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        riddles >> easy >> How Easy is a Golf Putt?
        
(Message started by: Sir Col on Oct 5^th, 2003, 7:07am)

Title: How Easy is a Golf Putt?
Post by Sir Col on Oct 5^th, 2003, 7:07am

Golfing Gary boasts that he putts perfectly, 3 out of every 5 times. Statistical Sarah argues that his claim is meaningless, without more information.

"I'd like to see you do any better!" blurts Gary, defensively.

"Oh dear," sighs Sarah, "I think I need to explain..."

By investigating different models and assumptions, based on given variables, how easy is a golf putt?

What about scoring a goal in football (soccer)?
How about scoring a basket in basketball?

Title: Re: How Easy is a Golf Putt?
Post by THUDandBLUNDER on Oct 5^th, 2003, 7:17am

Quote:

3 out of every 5 times

Does he really mean '3 out of every 5'?

Title: Re: How Easy is a Golf Putt?
Post by wowbagger on Oct 5^th, 2003, 10:31am

I'd like to know more about his notion of "perfect" if it's followed by something like "3 out of 5".

Title: Re: How Easy is a Golf Putt?
Post by Sir Col on Oct 5^th, 2003, 1:28pm

Are you guys serious? This problem is open-ended and is deliberate in its ambiguity. For those of you who are not up to solving these types of puzzles on your own...
Hint 1
::[hide]
Gary has made a typically un-mathematical statement. We could reasonably interpret this in the following way:
A putt is perceived, by Gary, to be perfect if it is a challenging distance from the hole and he gets it in. He claims that he succesfully putts 3 out of 5 of these challenging shots.
[/hide]::

Hint 2
::[hide]
Define a function that maps the distance from the hole to the "angle of success". Investigate this relationship numerically or graphically to formulate a hypothesis about the difficulty of the shot.
[/hide]::

Hint 3
::[hide]
Create a probability model based on this, and hence evaluate Gary's claim. What is your baseline to compare this with?
[/hide]::

The golf problem is relatively easy. The football and basketball are much more difficult.

Title: Re: How Easy is a Golf Putt?
Post by wowbagger on Oct 6^th, 2003, 4:12am

on 10/05/03 at 13:28:49, Sir Col wrote:

Are you guys serious? This problem is open-ended and is deliberate in its ambiguity. For those of you who are not up to solving these types of puzzles on your own...

Hm, we're supposed to "solve" an open-ended and deliberately ambiguous problem? Are you serious? ::)

Quote:

We could reasonably interpret this in the following way:
A putt is perceived, by Gary, to be perfect if it is a challenging distance from the hole and he gets it in. He claims that he succesfully putts 3 out of 5 of these challenging shots.

Why not reasonably interpret this in another way: A putt is perceiveed, by Gary, to be perfect if he gets it in.
Why should a shorter putt that he gets in not be considered "perfect"? Maybe Gary doesn't do so - I don't know any golfers personally. However, such necessary assumptions about the subjective meaning of "perfect" make me feel uncomfortable.

Anyway, apart from the function you proposed in hint 2, we would also need a distribution of lengths of the putts, I think.

Title: Re: How Easy is a Golf Putt?
Post by THUDandBLUNDER on Oct 6^th, 2003, 4:42am

Quote:

Are you guys serious? This problem is open-ended and is deliberate in its ambiguity.

Your 'puzzle' is an exercise in mathematical modelling.

As the Rugby Union World Cup starts in a few days, why not work out how easy is a goal kick/conversion? That is, where is the optimum point from which to kick at goal? To simplify matters, you may ignore the height of the crossbar.

Title: Re: How Easy is a Golf Putt?
Post by Sir Col on Oct 6^th, 2003, 10:08am

on 10/06/03 at 04:12:05, wowbagger wrote:

Why should a shorter putt that he gets in not be considered "perfect"?

Is a perfect goal in football one which is deflected in after a goal line scramble, or one in which the attacking player dribbles past the defenders, before chipping the keeper? Both would be most welcomed by the scoring team, but only one would be a goal of the month contender.

I did not propose this problem as an exercise in semantics; I believe it is finely stated anyway. Rather, it is an investigation that I found fascinating when I first encountered it many years ago.

Yes, T&B, globally it is an exercise in mathematical modelling, but it has many facets to be explored. Indeed, a conversion in rugby would be an interesting challenge, but I'd place it between football and basketball in terms of difficulty.

I suggest we start with golf...

Title: Re: How Easy is a Golf Putt?
Post by THUDandBLUNDER on Oct 6^th, 2003, 10:20am

Quote:

Indeed, a conversion in rugby would be an interesting challenge, but I'd place it between football and basketball in terms of difficulty.

It is different from your 'puzzles' in that, being a simple maximisation problem, it has a definite answer.

Title: Re: How Easy is a Golf Putt?
Post by James Fingas on Oct 6^th, 2003, 10:23am

If he's that good a putter, he should start putting right from the tee ;D. He'd be a world champion in no time.

Title: Re: How Easy is a Golf Putt?
Post by Sir Col on Oct 6^th, 2003, 10:30am

But you don't always have a choice about where to take the kick. You receive the ball from a pass, do you play a drop kick or run for the try? I suppose it depends how easy the goal is? Hmm, sounds familiar. ;)

Certainly feel free to investigate the optimum positions for a goal kick after scoring a try. For those who don't know, the ball can be placed at any position parallel to the touch (side) line on a line running through the point where the touch down occurred.

So... how easy is a golf putt?

Title: Re: How Easy is a Golf Putt?
Post by wowbagger on Oct 7^th, 2003, 3:35am

on 10/06/03 at 10:08:00, Sir Col wrote:

Obviously, this depends on what you consider a "perfect goal". While your last sentence may be true, this does not necessarily have anything to do with a perfect goal. This seems to be a good opportunity to let you know that I strongly dislike the inadequate use of language by many sports commentators.

Quote:

I did not propose this problem as an exercise in semantics;

I am well aware of that.