[BCrosby]

Let's begin with the conjecture that the Masters and The Open were played on more strategic courses than the US Open and the PGA in 2003.  

If our scoring dispersion theory is correct, The Masters and The Open should have higher TEP Values than the other two major venues.

Let's test it for 2003.

I took the 4th round scoring spread for each course. (I wanted to knock out the Gay Brewers and the Billy Caspers who skew scoring the first two days at The Masters. I also wanted to use as homogenous a group of golfers as I could get. So I used scores posted by the best golfers in the world when they are playing well enough to make the cut at a major.)

The higher the TEP value the more the scoring spread above and below par.

The Masters TEP Value - 56
US Open TEP Value - 35
The Open TEP Value - 50
PGA TEP Value - 31

My conclusion? The TEP Values are useful tools in measuring the extent to which a course plays strategically. Or non-strategically. Q.E.D.

Methodology and calculations provided on request.

Bob

[Mike Nuzzo]

Bob,
Here's my request.  I'm not up on the latest numbers...
I'm interested to hear.
Thanks
Mike

[CHrisB]

Methodology and calculations provided on request.

Bob,
Request!

I'm very interested in the methodology and calculations.

[RJ_Daley]

TRANSPARENT EXOPOLYMER PARTICLES (TEP)
Traditional Enrollment Pattern (TEP)
Thermoelectric power (tep)
Teacher Education Program (TEP)
transeliptical electric potential (TEP)

TEP  What the hell are you guys talking about?

[BCrosby]

                    UP     P      OP   UP/OP  UP+OP/P   TEP
Masters     156   540   189   89%      63%        56
US Open   172   712   339   50%      71%        35
The Open   229   747   338   67%      75%        50
PGA            160    714   386   41%      76%        31

Note that the perfect TEP Value would be 200.

Bob

P.S. My guess is that The Masters would have had a much higher TEP Value prior to the addtion of rough and length over the last couple of years. Ditto for Opens at TOC or other courses not as brutally set up as last years' venue.

[Scott_Burroughs]

My guess is that TEP stands for Thomas E. Paul, Doyen.

[Mike_Cirba]

I'm working on a Tepometer, which will register and calculate these scores automatically.  
 

Bob;

Which holes had the highest Tepmeter reading?

[BCrosby]

Mike - I didn't have time to do individual holes. I'll try to do some tonight.

Historically, 13 and 15 at ANGC have had the highest TEP Values measured to date. 13's number was even higher before they lenghtened the hole. Not as many birdies and eagles as there used to be.

Bob

[BCrosby]

The limiting (i.e. perfect) TEP Value happens when (using simple numbers):

UP  P   OP  

10  10  10, that is, there is perfect score distribution.

(i) UP/OP is 100%.

(ii)UP + OP (20)/P (10) is 200%.

(iii) (i) x (ii) = 200%, which in my shorthand is a 200 TEP Value.

Your other question is a very good one. It's one I've worried about because I've run across holes where there are more UP than OP. That gives you funky numbers if UP is always divided by OP.

This is my solution. What matters is the ratio, the spread. Not which category is the numerator or the denominator. Thus I have adopted a rule that you always divide the lower number by the higher number. It's a fudge, but the more I thought about it, the less I think it's a fudge that matters given the goal here is the ratio of the categories. It doesn't matter which is higher or lower. I just want the percentage of either one is to the other. Better mathematicians than I may find the foregoing reasoning problematical. I'm happy to be corrected if that is the case.      

Great question.

Bob

P.S. I just noticed that the post I was responding to has disappeared. Please repost. You asked some good questions.

[CHrisB]

Bob,
(Edit - I deleted my previous post because I thought I had figured it out before you could respond...)

OK, I think I've got the methodology now. If the UP/OP or (UP+OP)/P is >1, you just invert it, right? So the 200 comes from an equal number of UP, P, and OP scores. If so, then...

