and my partner and I lost on the 19th hole.  I thought of the situation today when Villegas sunk a putt on 17 after seeing Donald miss, and Faldo commented, "If these guys know the line, they usually make the putt."
     I find this kind of question fun, but maybe I'm a little pathetic.

Jim-Player A only picks up if he is putting for par. You did the right thing.

[JLahrman]

It depends on how much risk you want to take, but you should probably putt it.

If you don't putt it, you're giving your opponent a 5% chance to win the hole (he'll make 1 in 20)

If you putt it, you're giving him a 6.4% chance to win the hole:  You miss (24/25) * He makes (1/15).

However, you're also giving yourself a 3.7% chance to win the hole:  You make (1/25) * He misses (14/15).

So you've slightly increased the likelihood that your opponent will win the hole, but you're giving yourself a chance that you would otherwise pass up.  By putting, you're giving yourself a 3.7% chance to win the hole and you're only increasing his chances of winning the hole by 1.4%.

There is an 89.9% chance that you're going to halve the hole even if you both putt - a .3% chance that you will both make your putts and an 89.6% chance that you'll both miss.

This assumes that your opponent's team would make a 4 - either your opponent's partner is already in with 4 or your opponent will never three-putt.

[Jim_Coleman]

Professor Lahrman:  Thank you.  Excellent analysis.  Are you a rocket scientist?

[Greg Chambers]

If player A picks up, he's a douche.  And he'll lose the match anyway, because Karma is a byatch.

[JLahrman]

Professor Lahrman:  Thank you.  Excellent analysis.  Are you a rocket scientist?

No but I did stay at a Holiday Inn last night.

I worked as an actuary for four years.

I would only consider picking up if I were at a point in a match where it is more important to me to not lose the hole than it is for me to win the hole.  Perhaps if I'm dormie.

Otherwise, I would agree with Mr. Chambers.

[Jim_Coleman]

   It so happens, my partner and I were 2 up on the 16th green, so not losing was paramount.  I suggested that I pick it up.  My partner thought I was nuts, so I putted.

[Tim Martin]

  It so happens, my partner and I were 2 up on the 16th green, so not losing was paramount.  I suggested that I pick it up.  My partner thought I was nuts, so I putted.

How do you feel if you pick up and he drains it anyway?  

[Jim_Coleman]

    That's why I asked it as a math question.  As a tactics question, one can take either side.

[Jason Topp]

How about trying to slice a putt in the hole?  You get a slim chance at a make and give a goofy line.

[Mike Nuzzo]

so much weighs on your guessed probability of 1/20 to 1/15.
If the probability went to 1/10 then mathematically it would be better to pick up.

Greg
If a guy wants to win (by the rules), how is he a douche?

Cheers

[DMoriarty]

It depends on how much risk you want to take, but you should probably putt it.

If you don't putt it, you're giving your opponent a 5% chance to win the hole (he'll make 1 in 20)

If you putt it, you're giving him a 6.4% chance to win the hole:  You miss (24/25) * He makes (1/15).

However, you're also giving yourself a 3.7% chance to win the hole:  You make (1/25) * He misses (14/15).

So you've slightly increased the likelihood that your opponent will win the hole, but you're giving yourself a chance that you would otherwise pass up.  By putting, you're giving yourself a 3.7% chance to win the hole and you're only increasing his chances of winning the hole by 1.4%.

There is an 89.9% chance that you're going to halve the hole even if you both putt - a .3% chance that you will both make your putts and an 89.6% chance that you'll both miss.

This assumes that your opponent's team would make a 4 - either your opponent's partner is already in with 4 or your opponent will never three-putt.

JLahrman,

Interesting analysis, but I am not sure I follow completely.   I take it that the main concern was winning the match not the hole, and it sounds like A was dormey.  B needed to make the putt and have A miss to win the hole and square the match.  If A makes, A wins the match regardless.  If B misses, A wins regardless regardless.  
  
Odds of B tying match if A putts are the chance of A missing times chance of B making.  24/25*1/15 = 8/125 = 6.4%
Odds of B tying match if A doesn't putt are 1/20 = 5%

So from a statistical standpoint only, A should pick up.  Shouldn't he?  Or do I have something wrong?

[JLahrman]

so much weighs on your guessed probability of 1/20 to 1/15.
If the probability went to 1/10 then mathematically it would be better to pick up.

This is true.  Personally I think a decent player has much more than a 1 in 20 chance of making a 20 footer.

