*A note before I start this post: all of these calculations are really rough, back of the envelope sorts of calculations. The method is sound, but there are some issues with data that I will identify in italics throughout. The end results don’t change the answer that Cech is likely not worth 15 points as John Terry now famously said, but this sets up what I think is a decent first cut at assigning an actual point value to goalkeepers. Hopefully others can fix the bad assumptions to tighten up the actual values a little. *

John Terry famously said that Petr Cech would be worth 12-15 points for Arsenal, and we’ve seen several variations of this theme in the media with various goalkeepers (Lloris, De Gea, etc.) but no one really knows how to evaluate the actual value of a keeper to a team.^{1} Using data from Paul Riley (@footballfactman on Twitter) and my recent analysis of Michael Caley’s xG data against MOTSON’s predictions I think we can at least make an first cut here that makes sense and comes up with what I think are reasonable results.

**Step #1: Regress MOTSON’s Expected Points against xGD**

In my previous post, I showed that MOTSON predicts expected goals very well. So I did a quick, bivariate regression with Expected Points as my DV and xGD ^{2} as my IV. From this I get a model of:

ExpPoints = 26.73 +0.6723(xGD)

What this means is (as of today), each team starts with a baseline of 26.73 points, and then for every additional xGD you add 0.6723 to that value. Simple arithmetic can calculate each team’s expected points from here.

*Quick diagnostics: The predictions from this model correlate with my actual expected points at 0.83, and correlate with teams’ actual earned points at 0.77. These are very high numbers, certainly high enough to continue with the analysis.*

So each xGD is worth 0.6723 points in the league table. Next, I look at Paul Riley’s data showing all EPL keepers with more than 350 saves in the last 5 1/2 seasons. The data show Expected Goals Allowed (ExpGA) vs. Actual Goals Allowed, so I use this to calculate a goal differential for each goal keeper over the 5 1/2 time period, multiply this number by the regression coefficient calculated earlier ( 0.6723), and then divide by 5.5 to calculate a “per season” score.

*There are two assumptions implicit here: first is that each goalkeeper played a full 5 1/2 seasons in the EPL, which is a bad assumption. I didn’t want to look at each keeper’s history for what is supposed to be a quick blog post, but if you did you could easily just change the last number to whatever the number of seasons someone played is.*

*The second is that goalkeepers are 100% responsible for the difference between ExpGA vs. Actual GA, and have 0% responsibility for scoring goals. This seems relatively reasonable, or at the very least the error terms are random between all the keepers in this model. There might be great counter-attack starting goalkeepers in the world like Manuel Neuer who deserve some credit for goals scored, but even in that cause I’d imagine the number of small, at most. *

Below is the a graph of all the goalkeepers and their per season point values, and the table with the raw data is located at the end of this post. The top goalkeeper in the model is Adrian, and according to this method he’s worth about 2.4 points per year over a “neutral” goalkeeper, and a little more than 5 points per year over the lowest scoring keeper in the model. Petr Cech comes in 4th at 2.05 points per year, which is really good for a goalkeeper, but is well short of the 15 points John Terry asserted.

Like I said, this is a first cut at Expected Points for goalkeepers, but presents a way of quantifying their major contribution. Future work on the topic needs to look at error rates around xG calculations, sample size issues, and some other measurement issues with the model inputs, but overall I think it’s a really good first cut. Big thanks to Paul Riley for posting his data publicly and making this post possible and I’m looking forward to seeing how people can build on this.

Name | Expected Goals Allowed | Actual Goals Allowed | Goal Difference | Points Over 5.5 Seasons |
---|---|---|---|---|

De Gea | 168.09 | 149 | 19.09 | 2.33 |

Hart | 187.01 | 170 | 17.01 | 2.08 |

Cech | 166.8 | 150 | 16.8 | 2.05 |

Adrian | 108.63 | 89 | 19.63 | 2.4 |

Begovic | 207.14 | 197 | 10.14 | 1.24 |

Foster | 225.84 | 211 | 14.84 | 1.18 |

Vorm | 128.26 | 119 | 9.26 | 1.13 |

Schwarzer | 144.77 | 139 | 5.77 | 0.70 |

Mignolet | 226.63 | 221 | 5.63 | 0.69 |

Reina | 111.18 | 107 | 4.18 | 0.51 |

Jaaskelainen | 169.61 | 167 | 2.61 | 0.32 |

Lloris | 136.7 | 136 | 0.7 | 0.09 |

Howard | 217.39 | 219 | -1.61 | -0.20 |

Szczesny | 147.01 | 150 | -2.99 | -0.37 |

Friedel | 112.88 | 116 | -3.12 | -0.38 |

Hennessey | 119 | 124 | -5 | -0.61 |

Al Habsi | 158.87 | 165 | -6.13 | -0.75 |

Green | 146.87 | 153 | -6.13 | -0.75 |

Ruddy | 161.94 | 171 | -9.06 | -1.11 |

Guzan | 192.78 | 207 | -14.22 | -1.74 |

Krul | 241.88 | 264 | -22.12 | -2.70 |

- Goalimpact assigns values to keepers, but they’re notoriously even more difficult to quantify than defenders. ↩
- Expected Goal Difference ↩