Odds of beating a player rated x

[Steve West]

Maybe should have stated that for those with a stable rating, the score they would expect to average is whatever score matches their current rating.

Well then, here's to hoping my rating is anything but stable.

 

[grodney]

What is the SSA-to-length ratio for Brandywine and Iron Hill? Or length-to-SSA?

For the tournaments mullethead analyzed, anyway?

 

[grodney]

Okay, thanks. So two things to consider.

1) Slope Theory. Says that for two courses with the same SSA, lower-rated players will play worse (than their rating) on the tighter and more penal one.

2) Non-linear Theory. If I'm understanding what mullethead (and others) are saying, for two courses with different SSA, lower-rated players will play better (than their rating) on the higher SSA one.

I think it's entirely possible that both these things exist, and to some extent cancel each other out. If nothing else, they make it hard to isolate either one.

To show #1 well, you need courses with the same SSA but a different makeup (some tight, some open). For #2, you need courses with the same makeup, but different SSAs.

 

[Lewis]

I think it's entirely possible that both these things exist, and to some extent cancel each other out. If nothing else, they make it hard to isolate either one.

To show #1 well, you need courses with the same SSA but a different makeup (some tight, some open). For #2, you need courses with the same makeup, but different SSAs.

And you'd need enough rated rounds by a range of players across a range of dates to get any kind of reliable information about the nature of the courses. In the end, you may end up being able to say "this course has such and such tendencies", but not be able to identify the features that make it so.

 

[jeverett]

Okay, thanks. So two things to consider.

1) Slope Theory. Says that for two courses with the same SSA, lower-rated players will play worse (than their rating) on the tighter and more penal one.

2) Non-linear Theory. If I'm understanding what mullethead (and others) are saying, for two courses with different SSA, lower-rated players will play better (than their rating) on the higher SSA one.

I think it's entirely possible that both these things exist, and to some extent cancel each other out. If nothing else, they make it hard to isolate either one.

To show #1 well, you need courses with the same SSA but a different makeup (some tight, some open). For #2, you need courses with the same makeup, but different SSAs.

Honestly, I think to really be able to get at the potential underlying mathematics, we might have to take a step backwards. The problem with using rating system features like SSA for these kinds of analyses is that the system is cyclical/recursive. i.e. if there are problems with one aspect of the rating system, they will filter through all aspects of it: if there is a problem with slope/linearity, there may well be a problem with SSA's too.

To me, the biggest question that would need to be answered is this: are scores in disc golf distributed normally? i.e. if we take (only) round data, do we really see a nice, normal distribution? Is this normal distribution consistent across all courses/layouts? Getting sufficient sample size for this, however, is a challenge. Worse, we also need to ensure representative sampling (i.e. that the player pool we're sampling is truly representative of the range of player 'skill'). For example, from PDGA statistics, the average 2014 PDGA member had a rating of ~899.8. So in order to make sure we're observing a normal distribution, we'd also need to ensure that this 'skill' of player really is the average player quality (i.e. that there are the most of them in the player pool for each course/layout).