{"id":434,"date":"2011-04-06T18:14:56","date_gmt":"2011-04-06T23:14:56","guid":{"rendered":"http:\/\/godismyjudgeok.com\/DStats\/?p=434"},"modified":"2011-04-06T18:17:50","modified_gmt":"2011-04-06T23:17:50","slug":"bayesian-golf-ratings-and-masters-preview","status":"publish","type":"post","link":"http:\/\/godismyjudgeok.com\/DStats\/2011\/golf\/bayesian-golf-ratings-and-masters-preview\/","title":{"rendered":"Bayesian Golf Ratings and Masters Preview"},"content":{"rendered":"

That’s right, golf.\u00a0 I’m taking up where Ken Pomeroy left off.\u00a0 A year or two ago, he developed a rating system for golfers–basically, he created a huge regression of all players and all specific rounds at tournaments.\u00a0 Each round was assigned a level of difficulty, and each player was assigned an overall rating.\u00a0 His numbers, prior to the PGA Championship in 2009, are on his website<\/a>, including odds for each player to win.<\/p>\n

I’m attempting to both continue the effort and take it a step further.\u00a0 I’m creating a Bayesian rating system that best projects out-of-sample (future) performance.<\/p>\n

To do this, I compiled all tournaments on the European and PGA tours for this year and the previous 2 years.\u00a0 I didn’t grab any other tour’s data, since it was a little harder to get a hold of.<\/p>\n

Next, I looked at the number of variables.\u00a0 ~2000 players and ~200 tournaments (with ~4 rounds each).\u00a0 That’s 2800 unknowns right off the bat!\u00a0 Ouch.<\/p>\n

So I simplified.\u00a0 I chose a subset of “baseline golfers” that played a bunch of rounds in the last 2+ years, across both tours.\u00a0 These ~80 golfers I defined to sum to 0, to set the baseline for each course.\u00a0 I then took the 800 tournament rounds, split them into 7 chunks, and solved for each chunk and the 80 golfers simultaneously.\u00a0 Thus, the 80 golfers could vary amongst themselves, but they had to sum to 0–and then the tournament round difficulties were estimated against them.\u00a0 Thus, some rounds were assigned a difficulty of 73, others 68.<\/p>\n

Once I had set a difficulty level for each round in the past 2+ years, it was time to get Bayesian.\u00a0 I didn’t do it explicitly like I have previously.\u00a0 I gave a weight parameter, slightly less than 1, and weighted the results of each round for each player by the (weight parameter)^n, where n is the number of weeks since that tournament.\u00a0 I then added in a regression toward a fixed value (A), with a weight (R).\u00a0 All ready, then!<\/p>\n

I took the players that have played more than 140 rounds in the past 2+ years, and minimized the prediction error ^2 for each round in their past 10 tournaments played.\u00a0 This gave me the weight parameter, fixed value (A), and weight (R).<\/p>\n

In order to do a prediction of The Masters<\/a>, I had to find out how much the players varied from round to round.\u00a0 So I calculated sqrt(average(predictionerror^2)) for the last 15 tournaments for each player.\u00a0 For the players with the most data, this average 2.78.\u00a0 I then regressed each player’s standard deviation toward that mean of 2.78, to get a true estimate of the standard deviation going forward.<\/p>\n

Well then.\u00a0 That’s about it!\u00a0 We’ve got a Bayesian prediction for the next tournament, and a per-round standard deviation.\u00a0 Perfect for a Monte Carlo!<\/p>\n

