The methodology is exactly the same as before.The larger the sample size the more the keeper's true ability will overshadow random chance and the smaller the sample size then the less confidence we can ascribe to an individual's save percentage figure.
This is best illustrated in the case of Ben Amos who managed to coax two shots out of Stoke City in his one and only appearance for Manchester United last season.He saved them both to record a 100% save percentage enough to put him at the top of every list of raw save percentage.While it will be comforting for United supporters that Amos managed to keep out Stoke's best efforts,he's unlikely to record anywhere near that save percentage in larger trials.So his numbers are regressed over 90% towards the mean of last year's goalkeeping save percentage of around 68%.The credit he receives for keeping a clean sheet lifts his regressed save percentage a couple of points above average.
All 2011/12 keepers are listed below,the regressed save percentage in the final column is the most indicative figure of each players likely true ability.
Best EPL Keepers 2011/12.
| Keeper. | Shots on Target. | Saves. | Observed Save % | Regressed Save % |
| De Gea. | 131 | 102 | 77.9 | 76.4 |
| Hart. | 126 | 97 | 77.0 | 75.6 |
| Lindergaard. | 22 | 18 | 81.8 | 74.8 |
| Stockdale. | 58 | 44 | 75.9 | 73.7 |
| Mignolet. | 127 | 94 | 74.0 | 73.1 |
| Vorm. | 185 | 136 | 73.5 | 72.9 |
| Friedel. | 155 | 114 | 73.5 | 72.8 |
| Schwartzer. | 139 | 102 | 73.4 | 72.6 |
| Cerny. | 28 | 21 | 75.0 | 71.9 |
| Hilario. | 10 | 8 | 80.0 | 71.8 |
| Begovic. | 110 | 79 | 71.8 | 71.2 |
| Amos. | 2 | 2 | 100.0 | 70.8 |
| Foster. | 166 | 117 | 70.5 | 70.2 |
| Howard. | 135 | 95 | 70.4 | 70.1 |
| Guzan. | 28 | 20 | 71.4 | 70.0 |
| Doni. | 11 | 8 | 72.7 | 69.7 |
| Hennessey. | 238 | 165 | 69.3 | 69.2 |
| Reina. | 114 | 79 | 69.3 | 69.1 |
| Krul. | 165 | 114 | 69.1 | 69.0 |
| Given. | 143 | 98 | 68.5 | 68.5 |
| Ruddy. | 200 | 137 | 68.5 | 68.5 |
| Cech. | 123 | 84 | 68.3 | 68.3 |
| Gordon. | 6 | 4 | 66.6 | 68.0 |
| Rudd. | 9 | 6 | 66.6 | 67.9 |
| Sorenson. | 68 | 46 | 67.6 | 67.8 |
| Westwood. | 33 | 22 | 66.6 | 67.4 |
| Jaaskelainen. | 117 | 77 | 65.8 | 66.2 |
| Al Habsi. | 181 | 119 | 65.7 | 66.0 |
| Kenny. | 166 | 107 | 64.5 | 64.9 |
| de Vries. | 20 | 12 | 60.0 | 64.5 |
| Bogdan. | 100 | 63 | 63.0 | 64.0 |
| Turnbull. | 11 | 6 | 54.5 | 64.0 |
| Szczesny. | 133 | 84 | 63.1 | 63.9 |
| Kean. | 5 | 2 | 40.0 | 63.4 |
| Tremmel. | 2 | 0 | 0 | 63.0 |
| Fulop. | 3 | 0 | 0 | 60.7 |
| Bunn. | 14 | 5 | 35.7 | 56.2 |
| Robinson. | 167 | 71 | 42.5 | 45.7 |
While it's hardly a surprise that much of the EPL's keeping talent resides in Manchester,there is a definite practical use for the regressed numbers.As I've tried to illustrate in these posts on crossing and shooting the regressed figure is a much better indicator of performance in subsequent seasons than is the raw unregressed rate.The table below illustrates 14 cases of goalies returning to EPL action from the 2010/11 to the 2011/12 seasons and it is the regressed rate from 2010/11 and not the actual observed rate that gives a better indication of 2011/12 performance in 12 out of the 14 occasions.
David Stockdale's numbers well illustrate this point.His 81% save rate was achieved over just 32 attempts.After regressing that figure almost 60% towards the mean his corrected rate falls to 75.2% very close to the actual save % he produced in 2011/12 from almost twice as many shots.
What's the Best Indicator of Future Goalkeeper Save Percentage.
| Keeper. | Observed Save % 2010/11. | Regressed Save % 2010/11. | Observed Save % 2011/12 | Is the 2010/11 Regressed % Closest to the 2011/12 % |
| David Stockdale. | 81.3 | 75.2 | 75.9 | Yes |
| Joe Hart. | 77.1 | 74.2 | 77.0 | No |
| Petr Cech. | 75.0 | 73.5 | 68.3 | Yes |
| Asmir Begovic. | 75.0 | 73.5 | 71.8 | Yes |
| Mark Schwartzer. | 71.8 | 71.1 | 73.4 | No |
| Ali Al Habsi. | 70.5 | 70.2 | 65.7 | Yes |
| Craig Gordon. | 70.4 | 70.0 | 66.6 | Yes |
| Wojciech Szcsesny | 69.4 | 69.3 | 63.1 | Yes |
| Pepe Reina. | 69.0 | 69.1 | 69.2 | Yes |
| Tim Howard. | 69.0 | 69.1 | 70.4 | Yes |
| Simon Mignolet. | 67.6 | 68.1 | 74.0 | Yes |
| Thomas Sorensen. | 64.4 | 66.9 | 67.6 | Yes |
| Brad Friedel. | 64.4 | 65.5 | 73.5 | Yes |
| Tim Krull. | 57.8 | 61.9 | 69.1 | Yes |
First of all, great blog, keep up the good work. I can't remember how I first stumbled across your stats but I've found it fascinating and your explanations are clear. Also I read the recent news articles on penalty shoot-out statistics which set off alarm bells about sample sizes - this was the first place I visited to see if someone else had queried it.
ReplyDeleteAnyway, my question is about the regression method you use. From the first table, It appears that you have added 23.67 shots at the population mean save rate to each keeper's stats. Unless I have the method completely wrong, can you tell me how you arrived at this number? I understand the theory behind regression and the different variances, but my equations don't seem to come up with the right numbers.
I don't mean to copy your work, just trying to learn.
Cheers
Great work. It's a topic I've been looking into myself lately. Do you happen know what the r^2 for the observed 11/12% and the regression 10/11% is?
ReplyDelete