And I also do not think that seeing a putt struck on the similar line will benefit an amateur much, particularly if it is your home course where you both probably know the lines pretty well.

[JLahrman]

JLahrman,

Interesting analysis, but I am not sure I follow completely.   I take it that the main concern was winning the match not the hole, and it sounds like A was dormey.  B needed to make the putt and have A miss to win the hole and square the match.  If A makes, A wins the match regardless.  If B misses, A wins regardless regardless.  
  
Odds of B tying match if A putts are the chance of A missing times chance of B making.  24/25*1/15 = 8/125 = 6.4%
Odds of B tying match if A doesn't putt are 1/20 = 5%

So from a statistical standpoint only, A should pick up.  Shouldn't he?  Or do I have something wrong?

I didn't make the dormie assumption from Jim's post.

But if the match is dormie, then yes I agree with you, A should pick up purely from a statistical standpoint.  A could obviously win the match by making the putt, but the problem is that A is not likely to make the putt, and if we figure that B's chances of making the putt go from 1 in 20 to 1 in 15 purely from seeing the putt happen, then yes A should pick up.

That's why it a question of risk tolerance.  Pick up and the odds that hole is halved are 95%, but the 5% is all upside for B.

If A putts, the chances of halving the hole are down to 89.9%.  There is now a 3.7% chance that A wins the hole, and a 6.4% chance of B winning the hole.

But in a dormie match, halving the hole and A winning the hole are the exact same thing.  If A putts, he's lowered his chances of finishing off the match from 95% to 93.5%.  But if you were on the third hole of the match, A would probably figure it's worth accepting the risk of giving B a read in order to give yourself the chance to win the hole.

[Greg Chambers]

so much weighs on your guessed probability of 1/20 to 1/15.
If the probability went to 1/10 then mathematically it would be better to pick up.

Greg
If a guy wants to win (by the rules), how is he a douche?

Cheers

It's called sportsmanship.  If a person wants to win a match, they should try to win it, not hope the other guy loses.  Hence my "douche" comment.

[Mark Pearce]

so much weighs on your guessed probability of 1/20 to 1/15.
If the probability went to 1/10 then mathematically it would be better to pick up.

Greg
If a guy wants to win (by the rules), how is he a douche?

Cheers

It's called sportsmanship.  If a person wants to win a match, they should try to win it, not hope the other guy loses.  Hence my "douche" comment.

What Greg said.

[Sean_A]

so much weighs on your guessed probability of 1/20 to 1/15.
If the probability went to 1/10 then mathematically it would be better to pick up.

Greg
If a guy wants to win (by the rules), how is he a douche?

Cheers

It's called sportsmanship.  If a person wants to win a match, they should try to win it, not hope the other guy loses.  Hence my "douche" comment.

I unequivically disagree with this line of thinking.  Thats like saying you shouldn't win a match because a guy misses a three footer you could have given him.  Every match takes on its own life and calls for different decision-making.  In any case, I think it poor sportmanship to think a guy is a douche because he did what he thought best to win regardless of my opinion of his style. 

Ciao

[Bill Brightly]

If the match is just a nassau, you putt the 25 footer. This was obviously a club tournament of some importance, maybe even a "board" tournament, since they played extra holes. No one should criticize a legal competitive strategy such as picking up if that's what the opponents decide to do. If Jim's putt was a 40 footer, his chance of making is even lower, yet he risks providing the same information to his opponent, and picking up makes even more sense.

I would have no problem if an opponent picked up in front of me in such a case, and I would smile at their competitive spirit. However, it would lock in MY competitive focus and, as Greg suggests, I think the golf gods don't like people picking up

[Jim_Coleman]

    I agree that the answer depends on the accuracy of the odds I have assumed.  If I were playing a PGA pro and Sir Nick is right that "These guys almost never miss when they know the line," then I definitely should pick up.  The player B in my match actually said he probably would have missed it had he not seen the line.  Anyway, I thought it was a fun question.  My buddies say I have no life.

[Jim_Kennedy]

Jim,

"This happened to me in a club championship match."
I assume you meant it happened in a match that was part of a championship event held at your club. 

A further muddying of the waters:

http://www.pgatour.com/r/stats/filter/?1

[Brent Hutto]

As Mike pointed out, it all comes down to the specific numbers you assign to the probabilities. And at those distances the numbers are purely guesswork.

A larger factor is the golfer's personality, specifically the locus of control that is uppermost in their thinking. Are you the sort of person who wants all the weight on your own putting? Or someone who takes satisfaction in manipulating the situation so that "the probabilities" or what someone else does works to your advantage.