First, the ratings themselves, for the top 100 players of the US\/Euro tours:<\/p>\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
Rank<\/th>Players<\/th>Total Rounds<\/th>PGA<\/th>Euro<\/th>Bayesian Rating<\/th>Average Rating<\/th>Stdev<\/th>\n<\/tr>\n<\/thead>\n
1<\/td>Martin Kaymer<\/td>188<\/td>74<\/td>114<\/td>-1.45<\/td>-1.82<\/td>2.73<\/td>\n<\/tr>\n
2<\/td>Graeme McDowell<\/td>203<\/td>80<\/td>123<\/td>-1.40<\/td>-1.60<\/td>2.82<\/td>\n<\/tr>\n
3<\/td>Charl Schwartzel<\/td>233<\/td>68<\/td>165<\/td>-1.40<\/td>-1.68<\/td>2.92<\/td>\n<\/tr>\n
4<\/td>Lee Westwood<\/td>186<\/td>76<\/td>110<\/td>-1.39<\/td>-1.98<\/td>2.79<\/td>\n<\/tr>\n
5<\/td>Matt Kuchar<\/td>205<\/td>201<\/td>4<\/td>-1.32<\/td>-1.41<\/td>2.47<\/td>\n<\/tr>\n
6<\/td>Francesco Molinari<\/td>224<\/td>52<\/td>172<\/td>-1.31<\/td>-1.71<\/td>3.00<\/td>\n<\/tr>\n
7<\/td>Luke Donald<\/td>202<\/td>158<\/td>44<\/td>-1.21<\/td>-1.44<\/td>2.70<\/td>\n<\/tr>\n
8<\/td>Steve Stricker<\/td>175<\/td>171<\/td>4<\/td>-1.18<\/td>-1.77<\/td>2.70<\/td>\n<\/tr>\n
9<\/td>Nick Watney<\/td>206<\/td>194<\/td>12<\/td>-1.18<\/td>-1.32<\/td>2.95<\/td>\n<\/tr>\n
10<\/td>Rory McIlroy<\/td>208<\/td>98<\/td>110<\/td>-1.17<\/td>-1.68<\/td>2.89<\/td>\n<\/tr>\n
11<\/td>Paul Casey<\/td>166<\/td>106<\/td>60<\/td>-1.11<\/td>-1.64<\/td>2.50<\/td>\n<\/tr>\n
12<\/td>Phil Mickelson<\/td>193<\/td>167<\/td>26<\/td>-1.08<\/td>-1.39<\/td>2.82<\/td>\n<\/tr>\n
13<\/td>Tiger Woods<\/td>135<\/td>119<\/td>16<\/td>-1.04<\/td>-2.20<\/td>2.84<\/td>\n<\/tr>\n
14<\/td>Louis Oosthuizen<\/td>197<\/td>40<\/td>157<\/td>-1.01<\/td>-1.34<\/td>2.96<\/td>\n<\/tr>\n
15<\/td>Retief Goosen<\/td>236<\/td>164<\/td>72<\/td>-0.98<\/td>-1.39<\/td>2.77<\/td>\n<\/tr>\n
16<\/td>Raphael Jacquelin<\/td>232<\/td>6<\/td>226<\/td>-0.91<\/td>-0.98<\/td>2.56<\/td>\n<\/tr>\n
17<\/td>Thomas Aiken<\/td>196<\/td>14<\/td>182<\/td>-0.90<\/td>-1.10<\/td>2.63<\/td>\n<\/tr>\n
18<\/td>Anders Hansen<\/td>196<\/td>24<\/td>172<\/td>-0.88<\/td>-1.19<\/td>2.61<\/td>\n<\/tr>\n
19<\/td>Peter Hanson<\/td>202<\/td>48<\/td>154<\/td>-0.84<\/td>-1.37<\/td>2.87<\/td>\n<\/tr>\n
20<\/td>Justin Rose<\/td>210<\/td>176<\/td>34<\/td>-0.82<\/td>-0.98<\/td>2.69<\/td>\n<\/tr>\n
21<\/td>Dustin Johnson<\/td>190<\/td>186<\/td>4<\/td>-0.81<\/td>-1.13<\/td>2.86<\/td>\n<\/tr>\n
22<\/td>Hunter Mahan<\/td>209<\/td>205<\/td>4<\/td>-0.81<\/td>-1.13<\/td>2.69<\/td>\n<\/tr>\n
23<\/td>Richard Green<\/td>164<\/td>6<\/td>158<\/td>-0.80<\/td>-1.29<\/td>2.78<\/td>\n<\/tr>\n
24<\/td>Joost Luiten<\/td>145<\/td>0<\/td>145<\/td>-0.77<\/td>-1.03<\/td>2.75<\/td>\n<\/tr>\n
