Par Talk

[Steve West]

He obviously would. However, assuming that an expert can make a "recovery" shot, at some likelihood reasonably close to his likelihood of making an errant shot, the median score should still be par. The only time this wouldn't be the case is if you were dealing with a hole with excessively abundant and punitive hazards.

Let's look at the toughest possible median-score par 3, where barely 50% of the players get 3 or better. That means half the players have an unrecovered error, right?

To me, that says 79.37% of the players avoid making an unrecoverable error on the first throw, and 79.37% of the players avoid making an unrecoverable error on the second throw, so only 63.00%% are still on track for par. Then, on the third throw, 79.37% of the players avoid an unrecoverable error, leaving 50.00% of players successfully getting par.

Now tack on one more throw to that par 3 by moving the tee back one throw. Make that throw just as hard as the other 3, so that 79.37% of players can do it successfully. This par 4 takes the same quality of play as the par 3, so it should be just as tough, or the toughest possible par 4. Since only 39.69% of the players successfully completed all four throws, that would be the equivalent cutoff point for par 4.

This is why it's important to look beyond the statistics and look at how a hole physically plays to make a par determination. I think in many cases the median could reasonably indicate a par that is less than "throws to reach plus two", but I would suggest that if it ever indicated a par greater than that, the true par should be "throws to reach plus two".

I agree human review of the physical hole is good, no matter the statistic. That's why I would not define par according to a statistic.

I'm having trouble picturing a hole where the median score would be higher than "throws to reach plus two". Wouldn't that indicate it actually takes another throw to "reach"?

 

[Karl]

This par 4 takes the same quality of play as the par 3, so it should be just as tough, or the toughest possible par 4.

I'm thinking not - as while any one shot on any of those two (the 3par and the 4par) holes are equally hard, i.e. the "quality of play PER SHOT" is the same, there are more shots involved in the latter.

Did you ever analyze the PGA's stats for shots per type of hole and distances to the green per the same? A quick synopsis...

3pars = 3.0, longish
4pars = 4.1, shorter than "longish"
5pars = 4.7, shorter than "shorter than "longish""

Through golf "evolution", 3pars can be reached in 1, 4pars should be reached in 2 about the same amount of times (even after some less than stellar tee shots) as 3pars, and 5pars make up any egregious goofs along the way in the other 2 types.
Note that if 5pars were TRULY 3 shot holes, they'd have to be 900yds long and might median in at 6+ (even for PGA pros)
..read: no fun.

 

[Steve West]

I'm thinking not - as while any one shot on any of those two (the 3par and the 4par) holes are equally hard, i.e. the "quality of play PER SHOT" is the same, there are more shots involved in the latter.

Are you saying that the quality of play per shot to get 4 on a par 4 should be higher than what it takes to get a 3 on a par 3?

Did you ever analyze the PGA's stats for shots per type of hole and distances to the green per the same?

Not quite. What I did do is apply my formula to the golf scoring distributions. It reproduced virtually all the pars EXCEPT that on most courses my formula would say that two of the par 5s should be par 4s. I've read from a few discussions of course set-up that golf likes to have a couple of birdie hole par 5s. So, I think they know they're setting par too high on those.

 

[Karl]

Are you saying that the quality of play per shot to get 4 on a par 4 should be higher than what it takes to get a 3 on a par 3?

"Shot for shot", IMO, no. And I'm guessing they don't think so either. This is because there are more shots involved in a 4par than in a 3par. (I'm now guessing) they want 3s and 4s to be "about the same" with 5s to be 'glory holes' - therefore each shot on the 4s 'might' (or could) be a little easier.

It's very hard to improve on a "birdie" on any 3par or 4par, but getting worse than a bogie, and sometimes way worse, happens moreso (even for the best).

 

[Steve West]

"Shot for shot", IMO, no. ...

I think that means you're agreeing that a smaller percent of players need to get a 4 to call hole par 4 than the percent of players that need to get a 3 to call a hole a par 3.

What about the other way? If 50% of the players getting a 3 is enough to call a hole a par 3, can we call a hole a par 2 if 50% get a 2? Or, should we not call it a par 2 until 63% of the players get a 2?

 

[Karl]

I think that means you're agreeing that a smaller percent of players need to get a 4 to call hole par 4 than the percent of players that need to get a 3 to call a hole a par 3.

I think you (as do most people with a vested interest in one side of an argument) are cultivating your ability to ask leading questions to make your side of said discussion seem more credible. Don't take it personally - a lot of said same people don't even know they're doing such.

