Par Talk

[Steve West]

I'm gonna disagree with trying to do analysis via errorless throw.

Right now, we're talking about the pure definition. Specifically, what par we would get by watching experts play and disregarding any scores that included an errant throw, then picking the expected score from among those.

This is not about my method of choosing a par based on scores. By the way, I'm no longer using the label "errorless" for my method. I need a new name, because as you point out, it's not truly choosing from among the errorlessly-gotten scores.

After we think about what score would result from errorless play, then we can use that thinking to choose among methods of selecting par from all the scores.

One issue at question is: If we did look at the pool of errorless scores and picked the expected from them, would a smaller percent pf players get par on higher par holes for the toughest holes at each par?

If the thinking about what score would truly result from errorless play can answer that question, then we can use the answer to assess which score-based (or distance-based) methods are closer what the definition actually means.

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.

True, but not a problem. Just ask the player if that throw was good or not. If not, leave that score out of the pool.

For experts, I would think the good positions are about the same. For Recreational par, less so.

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.

Right. The score from that player would be ignored.

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.

That is a correct statement about my method of picking par based on scores. But, we're not talking about my method right now. We're trying to see what would happen if the definition were applied literally with perfect knowledge.

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?

Yeah, wouldn't that be what errorless means? (Unless it gave you the outcome through a lucky break.)

Isn't errorless play pretty much like designer intent? Nobody ever throws the disc exactly in the middle of the invisible pipe, but if it gets through the gap, doesn't it still count as playing the way the designer intended?

I'm pretty sure there is something like errorless. Maybe errorless isn't the right word, but we all know immediately when we make a bad throw. Most throws clearly fall into one of two categories: being disappointed with it or not. Errorless are the throws you are not disappointed with - excluding the throws that you are not disappointed with only because you got a lucky break.

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.

OK, back to my method for now. It was not designed to suss out the scores that resulted in errorless play. (That would be impossible, as you point out.) It was designed to have the highest chance of picking the same score that we would get if we could suss out errorless play from looking at scores. I called it errorless as shorthand because matching the errorless score was the goal (as opposed to matching the average or most common or any other stat).

 

[Karl]

"...I need a new name..."

EAI? (Executed As Intended)

 

[Steve West]

"...I need a new name..."

EAI? (Executed As Intended)

Thanks for playing.

I can't use EAI, because looking only at scores doesn't really tell us whether the player got the score they intended. Besides, it sounds more like what CRP is getting at.

A description would be: A method that picks the score where at least a specified percentage of throws for each parlecule are good enough for par.

 

[PMantle]

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".

Ah, you've identified Steve's birdie reduction dealio.

 

[DavidSauls]

The problem I have with trying to quantify "errorless" is that shots aren't clearly exceptional, expected, or errors. They come in all degrees along a spectrum.

Defining errors as shots that increase the score, reflected in the hole results, misses the point that a shot might be slightly below average, or a bit more below average, but whether it affects the score may be influenced by that player's other shots on that hole. Not necessarily exceptional shots or clear errors, but other shots that are a little bit better, or worse, than average.

It also seems a bit circular: Par is the score without errors, and errors are shots that increase the score.

 

[DavidSauls]

I can't use EAI, because looking only at scores doesn't really tell us whether the player got the score they intended. Besides, it sounds more like what CRP is getting at.

I'm not sure if, by EAI, Karl mean "as intended by the player" or "as intended by the designer."

 

[aphilso1]

Defining errors as shots that increase the score, reflected in the hole results, misses the point that a shot might be slightly below average, or a bit more below average, but whether it affects the score may be influenced by that player's other shots on that hole. Not necessarily exceptional shots or clear errors, but other shots that are a little bit better, or worse, than average.

Ball golf has a formula for this, as they calculate "strokes gained" from every possible distance/lie combination. This article does a good job of explaining it: http://www.strokesgainedgolf.com/How-Strokes-Gained-Works.html

It wouldn't be a direct correlation to disc golf but, given enough data inputs, could theoretically be used as a starting point.

 

[Steve West]

The problem I have with trying to quantify "errorless" is that shots aren't clearly exceptional, expected, or errors. They come in all degrees along a spectrum.