25<\/td>Alvaro Quiros<\/td>210<\/td>54<\/td>156<\/td>-0.75<\/td>-1.08<\/td>2.75<\/td>\n<\/tr>\n
26<\/td>Jamie Donaldson<\/td>209<\/td>0<\/td>209<\/td>-0.72<\/td>-1.01<\/td>2.83<\/td>\n<\/tr>\n
27<\/td>Edoardo Molinari<\/td>145<\/td>38<\/td>107<\/td>-0.71<\/td>-1.24<\/td>2.75<\/td>\n<\/tr>\n
28<\/td>Padraig Harrington<\/td>202<\/td>139<\/td>63<\/td>-0.71<\/td>-1.17<\/td>2.86<\/td>\n<\/tr>\n
29<\/td>Stephen Gallacher<\/td>163<\/td>8<\/td>155<\/td>-0.70<\/td>-0.83<\/td>2.60<\/td>\n<\/tr>\n
30<\/td>Robert Allenby<\/td>192<\/td>164<\/td>28<\/td>-0.70<\/td>-1.08<\/td>2.53<\/td>\n<\/tr>\n
31<\/td>Ernie Els<\/td>237<\/td>164<\/td>73<\/td>-0.70<\/td>-1.25<\/td>2.76<\/td>\n<\/tr>\n
32<\/td>Miguel Angel Jimenez<\/td>226<\/td>50<\/td>176<\/td>-0.69<\/td>-1.12<\/td>2.93<\/td>\n<\/tr>\n
33<\/td>Ian Poulter<\/td>188<\/td>118<\/td>70<\/td>-0.69<\/td>-1.15<\/td>2.80<\/td>\n<\/tr>\n
34<\/td>Anthony Wall<\/td>204<\/td>6<\/td>198<\/td>-0.69<\/td>-1.05<\/td>2.41<\/td>\n<\/tr>\n
35<\/td>Jim Furyk<\/td>182<\/td>182<\/td>0<\/td>-0.69<\/td>-1.32<\/td>2.57<\/td>\n<\/tr>\n
36<\/td>Rickie Fowler<\/td>150<\/td>144<\/td>6<\/td>-0.68<\/td>-0.79<\/td>2.72<\/td>\n<\/tr>\n
37<\/td>Tim Clark<\/td>197<\/td>175<\/td>22<\/td>-0.65<\/td>-1.12<\/td>2.47<\/td>\n<\/tr>\n
38<\/td>David Lynn<\/td>197<\/td>0<\/td>197<\/td>-0.65<\/td>-0.93<\/td>2.83<\/td>\n<\/tr>\n
39<\/td>Chris Wood<\/td>195<\/td>16<\/td>179<\/td>-0.63<\/td>-1.02<\/td>2.62<\/td>\n<\/tr>\n
40<\/td>Martin Laird<\/td>206<\/td>190<\/td>16<\/td>-0.62<\/td>-0.36<\/td>3.04<\/td>\n<\/tr>\n
41<\/td>Charles Howell III<\/td>234<\/td>234<\/td>0<\/td>-0.62<\/td>-0.72<\/td>2.75<\/td>\n<\/tr>\n
42<\/td>Robert-Jan Derksen<\/td>207<\/td>0<\/td>207<\/td>-0.61<\/td>-1.01<\/td>2.40<\/td>\n<\/tr>\n
43<\/td>Jean-Baptiste Gonnet<\/td>194<\/td>0<\/td>194<\/td>-0.61<\/td>-0.64<\/td>2.94<\/td>\n<\/tr>\n
44<\/td>Spencer Levin<\/td>225<\/td>225<\/td>0<\/td>-0.59<\/td>-0.55<\/td>2.88<\/td>\n<\/tr>\n
45<\/td>Bill Haas<\/td>214<\/td>210<\/td>4<\/td>-0.59<\/td>-0.68<\/td>2.82<\/td>\n<\/tr>\n
46<\/td>Gregory Bourdy<\/td>230<\/td>8<\/td>222<\/td>-0.58<\/td>-0.76<\/td>2.27<\/td>\n<\/tr>\n
47<\/td>Ben Crane<\/td>194<\/td>190<\/td>4<\/td>-0.57<\/td>-0.89<\/td>2.72<\/td>\n<\/tr>\n
48<\/td>Ross Fisher<\/td>187<\/td>70<\/td>117<\/td>-0.57<\/td>-0.98<\/td>2.86<\/td>\n<\/tr>\n
49<\/td>Rafael Cabrera-Bello<\/td>227<\/td>4<\/td>223<\/td>-0.57<\/td>-0.72<\/td>2.66<\/td>\n<\/tr>\n
50<\/td>David Toms<\/td>204<\/td>204<\/td>0<\/td>-0.56<\/td>-0.92<\/td>2.64<\/td>\n<\/tr>\n
