1. First off, this is good stuff, it’s nice to see someone with a brain try to rate golfers as opposed to Jason Sobel.

For the past couple of years, I’ve calculated a world golf ranking based on standardized scores across the world’s three biggest tours (PGA, NW, EPGA). You can see my full masters rankings here.

I think you have a couple of problems, though. For one, the European Tour is weighted to highly. I can tell you this, because I think I did a similar thing. I used to make no difference between playing on the European and PGA Tour and my odds looked a lot like that. In reality there is about a .21 standard deviation difference (~.6 strokes per round) between the PGA and European Tours. It’s about .35 for the NW Tour to PGA Tour.

I think that’s reason you are so high on the European Tour players like Schwartzel and Molinari.

I’d like to know how much of an impact recent play has in your rankings, because just looking at these off the top of my head I think it might be too much. I know in my rankings a player that is playing well recently should get a max bonus of around .2- .3 strokes per round. That is somewhat empirically derived, but mostly I came up common sense observation and by adjusting Vegas odds to my rankings.

Finally, using standard deviation of the sample I don’t think is accurate. I’m not sure positive about this, but from what I’ve done a players true standard deviation has a direct correlation between the players average score in relation to the field. There is no correlation in a single players standard deviation from year to year. Some years Tiger has a really low standard deviation, others he’s had a really high. This applies to almost every single player who has played a large sample of rounds from every year since 2002.

Hope that gives you something to think about and helps going forward.

• DanielM

Thanks for the very informative post!

1) Theoretically, if I have good connectivity between tours, the European events will be adjusted appropriately automatically. I’m rating each player at each event NOT vs. “other players” but against the “baseline” for that round. This baseline is calculated as the average of how the 80 “baseline golfers” did in that round.

That group could be only 10 in any given round, and not all of those golfers played on both tours. My regression may not properly capture the difference between the tours in difficulty of round. I’ll look at it a bit more today.

That said–the 0.6 per round. Is that just a general average? Because the difficulty of each round varies WIDELY based on weather/course/etc.

2) The best fit for projecting out of sample tournament results yielded a weighting that dropped from 1 in the most recent events to about 0.05 in the events and the start of 2009. Then, everybody is regressed with about 6.5 rounds (weighted at 1) of +2.5 or so golf. The weighting towards recency seemed a bit strong to me, as well.

3) Regarding standard deviation: you may be right on this. Perhaps I should just assign everyone a consistent standard deviation? That said, I did regress each player’s standard deviation to the mean pretty hard via Bayesian inference with a prior of Avg.

Do “Average Rating” and “Bayesian Rating” have the same baseline? If so, that’s a huge regression effect. Though maybe you need a huge regression effect with only two years of data.

• DanielM

Yes, they have the same baseline. There’s more than just the regression effect going on, though. There’s also the deprecation of the older results. Tiger’s oldest results are also his best results, so when they get weighted only 10% as strongly as his most recent results, that drops him a ton. There’s also regression to a baseline of +2.5 or so, but there’s only 6 rounds of +2.5 added to the weighted average–and a lot of guys have over 200 rounds. That effects the players with few rounds played a lot more.

3. DanielM

I’ll probably, if I have time today (I’m busy), try to revise the way I did the 80 baseline golfers to include a larger group and get a better connection between European and PGA tours. I agree with the various comments (twitter and here): it does look like the Euro players are rated unusually highly.

4. “That said–the 0.6 per round. Is that just a general average? Because the difficulty of each round varies WIDELY based on weather/course/etc.”

Yes.

The first thing I do is standardize the scores against everyone in the field. Obviously, it doesn’t matter if the course average is 75 or 69, the player’s relation to the field average is all that counts. That’s not to say a course plays at the same difficulty for someone playing at 8 a.m. as opposed to 1 p.m. I just hope most of that is randomness and balanced out in the long run, which I think it is pretty well.

The next step is to assign a field difficulty based on everyone’s raw average from above over a three-year period.

Finally, I take the adjusted z-scores and compare players rounds across tours. Over about 2000 rounds each way, players are on average .6 strokes better in relation to the field when they play on the European Tour. However, it does vary, like you said. The Dubai Desert Classic still boasts a stronger field than the Puerto Rico Open even though the European players raw rankings are inflated.

• DanielM

I see. I’m taking a different approach, but if we’re each doing it right the answer should be the same. I’m standardizing against a group of “baseline players”, and there should be enough of them that play each round to get a good grasp of how hard the round was. I’m going to re-run the regression with over 140 players as baseline, using a slightly different procedure.

I wish I weren’t getting a “cannot allocate memory for vector” error problem with R when I try to run it all that way. Apparently, no 2-300 MB block of contiguous RAM available?

5. EvanZ

Daniel, you had McIlroy top 10. Pretty good!

• Ben

Daniel’s looking even better today!

6. Neil Paine

Schwartzel!!!!!!

7. EvanZ

lol

“Who is Charl Schshwartszel? Did I misspell that? Will we set an all-time record for misspellings of contenders?”