Defining errors as shots that increase the score, reflected in the hole results, misses the point that a shot might be slightly below average, or a bit more below average, but whether it affects the score may be influenced by that player's other shots on that hole. Not necessarily exceptional shots or clear errors, but other shots that are a little bit better, or worse, than average.

It also seems a bit circular: Par is the score without errors, and errors are shots that increase the score.

Recursive, not circular. Recursive leads to a solution, even though the formula depends on itself. Circular would allow for any value of par to be the result of inputting that same value of par.

Fortunately, the fuzzy definition of errorless works OK because par is - in a sense - the big fat part of the scoring distribution; it's an easy target. As long as everyone uses 1000-rated play.

For example, if we merely labeled everything that was not clearly exceptional nor clearly an error as erroless, we would narrow down the range of possible par scores quite a bit. Then, take the second step of picking the expected score from among those, and it's hard to see how you would end up with a bad par.

 

[Steve West]

Ball golf has a formula for this, as they calculate "strokes gained" from every possible distance/lie combination. This article does a good job of explaining it: http://www.strokesgainedgolf.com/How-Strokes-Gained-Works.html

It wouldn't be a direct correlation to disc golf but, given enough data inputs, could theoretically be used as a starting point.

I really liked strokes gained. It's the ultimate stat for golf. I hope we can get there for disc golf, but it will be a while. Not only do we need to track millions of throws first, I think we will need to add at least one more dimension. (Unless disc golf hole become as homogenized as golf holes.) That means we'll need a lot more data than golf.

We have so many more lie types. We can't even say the tee is the same kind of lie for all holes. Some tees have a big tree in front of them, or a narrow gap to hit. Not too mention the different materials. There's no way to say that since this a 450 foot hole and the player is on the tee, their expected score is the same as every other 450 foot hole.

As for lie types, just think of the difference between being behind a tree where you can reach far enough to throw around it from a standstill vs. behind a tree where you can do a run-up, vs. being behind a tree where you have to pitch backwards.

But, to tie it back because it is a good concept to pursue, how many strokes gained does it take for a golf shot to be errorless? I would think it would be some range on both sides of zero.

 

[DG_player]

The problem I have with trying to quantify "errorless" is that shots aren't clearly exceptional, expected, or errors. They come in all degrees along a spectrum.

Defining errors as shots that increase the score, reflected in the hole results, misses the point that a shot might be slightly below average, or a bit more below average, but whether it affects the score may be influenced by that player's other shots on that hole. Not necessarily exceptional shots or clear errors, but other shots that are a little bit better, or worse, than average.

It also seems a bit circular: Par is the score without errors, and errors are shots that increase the score.

That's the problem with using a complicated statistical method to define par.

It makes much more sense to look at the physical layout of a hole, and come to a reasonable conclusion of how many shots it should take for an expert to hole out assuming they don't screw up. If you want to back that up with a simple statistical method, such as an average or median, to determine if the original conclusion was accurate, that's fine. However I don't see the benefit in doing anything more complicated than that.

 

[DavidSauls]

That's the problem with using a complicated statistical method to define par.

It makes much more sense to look at the physical layout of a hole, and come to a reasonable conclusion of how many shots it should take for an expert to hole out assuming they don't screw up. If you want to back that up with a simple statistical method, such as an average or median, to determine if the original conclusion was accurate, that's fine. However I don't see the benefit in doing anything more complicated than that.

I look at the statistics as a validation, not setting par. Set it based on expectations. Look at the numbers to see if that expectation was realistic.

But if the numbers show that reality didn't meet the expectations, high or low, should those results affect future expectations? If you expect a 4 and 70% get 3s, next year should you expect 4s, or 3s? If so, are statistics then setting par? Or merely advising it?

 

[DG_player]

I look at the statistics as a validation, not setting par. Set it based on expectations. Look at the numbers to see if that expectation was realistic.

But if the numbers show that reality didn't meet the expectations, high or low, should those results affect future expectations? If you expect a 4 and 70% get 3s, next year should you expect 4s, or 3s? If so, are statistics then setting par? Or merely advising it?