51<\/td>Kevin Na<\/td>211<\/td>211<\/td>0<\/td>-0.56<\/td>-0.90<\/td>2.52<\/td>\n<\/tr>\n
52<\/td>Sergio Garcia<\/td>188<\/td>118<\/td>70<\/td>-0.55<\/td>-1.00<\/td>2.81<\/td>\n<\/tr>\n
53<\/td>Thongchai Jaidee<\/td>207<\/td>36<\/td>171<\/td>-0.55<\/td>-1.09<\/td>2.75<\/td>\n<\/tr>\n
54<\/td>Vijay Singh<\/td>171<\/td>169<\/td>2<\/td>-0.54<\/td>-0.65<\/td>2.63<\/td>\n<\/tr>\n
55<\/td>Zach Johnson<\/td>200<\/td>200<\/td>0<\/td>-0.54<\/td>-1.06<\/td>2.39<\/td>\n<\/tr>\n
56<\/td>K.J. Choi<\/td>189<\/td>171<\/td>18<\/td>-0.53<\/td>-0.79<\/td>2.60<\/td>\n<\/tr>\n
57<\/td>Matteo Manassero<\/td>96<\/td>14<\/td>82<\/td>-0.53<\/td>-0.97<\/td>3.02<\/td>\n<\/tr>\n
58<\/td>Rory Sabbatini<\/td>223<\/td>193<\/td>30<\/td>-0.52<\/td>-0.61<\/td>3.02<\/td>\n<\/tr>\n
59<\/td>Stewart Cink<\/td>178<\/td>174<\/td>4<\/td>-0.52<\/td>-0.68<\/td>2.56<\/td>\n<\/tr>\n
60<\/td>Bo Van Pelt<\/td>220<\/td>220<\/td>0<\/td>-0.51<\/td>-0.80<\/td>2.56<\/td>\n<\/tr>\n
61<\/td>Darren Clarke<\/td>211<\/td>30<\/td>181<\/td>-0.51<\/td>-0.72<\/td>2.95<\/td>\n<\/tr>\n
62<\/td>Bubba Watson<\/td>174<\/td>174<\/td>0<\/td>-0.51<\/td>-0.83<\/td>2.82<\/td>\n<\/tr>\n
63<\/td>Thomas Bjorn<\/td>168<\/td>6<\/td>162<\/td>-0.50<\/td>-0.70<\/td>2.81<\/td>\n<\/tr>\n
64<\/td>Robert Dinwiddie<\/td>139<\/td>0<\/td>139<\/td>-0.50<\/td>-0.63<\/td>2.78<\/td>\n<\/tr>\n
65<\/td>J.B. Holmes<\/td>203<\/td>201<\/td>2<\/td>-0.49<\/td>-0.51<\/td>2.84<\/td>\n<\/tr>\n
66<\/td>Robert Karlsson<\/td>151<\/td>64<\/td>87<\/td>-0.48<\/td>-0.90<\/td>2.99<\/td>\n<\/tr>\n
67<\/td>Peter Lawrie<\/td>215<\/td>0<\/td>215<\/td>-0.47<\/td>-0.97<\/td>2.84<\/td>\n<\/tr>\n
68<\/td>Brendon de Jonge<\/td>239<\/td>239<\/td>0<\/td>-0.47<\/td>-0.43<\/td>2.86<\/td>\n<\/tr>\n
69<\/td>Gary Woodland<\/td>100<\/td>100<\/td>0<\/td>-0.46<\/td>0.02<\/td>2.93<\/td>\n<\/tr>\n
70<\/td>Johan Edfors<\/td>195<\/td>10<\/td>185<\/td>-0.46<\/td>-0.86<\/td>3.00<\/td>\n<\/tr>\n
71<\/td>Bradley Dredge<\/td>207<\/td>4<\/td>203<\/td>-0.46<\/td>-0.90<\/td>2.85<\/td>\n<\/tr>\n
72<\/td>Ryan Moore<\/td>190<\/td>186<\/td>4<\/td>-0.46<\/td>-0.71<\/td>2.98<\/td>\n<\/tr>\n
73<\/td>Ignacio Garrido<\/td>229<\/td>4<\/td>225<\/td>-0.46<\/td>-0.89<\/td>2.86<\/td>\n<\/tr>\n
74<\/td>John Senden<\/td>240<\/td>234<\/td>6<\/td>-0.46<\/td>-0.74<\/td>2.69<\/td>\n<\/tr>\n
75<\/td>Simon Dyson<\/td>222<\/td>26<\/td>196<\/td>-0.46<\/td>-1.01<\/td>2.83<\/td>\n<\/tr>\n
76<\/td>Damien McGrane<\/td>245<\/td>2<\/td>243<\/td>-0.45<\/td>-0.91<\/td>2.92<\/td>\n<\/tr>\n
77<\/td>J.J. Henry<\/td>220<\/td>220<\/td>0<\/td>-0.44<\/td>-0.51<\/td>2.74<\/td>\n<\/tr>\n