Using the data from the 2003 Masters (all 4 rounds), the highest TEP scores are:
64 (7th hole)
59 (13th hole)
48 (3rd hole)
39 (8th hole)
Small targets, hit 'em and birdie is likely, miss 'em and bogey is likely.

and the lowest TEP scores are:
9 (1st hole)
9 (18th hole)
13 (11th hole)
14 (5th hole)
Tough par 4's with few birdies.

From just the 4th round only,
the highest TEP scores are:
64 (13th hole)
56 (3rd hole)
46 (16th hole)
37 (7th hole)
Small targets, hit 'em and birdie is likely, miss 'em and bogey is likely.

and the lowest TEP scores are:
3 (12th hole)
7 (2nd hole)
7 (18th hole)
13 (15th hole)
Par 5's that most everyone birdies, the long par-4 18th, and the 12th where everyone plays left of the Sunday pin and makes par or worse.

Thoughts about the TEP score:
(1) I don't really think you can calculate a reliable TEP score for an entire course, because it is possible for a course to have a high TEP number while at the same time every hole on the course has a low TEP number. For example, if you have 9 really hard holes with scores skewed over par, and 9 really easy holes with scores skewed under par, then the course will have a high TEP score, which would indicate a very strategic course with no strategic holes!!
(2) Does the TEP score rely too heavily on par? Take a 490-yard par 4 and, because of its length alone, it will probably have a low TEP score with few birdies. But lengthen it 10 yards and make it a par 5, and all of the sudden all those pars become birdies and the TEP number changes. Better example: take #13 at ANGC...change nothing but the par from 5 to 4 and the TP number changes from 50 (for the 2003 Masters) down to 1, because only 3 3's were made there. I'll bet the TEP number would indicate very few great "strategic" long par 4's (or 3's).

(Sorry to get overly statistical, but it's a fun exercise for a former stat guy like me!)

[BCrosby]

ChrisB -

You and I gotta get a room. Great stuff.

Your questions in order:

1. I agree. Course-wide TEP Values may not be reliable for the reasons you give. I don't think those reasons apply to the courses played for the 2003 majors. But I haven't checked it out in detail. Will do so. But your point is certainly a valid one.

2. The TEP Value depends on par, yes. This was the subject of some very long discussions when I first trotted out the concept about a year or so ago. I think that is a strength, not a weakness, of the theory. To cut the the quick, the par of a hole matters in a medal play tournament because it sets playing expectations at the margins. It is at the half par holes we all like so much - ANGC 13. TOC 17. CPC 16 - where those marginal decsions - the go/no go - plays out most forcefully and often. There the line between success and failure is most stark. Those also happen to be the holes that tend to have the highest TEP Values. Usually. (But see note below re: no. 15 at ANGC)

A note:

I come up with different TEP values for your four highest scoring holes during the 4th round. (You may have skipped the last step in your calcs.?) I get:

13 - TEP 64
16 - TEP 45
3   - TEP 56
7   - TEP 37

That suggests, I think, that the existence of the Gay Brewers et al. in the field the first two days materially skewed the composite scoring.

And let's talk about how strategic little no. 3 is. Wow.

Also interesting is that no. 15 comes out with an abysmal TEP Value of 14 on Sunday. The field had only 3 bogies on the hole. All other scores were bunched at par and birdie.

Getting back to your point about the system's reliance on par, this result on 15 would suggest that the hole is mis-parred. It should be a par 4.

Which yields a corollary to the TEP Theorem which states:

Par on any hole should be set at a number that maximizes the TEP Value for that hole.

We'll call that the ChrisB Corollary.

Bob
 

[TEPaul]

Bob:

This all looks like some interesting stuff and I thank you very much for creating the mathematical procedure and coming up with the results. It also shows what a complete mathematical dunce I am--I've no real understanding of the formula. I'm also a little hazy why the actual par matter--or does it really when you say the so-called "half pars" seem to be the most interesting anyway? What do you suppose this says about what the (perhaps) "reality par" is for the tour pro set? In other words you just said #15 is in results basically a par 4.