It's easy to "control" the direction of a discussion through the asking of (all) the questions. Lawyers, politicians, and reporters do it all the time...and we wonder why "the news" comes out like it does.
Let people speak for themselves.
I personally have no skin in this game, and am just stating facts, playing devil's advocate, and calling out those who try to mislead others.

Ps: I haven't had the chance to think about your latest question(s).

 

[Karl]

Had a chance (to digest your questions in #3425).
In a nutshell, I don't need "statistics" to determine the par for a hole. Never have, never will.

 

[DG_player]

Let's look at the toughest possible median-score par 3, where barely 50% of the players get 3 or better. That means half the players have an unrecovered error, right?

To me, that says 79.37% of the players avoid making an unrecoverable error on the first throw, and 79.37% of the players avoid making an unrecoverable error on the second throw, so only 63.00%% are still on track for par. Then, on the third throw, 79.37% of the players avoid an unrecoverable error, leaving 50.00% of players successfully getting par.

Now tack on one more throw to that par 3 by moving the tee back one throw. Make that throw just as hard as the other 3, so that 79.37% of players can do it successfully. This par 4 takes the same quality of play as the par 3, so it should be just as tough, or the toughest possible par 4. Since only 39.69% of the players successfully completed all four throws, that would be the equivalent cutoff point for par 4.

I'll just re-quote myself because I think you're example fits what I was referring to:

"However, assuming that an expert can make a "recovery" shot, at some likelihood reasonably close to his likelihood of making an errant shot, the median score should still be par. The only time this wouldn't be the case is if you were dealing with a hole with excessively abundant and punitive hazards."

I'm having trouble picturing a hole where the median score would be higher than "throws to reach plus two". Wouldn't that indicate it actually takes another throw to "reach"?

It wouldn't necessarily mean that. It could mean the throws to reach are very difficult and missing them carries a severe penalty. I know I've watched a few holes on coverage where the commentators said the average score was a stroke higher than par, even though the hole was theoretically reachable (albeit with 2 spectacular shots with a decent dose of good fortune).

 

[DG_player]

So, is your logic: Because tweener holes exist, Recreational par is OK to use for Open players?

Not saying it is or isn't. I just don't think it's a big deal either way. Everyone watching, everyone playing knows a birdie is a must (or a par depending on the par).

You don't see a big uproar in ball golf over reachable par 5s. Usually it's just some commentary like: "Not sure player A's score will hold up, player B's still on the course with 2 par 5s ahead of him."

 

[DavidSauls]

You don't see a big uproar in ball golf over reachable par 5s. Usually it's just some commentary like: "Not sure player A's score will hold up, player B's still on the course with 2 par 5s ahead of him."

Is that because player B is expected to get 4s of them? Or just has a reasonable chance to get a 4 on either, or both, like a basketball team down 3 with time for one shot?

In all honesty; I don't follow golf enough to know. If player B has a 40% chance of getting 4s on each of those holes, a 1-shot lead by player A in the clubhouse is a bit tenuous. If player B is likely to get 4s on them, even more so.

 

[DavidSauls]

Steve: By trying to quantify errors, aren't you wandering away from expected score for a given hole, towards expected result for each shot?

 

[Steve West]

Not saying it is or isn't. I just don't think it's a big deal either way. Everyone watching, everyone playing knows a birdie is a must (or a par depending on the par).
...

Then why not just call it whichever score everyone knows they need to get?

That's a semi-serious question, what is stopping us from doing that?

With 20% growth every year, we can never say "everyone knows". The new players don't.

 

[Steve West]

Steve: By trying to quantify errors, aren't you wandering away from expected score for a given hole, towards expected result for each shot?

Yes, away from expected score, but toward expected score with errorless play. Par isn't just the expected score. First, you throw out all the scores that were not a result of errorless play. The expected among those - and only those - scores is par.

For holes with more throws, there are more errors, so after you throw those out, there are fewer scores left. So, the threshold for setting par needs to be a smaller percentage of players.

 

[DG_player]

Yes, away from expected score, but toward expected score with errorless play. Par isn't just the expected score. First, you throw out all the scores that were not a result of errorless play. The expected among those - and only those - scores is par.

For holes with more throws, there are more errors, so after you throw those out, there are fewer scores left. So, the threshold for setting par needs to be a smaller percentage of players.

Consider the following throws to complete a random hole:

#1 exceptional shot - errorless shot
#2 errorless shot - errorless shot - errorless shot
#3 errant shot - exceptional recovery shot - errorless shot
#4 errant shot - errorless shot - errorless shot - errorless shot

I'm assuming you would discard #4 from calculating par and use #1 and #2, however would you discard #3 as well?

