Introduction
As I’ve watched soccer over the years, I’ve become more convinced that goalkeepers are undervalued. My basic reasoning was that the most highly valued players, strikers, are involved in maybe half of a team’s goals scored. But goalkeepers are involved in every goal prevented. With extra free time due to the pandemic, I’ve decided to explore this hypothesis.
My logic is:
- A goal scored is worth (roughly) the same as a goal prevented
- The best goalies prevent (roughly) the same number of goals below average as the best strikers score goals above average
- Therefore goalies are worth (roughly) the same as strikers, but their transfer fees do not reflect this
Let’s explore.
A goal scored is worth (roughly) the same as a goal prevented
The objective in professional soccer leagues is to get as many points as possible: three points for a win, one point for a draw, no points for loss. We need to calculate how much an additional goal scored and how much an additional goal prevented is worth in points.
In the last two Premier League seasons, teams averaged 1.4 points per game. At the same time, they averaged 1.5 goals scored per game which means they averaged 1.5 goals allowed per game. The chart below illustrates the average points for each level of goals scored (0, 1, 2, etc.) and goals allowed (note that one less goal allowed is equivalent to one extra goal prevented).
While the change in points is not consistent for each step in goals scored or goals allowed, we can roughly estimate the effect of an extra half goal scored or half goal prevented. If the average team scored a half a goal more per game they would score 2.0 goals per game. This would lead to a .8 point increase, from 1.4 points per game to 2.2 points per game.* Similarly, if the average team prevented an extra half a goal per game they would allow 1.0 goals per game. This would lead to a .3 point increase, from 1.4 points per game to 1.7 points per game.
This is a larger gap than I expected, but it makes sense. You cannot allow less than zero goals, but even allowing zero goals doesn’t guarantee a win. On the flip side, teams that scored three goals win over 90% of their games and teams that scored four or more goals always win.
For the average team an extra goal scored is worth 167% more than an extra goal prevented (.8 vs .3 points).
The best goalies prevent (roughly) the same number of goals above average as the best strikers score goals above average
The value of an extra goal scored or prevented is only half the equation. We also need to know how much of that to attribute to the player scoring or preventing the goal. To measure this, we need a metric similar to baseball’s wins above replacement. For goalies this is straightforward, but for strikers it is not.
Post shot expected goals is the goalie equivalent of wins above replacement. It measures the likelihood a ball will go into the net just after it leaves the attackers’ head, foot, etc. It accounts for speed of strike, angle to the goal, and distance to the goal, among other factors. Goalies can easily be compared by total post shot expected goals faced minus goals conceded. This can be used as a rate statistic per 90 minutes. Usually, the best keeper in the Premier League manages to stop .3 goals per game better than the average Premier League keeper.
Finding a similar metric for strikers is a lot more complicated. Many people are working on it but there is not much publicly available. Here is a rough estimate. The best striker in the Premier League averages about .7 goals per game. Of course, scoring a goal cannot solely be attributed to the goal scorer, they need the rest of the team to space the field, make passes, draw defenders, and the opposing goalkeeper skill/luck matters. I estimate that most goal scorers deserve around 50%** of the credit. That gives .35 goals per game of credit. Strikers also contribute with assists, winning penalties, and other actions. Let’s say that the top strikers contribute .15 goals per game through these other actions. Giving .5 goals per game total.
Keep in mind the best striker usually plays on one of the best teams and the average striker plays on an average team. How much is that worth? By eyeballing some strikers who recently made moves from mid level teams to top teams and vice versa, the effect may be worth .2 goals per game. This leaves .3 goals per game of credit for a top striker on an average team.
Finally, we are interested in goals per game better than average. Again, by eyeballing the numbers of some average strikers on average teams, I estimate that they average .3 goals+assists per game. Since they only get half credit, that leaves .15 goals per game of credit. Comparing this number to .3 for top strikers gives .15 goals per game of credit above average for the top strikers.
We’ll ignore the buildup play and defensive contributions of strikers. While there may be differences and the quality of buildup play and defensive contributions from striker to striker, the effect on goals scored and prevented is minimal. I think we can safely ignore the on-ball contributions of goalies as well.
Therefore goalies are worth (roughly) the same as strikers, but their transfer fees do not reflect this
The top strikers earn .15 goals per game of credit while the top goalies earn .3 goals per game. Given the top players play for the top teams, let’s consider the average “big 6” team which scores 2 goals per game and allows 1 goal per game. That gives .36 points/additional goal scored and .54 points/additional goal prevented. Multiplying out: the top goalkeepers are worth .3 (goals prevented/game) x .54 (points/goal prevented) =.16 points per game. The top strikers are worth .15 (goals scored/game) x .36 (points/goal scored) = .05 points per game. The top goalkeepers are worth 220% (=(.16-.05)/.05) more points per game to the “big 6”. The table below shows the percentage difference at each level of scoring (positive is in the goalies favor).
| Points Increase of Signing a Top GK vs a Top FW | |||||
| If team currently | scores | ||||
| allows | 0.5 | 1 | 1.5 | 2 | 2.5 |
| 0.5 | 131% | 48% | 48% | 222% | 222% |
| 1 | 131% | 48% | 48% | 222% | 222% |
| 1.5 | 178% | 78% | 78% | 288% | 288% |
| 2 | 178% | 78% | 78% | 288% | 288% |
| 2.5 | 7% | -32% | -32% | 49% | 49% |
So is there a gap in team contribution and transfer fee? The top 10 strikers are valued at an average of $120 million. The top 10 goalkeepers are valued at an average of $50 million. That’s 140% more in the wrong direction. My recommendation: buy 11 goalkeepers.
All data from fbref.com, except transfer market value from transfermarkt.us
*Holding all else constant, which is reasonable because scoring goals and allowing goals are independent.
** For example, penalties have an 80% a chance of going in, so a penalty kick scorer only gets 20% of the credit (assuming the goalie did not make an error). The other 80% should be distributed to the other players involved in the build up play and winning the penalty.