There are some people who, no matter what the probabilities, want to make the entire game about what they do. This sort of person mentally begrudges the fact that you have an opponent to deal with at all. Very self-focused individuals. This guy wants to make the putt and only secondarily cares what happens to the other guy or how that affects the match

There are others who really enjoy giving golf a little of the thrust-and-parry, dish it out and take it confrontation that most other sports offer. This guy probably loves match play in part because occasionall it offers this kind of opportunity to "outsmart" the opponent or engage in lateral thinking that's fundamentally pretty un-golf-like.

[jeffwarne]

    Since it took me two years to get through geometry, and I never really got through algebra !!, I have no shot at answering this.  But, there must be a math whiz here who can:
     Player A has a 25 ft. birdie putt.  (His partner already has a par.)  Assume his chances of making the putt are one in 25.  Player B has a 20 foot putt on the same line.  Assume Player B's chances of making his putt are one in 20 if he doesn't see the line before putting, and one in 15 if Player A putts first.  Should Player A try to make the putt, or pick up?
     This happened to me in a club championship match.  I (as player A) missed; player B made; and my partner and I lost on the 19th hole.  I thought of the situation today when Villegas sunk a putt on 17 after seeing Donald miss, and Faldo commented, "If these guys know the line, they usually make the putt."
     I find this kind of question fun, but maybe I'm a little pathetic.

Why not be a closer and make the putt, then B is putting for a tie.

Once you suggested you pick up you had no chance to make it (let's just say we wouldn't be partners next year)

[Ross Tuddenham]

In dave peltz short game bible he put together some putting stats for the probability of holing different length putts.  I think the data is based on pro's, so for us normal folk we can assume the probabilities are lower.

percentage of putts holed from 25 foot is 5%, and from 20 foot around 8%.  There is no mention of how these odds are improved if you see the line beforehand.  If seeing the putt was the equivalent to moving 5 feet closer, so player B now faces a 15 foot putt (or at least equivalent) the chances of holing it are 15%.

And in your scenario you are currently 1 up on 18, and playing partner has guaranteed a par. With no mention of player two's partner, I assume they are out of the hole.


So the scenario that looses you the match is player B holing and you missing, where picking up is the same as missing.

If you pick up the chances of loosing the hole are 0.08, his probability of holing an unassisted 20 footer.

The other scenario is you taking the putt but missing (0.95), and player B holing an assisted putt from 20 foot (0.15).  The probability of this happening is 0.1425. (0.95x0.15)

This of course depends on what the actually probability is for holing an assisted putt from 20 foot. If it is as much as the number quoted above (0.15) then you should pick up as 0.08<0.1425. (you want to minimise chance of loss)

But in general you should only pick up if the probability of holing the assisted putt is deemed to be greater than 0.08421 (for these distances).  


Now try working that out standing on 18th while one up.

[Tim Martin]

In dave peltz short game bible he put together some putting stats for the probability of holing different length putts.  I think the data is based on pro's, so for us normal folk we can assume the probabilities are lower.

percentage of putts holed from 25 foot is 5%, and from 20 foot around 8%.  There is no mention of how these odds are improved if you see the line beforehand.  If seeing the putt was the equivalent to moving 5 feet closer, so player B now faces a 15 foot putt (or at least equivalent) the chances of holing it are 15%.

And in your scenario you are currently 1 up on 18, and playing partner has guaranteed a par. With no mention of player two's partner, I assume they are out of the hole.


So the scenario that looses you the match is player B holing and you missing, where picking up is the same as missing.

If you pick up the chances of loosing the hole are 0.08, his probability of holing an unassisted 20 footer.

The other scenario is you taking the putt but missing (0.95), and player B holing an assisted putt from 20 foot (0.15).  The probability of this happening is 0.1425. (0.95x0.15)

This of course depends on what the actually probability is for holing an assisted putt from 20 foot. If it is as much as the number quoted above (0.15) then you should pick up as 0.08<0.1425. (you want to minimise chance of loss)

But in general you should only pick up if the probability of holing the assisted putt is deemed to be greater than 0.08421 (for these distances).  


Now try working that out standing on 18th while one up.

Regardless of the statistical data I can`t fathom picking up a putt that gives me a chance to win outright.

[Jud_T]

It's obvious that you should pick up unless it's a must-win situation for you.  You've got a 4% chance of draining it and you're improving your opponents chances of making by 25%.  And the douche is the guy who's grumbling about gamesmanship tactics as he buys the first round in the clubhouse for losing...