 

[Steve West]

Consider the following throws to complete a random hole:

#1 exceptional shot - errorless shot Score=2
#2 errorless shot - errorless shot - errorless shot Score=3
#3 errant shot - exceptional recovery shot - errorless shot Score=3
#4 errant shot - errorless shot - errorless shot - errorless shot Score=4

I'm assuming you would discard #4 from calculating par and use #1 and #2, however would you discard #3 as well?

I would exclude #3 if I could. For example, if I were setting par by actually watching experts play the hole and noting who did what. I would exclude #1 as well.

My method (or any score-based method) cannot automatically exclude #3, because the knowledge of how the player got the score is lost. Nevertheless, these methods work for a large majority of holes because there are more errorless throws than errant or exceptional.

#1 is easier to deal with, because the only way to get a score below par is with an exceptional throw, so we know what to do with those scores.

Perhaps one day Udisc will make all the stats easily accessible (by player and hole) so we can identify #3 directly.

 

[DG_player]

I would exclude #3 if I could. For example, if I were setting par by actually watching experts play the hole and noting who did what. I would exclude #1 as well.

My method (or any score-based method) cannot automatically exclude #3, because the knowledge of how the player got the score is lost. Nevertheless, these methods work for a large majority of holes because there are more errorless throws than errant or exceptional.

#1 is easier to deal with, because the only way to get a score below par is with an exceptional throw, so we know what to do with those scores.

Perhaps one day Udisc will make all the stats easily accessible (by player and hole) so we can identify #3 directly.

I understand #3 and #4, but why would you exclude #1? It's a score absent an "errant throw".

 

[Steve West]

I understand #3 and #4, but why would you exclude #1? It's a score absent an "errant throw".

Par is the expected score among errorlessly obtained scores. By definition, (exceptional throw) this score is not expected.

If I were following players and saw a 200 foot throw-in, I would not think that player expected that score. So, it would be cleaner and easier to leave it out of the pool of par quality scores, rather than try to tease it out later.

However, it probably does not matter whether it is included in the errorless pool or not. At the end of the day, there won't be enough of them to call that score par anyway.

To be clear, in the formulas like "at least x% get", it does contribute to the "at least" part. So, the formulas leave it in. The reason is that an exceptional throw is one that reduces the eventual score on the hole by one throw, compared to a non-exceptional throw. So, we can infer that if they go n-1 with an exceptional throw and an errorless throw, it is very likely they could have gotten n with three errorless throws.

So, you can leave it in and see later by the numbers that it was not expected, or recognize it as unexpected and leave it out from the start. No real difference, but we're talking high concepts here, not practicalities.

 

[lyleoross]

I'm gonna disagree with trying to do analysis via errorless throw. To start with, a bad throw for one player, disc in position a, might be a good throw for another player, disc also in position a, depending on throwing styles. You're still looking at outcomes. Furthermore, a spanked throw that hits the tree and bounces into a nice lie isn't an errorless throw, no matter what the outcome.

Your errorless only has meaning when looking at outcomes, via math. Math doesn't go, "Oh, errorless play!" It says these throws, when examined in this way, give this result. You can call a subset errorless, if it makes you feel good.

Folks are too enamored with the notion of errorless play. There is no such thing. There is play that is better than your opponent's play. I've never seen an errorless throw. Anyone who thinks they have are looking at outcomes and saying errorless cause they got the outcome they wanted. I suppose you can say a throw that gives the outcome you want is an errorless throw?

That isn't to say you can't do analysis, but you may not be looking at what you think you're looking at, as entertaining as it might be.

 

[DG_player]

Par is the expected score among errorlessly obtained scores. By definition, (exceptional throw) this score is not expected.

If I were following players and saw a 200 foot throw-in, I would not think that player expected that score. So, it would be cleaner and easier to leave it out of the pool of par quality scores, rather than try to tease it out later.

I don't see how you get that out of the definition. The entire pool of expert scores includes bad, good throws, and great throws. If you're going to define par as the expected expert score with errorless play, it seems you should merely look at the subset of scores that do not include errant play. This subset would include scores that had exceptional throws. If an expert player occasionally will make a throw in, than it's expected that this will happen at some rate, and should be included in calculating par. The definition doesn't say "errorless, non-exceptional play".

 

[Steve West]

I don't see how you get that out of the definition. The entire pool of expert scores includes bad, good throws, and great throws. If you're going to define par as the expected expert score with errorless play, it seems you should merely look at the subset of scores that do not include errant play. This subset would include scores that had exceptional throws. If an expert player occasionally will make a throw in, than it's expected that this will happen at some rate, and should be included in calculating par. The definition doesn't say "errorless, non-exceptional play".

Good logic, I'll agree with that.