Odds of beating a player rated x

[Cgkdisc]

I gave the example I did because it explains the phenomenon better. Unfortunately, we can only score in one-throw increments in our game. There's not such a thing as 0.7 throw or 0.2 which would add more precision. Throws are a little blunter instrument for measuring performance versus ratings but at least they are known values as you play. But ratings can be more precise as indicated in previous posts. It's a fact that one throw is legitimately worth more rating points on a lower SSA course than higher SSA course. It's a fundamental fact of the ratings process, not just because I says so, but the math dictates it has to be that way. So if two players play a course with a higher SSA and one with a lower SSA and they tie in total score, if one shot better on the lower SSA course, that player actually shot better overall.

 

[jimimc]

Your comparing scores at different courses at different times. I'm comparing shooting the same courses at the same time. Why should playing better on the harder course count against you. I understand the compression of scores on the harder course, but the ratings on the harder courses should be weighted more. I know the ratings on a 27 hole course are weighted. What's the difference in shooting a 75 on an 18 hole course or a 27 hole course. Same amount of throws should be weighed the same. And yes I know your formula uses a per hole average, but beating some one by one stroke on a par 3 shouldn't actually count more than beating some one by one on a par 4. Using the compression system it does. A par 54 course counts about 10 points per stroke while a par 72 comes out to 5 points.

 

[jimimc]

Better example. I beat some one by 18 strokes at Brandywine. Par 54. I win by 180 ratings points. I beat the same person, once again by 18 strokes at Iron Hill. Par 72. I win by 90 ratings points. It's the only flaw I see in your system.

 

[biscoe]

The least probable round is the best round regardless of course length/difficulty. Probability of round scores will plot out as a bell curve rather than a straight line. The linear math used in the ratings system does not fit the real world data therefore the need for compression.

Arrgghh! Been there done that- swore I wouldn't anymore. I'm done here.

 

[jimimc]

And the flaw I see is it's not weighted. I don't want my other 90 ratings points, but it should count more when I play better on the harder course.

 

[Cgkdisc]

You talk about compression like I made it up. We discovered it, did not create it. If two players 50 points apart in ratings (say 1000 and 950) average 5 throws apart in scores at SSA 50 but average 7 throws apart on an SSA 70 course, one throw is worth 10 points (50/5 throws) on the SSA 50 course and it's worth 7 pts on the SSA 70 course (50/7). We didn't create that in the system. We discovered it from the data over 10s of thousands of rounds.

Even more surprising might be that the same par 4 hole will impact ratings differently based on the total course par. That's because the unit of measurement for calculating ratings is a course score, not individual hole scores. A hole contributes its percentage to the total score on the course. So the same par 4 that averages 4.0 for 1000 rated players will contribute 4/72 to a par/SSA 72 course = 5.5% but it will contribute 4/54 to a par/SSA 54 course = 7.4%. So you can see why one throw is worth more on the lower SSA course because it contributes a higher percentage to the total course score/rating.

 

[Cgkdisc]

The least probable round is the best round regardless of course length/difficulty. Probability of round scores will plot out as a bell curve rather than a straight line. The linear math used in the ratings system does not fit the real world data therefore the need for compression.

Arrgghh! Been there done that- swore I wouldn't anymore. I'm done here.

A lower score is less probable overall but not to each player. The score that matches a player's rating on the course has the same probability for each player. McBeth has the same expectation of shooting 46 on an SSA 50 course as a player at 950 rating has of shooting a 55 or an 830 player has of shooting a 67. The overall expectation of scores being thrown is irrelevant to the linearity of probabilities for each player's performance.

 

[jimimc]

I get the compression. I get that a better player should beat the other player by more on the harder course. I'm just saying it should weigh more. If I'm expected to beat a player by 27 on a par 3 27 hole course, it should count the same if I'm suppose to beat him by that same 27 on an 18 hole course.

 

[jimimc]

OK don't be offended. Is it possible the compression is slightly off. When ever we have just lower rated players playing the course, the SSA goes down by 1 or 2 and when we have just higher level players playing the course the SSA goes up.