78<\/td>Brandt Snedeker<\/td>195<\/td>193<\/td>2<\/td>-0.42<\/td>-0.65<\/td>2.88<\/td>\n<\/tr>\n
79<\/td>Gonzalo Fernandez-Casta<\/td>198<\/td>28<\/td>170<\/td>-0.42<\/td>-0.93<\/td>2.90<\/td>\n<\/tr>\n
80<\/td>Paul Lawrie<\/td>181<\/td>6<\/td>175<\/td>-0.42<\/td>-0.76<\/td>2.68<\/td>\n<\/tr>\n
81<\/td>Steve Marino<\/td>205<\/td>199<\/td>6<\/td>-0.42<\/td>-0.77<\/td>2.82<\/td>\n<\/tr>\n
82<\/td>Jaco Van Zyl<\/td>46<\/td>0<\/td>46<\/td>-0.42<\/td>-1.32<\/td>2.78<\/td>\n<\/tr>\n
83<\/td>Brian Gay<\/td>229<\/td>221<\/td>8<\/td>-0.42<\/td>-0.58<\/td>2.49<\/td>\n<\/tr>\n
84<\/td>James Kingston<\/td>187<\/td>12<\/td>175<\/td>-0.41<\/td>-0.60<\/td>2.99<\/td>\n<\/tr>\n
85<\/td>Soren Hansen<\/td>222<\/td>42<\/td>180<\/td>-0.41<\/td>-1.00<\/td>2.31<\/td>\n<\/tr>\n
86<\/td>Geoff Ogilvy<\/td>181<\/td>151<\/td>30<\/td>-0.41<\/td>-0.99<\/td>2.68<\/td>\n<\/tr>\n
87<\/td>Nicolas Colsaerts<\/td>102<\/td>0<\/td>102<\/td>-0.40<\/td>-0.83<\/td>2.78<\/td>\n<\/tr>\n
88<\/td>Gareth Maybin<\/td>216<\/td>6<\/td>210<\/td>-0.40<\/td>-0.92<\/td>3.04<\/td>\n<\/tr>\n
89<\/td>Jonathan Byrd<\/td>194<\/td>194<\/td>0<\/td>-0.39<\/td>-0.59<\/td>2.86<\/td>\n<\/tr>\n
90<\/td>Adam Scott<\/td>172<\/td>136<\/td>36<\/td>-0.38<\/td>-0.67<\/td>2.88<\/td>\n<\/tr>\n
91<\/td>Aaron Baddeley<\/td>195<\/td>183<\/td>12<\/td>-0.38<\/td>-0.41<\/td>2.90<\/td>\n<\/tr>\n
92<\/td>Fredrik Jacobson<\/td>192<\/td>192<\/td>0<\/td>-0.38<\/td>-0.55<\/td>2.69<\/td>\n<\/tr>\n
93<\/td>Jerry Kelly<\/td>211<\/td>207<\/td>4<\/td>-0.36<\/td>-0.57<\/td>2.72<\/td>\n<\/tr>\n
94<\/td>Soren Kjeldsen<\/td>211<\/td>42<\/td>169<\/td>-0.36<\/td>-0.89<\/td>2.68<\/td>\n<\/tr>\n
95<\/td>Scott Verplank<\/td>172<\/td>172<\/td>0<\/td>-0.33<\/td>-0.64<\/td>2.83<\/td>\n<\/tr>\n
96<\/td>Jeev Milkha Singh<\/td>230<\/td>104<\/td>126<\/td>-0.33<\/td>-0.64<\/td>2.77<\/td>\n<\/tr>\n
97<\/td>Danny Willett<\/td>195<\/td>2<\/td>193<\/td>-0.33<\/td>-0.95<\/td>3.12<\/td>\n<\/tr>\n
98<\/td>Webb Simpson<\/td>215<\/td>215<\/td>0<\/td>-0.33<\/td>-0.34<\/td>2.70<\/td>\n<\/tr>\n
99<\/td>Alexander Noren<\/td>188<\/td>6<\/td>182<\/td>-0.30<\/td>-0.82<\/td>2.78<\/td>\n<\/tr>\n
100<\/td>Marc Leishman<\/td>224<\/td>216<\/td>8<\/td>-0.30<\/td>-0.39<\/td>2.88<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n

And here are the Monte Carlo simulation results, for this year’s Masters.\u00a0 Some players did not have enough data to make a projection; I’ll assume none of them win (that would be old champs, a few Asian players, and the amateurs.)<\/p>\n

Notes on the results:<\/p>\n