Hopefully you would use the information to tweak the hole in the future. If that's not an option for whatever reason, I guess changing par is an option, but I would still view the statistics as being in an advisory role.

 

[DavidSauls]

Hopefully you would use the information to tweak the hole in the future. If that's not an option for whatever reason, I guess changing par is an option, but I would still view the statistics as being in an advisory role.

Yes, always advisory.

Tweaking makes sense if it produces too much of the same score, or too wide a gap (more 2s and 4s than 3s). If possible.

But par must be assigned to good holes and bad holes alike.

In brief, the expected score. If the results tell us that we should have expected something other than what we initially thought, then in the future we should probably expect something different, too.

*

I only have to worry about this for one course and, without a lot of 1000-rated players and no events catering to them, it doesn't matter a whole lot. So we look at it subjectively: the way the holes were designed and intended to play. We look at the results---the median score, the most common score, even the average---and use judgment as to whether we should modify the pars we set.

 

[biscoe]

So we look at it subjectively: the way the holes were designed and intended to play. We look at the results---the median score, the most common score, even the average---and use judgment as to whether we should modify the pars we set.

How many have you had to change over the years (par, not the hole itself)?

 

[DavidSauls]

How many have you had to change over the years (par, not the hole itself)?

Two come to mind. They are holes that play well, are cool and fun to play, and we were arguing about the par to begin with. The best data we had was the open division and, after seeing their scores over a few years, I relented to setting the higher par. I still whine about it, and am surprised that the holes score as high as they do. If I was sole owner, I might have left them as originally set.

But that's being fairly casual about par because, as I said, we're not hosting elite-level events or a lot of 1000-rated players. For the past few years we haven't held singles tournaments, so it matters even less.

 

[Steve West]

...For the past few years we haven't held singles tournaments, so it matters even less.

So, should we get started talking about appropriate pars for doubles play?

 

[DavidSauls]

So, should we get started talking about appropriate pars for doubles play?

I don't even want to see how complex the formulas would be.

Our main event is a 4-man team-play events, with combinations of match play, best disc, and other formats. So even that wouldn't help us much.

But casual players keep asking "What's par on this hole", and we need an answer. Sometimes I have to stop and think, because it doesn't matter enough to me to keep them fresh in my mind. I'm a little uncomfortable with skill-level pars, but I suspect that our pars are blue-level ones.

 

[DG_player]

So, should we get started talking about appropriate pars for doubles play?

That's crazy talk!

 

[Steve West]

I don't even want to see how complex the formulas would be. ...

Well . . . too bad.


Because you'll not be able to look away. Actually, it's pretty simple if you use my method of setting par.

Let's take a step back. It's probably OK, and certainly the most practical, to just use the singles pars and see a lot of birdies or bogeys.

However, I want to know the theoretical expected (etc.) score of a pair of expert players.

And, since we don't have enough data about two 1000-rated players playing each hole, I wanted to find a method that uses the 1000-rated single-player scoring distributions.

Since my method is based on the chance that the player will make a good enough throw to get par, it's easy to extrapolate to doubles. If a single player has, say, a 90% chance of making a good enough throw, then in best throw a pair of 1000-rated players would have a 99% chance of making a good enough throw to get par.

So, I just need to adjust the exponents in my method. For best throw it means doubling the exponents. For example, for a par 3, the cutoff is 7/9ths raised to the sixth power instead of the 3rd. For Worst throw, the exponents are halved. For Tough throw, it's a combination since tough throw is best throw for the last throw, and worst throw for the rest.

Anyway, that leads to the following table:

To get par for each kind of play, pick the lowest score which at least the following percentages of singles 1000-rated players get.

Par	 Singles	    Best	   Worst	   Tough
  2	     60%	     37%	     78%	     53%
  3	     47%	     22%	     69%	     47%
  4	     37%	     13%	     60%	     41%
  5	     28%	      8%	     53%	     37%
  6	     22%	      5%	     47%	     32%

 

[biscoe]

Doubles par= singles par= triples par for the same level player. Of course the scores relative to it will be lower...