How would you perceive a hole for its strategic value that has a fairly equal amount of pars and birdies like Riviera's #10 and not much in the way of bogies or worse? If there were something like 30% pars, 30% birdies and 20% bogies and 20% worse what would the basic TEP value show on that?

[TEPaul]

"Which yields a corollary to the TEP Theorem which states:
Par on any hole should be set at a number that maximizes the TEP Value for that hole.
We'll call that the ChrisB Corollary."

Bob:

Really? That's fascinating. Does that mean if golf firmly applies the "ChrisB Corrollary" and rearranges hole pars all over the place that it'll turn professional golfers and such into true strategic practioners or even strategic geniuses?  How cool! If so lets make the USGA/R&A convert par to the "ChrisB Corollary".  

[CHrisB]

Bob,
Oops...forgot the doubles and triples...I've recalculated and edited my previous post.

Interesting that the 7th has the highest TEP score from the 2003 Masters. Definitely a hole that can be birdied because the target is small but the slope of the green makes getting up and down tough. So it is a good tournament hole but is it necessarily "strategic"?

Getting back to your point about the system's reliance on par, this result on 15 would suggest that the hole is mis-parred. It should be a par 4.

Actually, the TEP number suggests that it wouldn't be any better as a par 4, because only 5 3's were made there in the tournament, compared to 183 scores of >=5. But maybe it's a great 4 1/2!

[Jim_Kennedy]

BCrosby,
I'm not going to say that I understand your formulations but I am still going to ask you a question.

Do you think you'd arrive at more reliable conclusions if you were to use only the last two rounds of major championships?
Players near the cut, slightly under or over it and those comfortably positioned for the weekend may play quite differently on Thur/Fri than on Sat/Sun. Heck, Sunday alone could very well be the truest scoring day.

[BCrosby]

Jim -

Yes, I agree. I mention a couple of times above that the Gay Brewers and Arnold Palmers playing the first two rounds at The Masters really skew the numbers. To a lesser extent the same would be true in a normal Tour event. Using 3rd or 4th round scores would be more reliable.

I did the TEP's for the last round of last year's Masters and they seem to fall more into place.

The whole point of this exercise is to see if there is a way to quantify the degree to which a hole plays strategically. It is intended as a measure of the extent to which a hole allows players to take different approaches in playing it. We are, in essence, testing an empirical thesis that scoring dispersion is a sign of such holes. Obviously, then, to the extent you can homogenize the skills of the players posting scores, the more reliable your scoring spread numbers. So yes, using fourth round scores would be the best data.

ChrisB -

15 at ANGC is a doozy. Very odd scoring there last year. Not unlike the scoring this year at the 10th at Riviera. Lots of birdies, lots of pars, no bogies. Both may be one time aberrations or both may be hinting at changes in the game that are rendering the shot options on those holes less interesting. Or maybe the TEP Conjecture is missing something. I don't know.

Also note the differences between the full four round TEP Value for 7 at 63 (pretty good) and the the last day TEP Value of 36 (pretty mediocre). As noted above, the existence of the Gay Brewers in the field may account for the difference.

I think the ChrisB Corollary works. The result for 15 is as you say, it ought to be a par 4.5. But, heck, if you've got the data to back up that conslusion, its not just rank speculation. And that alone is progress. N'est-ce pas?

Tom Paul -

I have no idea where this is going, but it is fun to mess around with it. Don't tell anyone I said this, but I think the TEP Conjecture is on to something interesting and could be used for lots of purposes when talking/arguing about golf architecture.

For example, it highlights the stark contrast in scoring spreads between USGA type set-ups and more open, more strategic set-ups and, thus, explains (to me at least) why one type of tournament is less interesting to watch than the other.

But time will tell if it has any untility. We'll see.

Bob  

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