 

[jimimc]

It's also much harder for a good player to shoot above his rating on a higher SSA course than it is a lower level player.

 

[Cgkdisc]

The SSA is contingent on the playing conditions including tournament pressure. That's why you see higher SSAs when higher rated players play a course because it's usually in higher tier tournament mode. It's only a 5-7% effect but it's been confirmed it's there. That's why league SSAs are consistently lower than tournament SSAs everywhere.

 

[Cgkdisc]

It's also much harder for a good player to shoot above his rating on a higher SSA course than it is a lower level player.

Where's your proof? There's no statistical basis we've seen. It may be more of a problem with low SSA courses because good players are already shooting near their best and sometimes don't have room to go lower without acing.

 

[Cgkdisc]

You should limit the analysis to just propagators, not the whole field of players. Propagators have their ratings shown in bold type on the tournament scores page. I would also suggest that the two fields for analysis be split at the rating of the propagator average versus 1000.

It wouldn't surprise me that you see more top players not doing as well getting better ratings at Iron Hill and also other wooded courses with certain types of hole designs. Castle Hayne has been notorious for not giving up good ratings for top players and I suspect for similar reasons.

When the SSA comes out close to the legit par value, it means there are several more holes where the gold scoring average is above par such that preventing bogey is the goal versus the ability to birdie. These types of holes can exist on open courses like Winthrop Gold. But on those types of holes, the challenge comes from OB, not vertical obstacles like wooded courses. So top players have a better chance to regularly shoot a hot round on these open holes and avoid the OB. On wooded courses with these types of holes, every player has to deal with the tight fairways and especially the doglegs that cannot be defeated with power.

 

[Cgkdisc]

General statement. I think players have an expectation that all courses with the same SSA will have a similar range of ratings for the same pool of players. That's not the case based on the type of hole designs on the courses which will narrow or expand the potential range. This is what Jimimc was concerned about. It's a legit concern. But we don't have enough data or taken the time to drill down to hole designs to provide guidance on this element.

 

[paulw]

I was waiting for the reason that the golfer who shot better on the lower SSA course should win since his variation of score is more meaning, if he played his best on the lower SSA course it will translate to less overall throws.

Not really clear in the above statement.

If a current 1040 player played every round over the next 2 years at the weekly PDGA tournament at IH with plenty of propragators, barring injury and other non-IH factor on his round scores, would you expect his rating to be 1040?

 

[Cgkdisc]

Usually a player will need to continue playing a similar mix of tournaments, courses and levels of competition to maintain the rating they earned from playing that mix of courses and level of competition. One player example that shows how focusing on playing the course versus your competition is important is Darrell Nodland in North Dakota. This guy has maintained a high level of excellence even though it's rare that he gets to play anyone within 20 points of his rating. He continues to destroy in smaller events even when he doesn't have to to win and plays a wide mix of course SSAs in the process. Take a look at Patterson Lake for example. http://www.dgcoursereview.com/course.php?id=743

 

[Cgkdisc]

All pros played the same day but it was tee times. So that sometimes messes things up a bit if there are variable wind conditions.

 

[Cgkdisc]

If you are only looking at MPO, then of course they played the same tees. However, I think some of the pro divisions including FPO may have played two shorter tees at Fountain. You can easily confirm any differences by looking to see if the rating for the same score in FPO or MPG matches the rating for MPO that round.

 

[Steve West]

... The score that matches a player's rating on the course has the same probability for each player. McBeth has the same expectation of shooting 46 on an SSA 50 course as a player at 950 rating has of shooting a 55 or an 830 player has of shooting a 67. ...

Really? On the course where I expect a 67 (with my 830 rating), I am not surprised by any score from 62 to 72. It would seem that McBeth would be shocked to get a 41 or a 51. Isn't my range of scores more spread out?

I don't doubt that my most likely score is 67, but I would think I would hit it on the nose less often than McBeth would hit his 46.

Or did you mean to say " 46 or better"?

 

[Cgkdisc]

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.