Calculating "hardest hole"

[mike_malone]

 As I looked at the listing of the hardest holes at Rolling Green for the U.S Amateur Qualifier   I thought something was amiss. I am not some statistical wizard , but I "felt" that two of the par threes (#14 and#10) were the hardest holes not the par four(#13).

    The calculation  they used was the stroke average . This was 4.742 for #13 and 3.656 and 3.574 for #14 and#10.  

    If you consider the "difficulty " realitive to par aren't the par three totals harder? I tried to divide the average scores by the par on the holes. This led to the conclusion that the par threes were "harder".

     Has anyone else found this in their experience? Does this make sense?


   I have always felt that par threes are the hardest holes.

[Kevin_Reilly]

I think the absolute fraction of a stroke above par on each hole should be compared.  If all holes were bogeyed, then par 3s would be 33% above par, par 4's 25% and par 5's 20%.  So in that example the 3s would be the most difficult, while that doesn't make sense because all of the holes were bogeyed.

So look at the strokes above par and ignore it as a percentage of the par on the hole.

[mike_malone]

 Kevin,

    Since more stokes are expected on a par five than a par three , isn't a bogey  more over par on the three than the five?

[BCrosby]

Mayday -

I'm not sure that  makes sense. Par already reflects the number of strokes a player ought to have on a given hole. The relative scoring expections of a hole (usually based on length) are built into par. It follows that a bogey on a par three is no worse than a bogey on a par 5. In other words, bogies are not relative to a hole's difficulty. They are an absolute, non-relative measure.  

The extra stroke (a bogey) on a par 3 may be a higher percentage of all strokes played on that hole (vs. a par 5, say), but that does not impy that the par 3 is somehow a harder hole than the par 5.

Bob  

[mike_malone]

 Indeed that would be a very hard hole to par, Shivas.


    I do think par threes are usually the hardest holes because there are fewer shots to use for recovery.

   When I used my calculation  for my course the holes lined up as I experience them "relative to par".

   I think #18 TPC is usually rated hardest but I see #17 as harder when I watch. I wonder if the ranking would change when dividing the stroke average by the par.

[BCrosby]

Mayday says:

"I do think par threes are usually the hardest holes because there are fewer shots to use for recovery."

I agree. And that is reflected in the fact that average scores on par 3's are often among the highest. As at RG.

The fact that you have - overall - fewer strokes on par threes does not mean that average scores understate the difficulty of par 3's, however. When comparing average scores on holes - even between holes with different pars - you are comparing apples to apples.

Bob

[mike_malone]

 I guess you are right Bob .In fact #14 was ranked second and #10 was fourth on the sheet I saw.

[wsmorrison]

Mike,

Your notion of looking at a ratio consisting of the average score on a hole with the par makes no sense whatsoever.  It is a misleading statistic skewed towards par 3s.

I disagree with you and Bobsy (surprised he agreed) with the general notion that par 3s are the hardest holes because there are fewer shots for recovery.  The approach to the green on a par 3 is as preferred a lie as you like and when compared to uneven lies for approaches to par 4s and par 5s the difficulty is clearly with the non-par 3 holes.

Any given hole has a whole-number par while the average score for a field of scratch golfers is a non-whole number (lower or higher than the given whole number par).  The most significant statistic is to look at is the average number of strokes or fraction of strokes over par if the assigned par is reasonable.  

You can't even look at average strokes versus yardage as some holes are flat, some uphill and some downhill.  Yardage in and of itself is not indicative of difficulty.

What was the average score on the 18th hole?  If it was 4.44 or under, it would should be a par 4 not soley based on the statistic but also where it comes in the routing progression and the resulting psychological effect.

What was the average score for the 7th hole?  Even if it were the approximately the same as the 18th (maybe it was lower) it should still be a par 5 because it is in the middle of the routing progression and it preceeds 3 difficult holes.

Then again, given the conditions courses in the "death zone" from here to Washington, DC, you have to factor out the green condition of the 16th in any degree of difficulty analysis.  There was hardly and grass on the green and even a straight putt from 5 feet was an adventure.

One thing I noticed in a superficial look at the scores at Rolling Green was there were a few outliers (63 and 90) but most of the scoring was more over par than I thought given the soft conditions of a course playing around 6700 yards.

[mike_malone]

18--4.517-----7--4.89

[wsmorrison]

I think it safe to say if 13 is a par 4 then 18 can be as well.  I'm a bit surprised that 7 was that high.  Guys must have had some difficulty off the tee.  Probably too many hit driver rather than 3-wood.  Nice to know though.  I like 7 as a par 5 with 8-10 coming up.  Do you have all the hole scoring averages?  If so, please send IM or here.  Thanks.

[Jim Thompson]

You are forgetting the purpose of calculating the hole difficulty in the first place - the distribution of strokes for MATCH PLAY,  NOT STROKE PLAY.  Therefore the distribution of strokes is not relative to the difficuty against weighted par, but rather the instances where the weaker player most needs the strokes for a good match.  The reason par threes are rarely in the top half of hole stroke distribution is that a lesser player can always make one good shot or even two but it is more difficult to string together multiple good shots.  The reason par fives do not receive as much due in stroke distibution is that few are still three shotters and the extra shot serves as a make up stroke on on the relative par 4 1/2s we call par fives.  Remember, stroke hole handicapping is based on match play betting not stroke difficulty or average scoring.  Par threes always average more over than they do on the fives but who would want to give a stroke on a three in match pay rater than four?

Cheers!

JT

[Rob_Waldron]

Mayday

Have you lost your mind man? You must be suffering from "Paralysis from overanalysis". Obviously a hole with an average score of 4.742 is more difficult than holes with average scores of 3.656 and 3.574.

Even when you consider the average strokes over par, the measure the USGA uses to determine handicap holes, the 4.742 hole is more difficult. Since everything in golf is measured against par the holes with the greatest average above par can only be considered as the most difficult, at least for the days of the competition. Unfortunately your data was collected from two days with only one pin placement.

BTW what was the average putts for each hole of the qualifying?? Should the green with the highest average putts be now and forever known as the toughest green at Rolling Green?