The Peter Crouch Myth

The Peter Crouch Myth


It seems to be widely accepted as fact that Peter Crouch only scores goals for England when faced with weak opposition. Having never felt that this reputation was justified, I have investigated statistically and found startling results that show that he is an incredibly prolific and underrated international centre forward and will change the face of Peter-Crouch-only-scores-against-rubbish-teams-ology forever.

I am going to compare Peter Crouch to his most-capped contemporaries in the England strike force as well as the other major centre forwards from England’s recent past. The line-up, starting with the earliest capped, is Gary Lineker, Alan Shearer, Teddy Sheringham, Michael Owen, Emile Heskey, Wayne Rooney, Peter Crouch, Jermain Defoe and Darren Bent.

Appearance and goal records are up to date for the end of the 2010-11 season  – the last match included is the Euro 2012 qualifier against Switzerland on 4th June 2011.

This post uses the ranking based on the World Football Elo Ratings to quantify the quality of international teams. A country’s rank for a particular match is considered to be where they were ranked in the world just before that match began.

I’ll start by having a look at basic scoring rates without considering the quality of opponents.

Peter Crouch has a record of over one goal every other game and is second in this list only to Gary Lineker. His record becomes even more impressive when we consider how many minutes Crouch averages on the pitch per England appearance.

Crouch plays an average of only 52 minutes for every cap he earns. This is lower than all except Defoe and, crucially, half an hour less per match than Lineker, the only player to best him in goals per appearance. Here are revised figures of goals per match, but now a match is defined by 90 minutes of aggregated international playing time:

Peter Crouch’s goals per ninety minutes figure of 0.91 is exceptional and significantly better than those of celebrated England strikers Gary Lineker, Alan Shearer, Michael Owen and Wayne Rooney. So what if Crouch’s goals only come against weak teams? Goals against weak teams are valuable; I seem to remember England failing to beat an 80th ranked Macedonia side in qualifying for Euro 2008 – one England goal in that match would have ultimately seen them qualify for the finals. I also recall England failing to beat an 82nd ranked Algeria side at the 2010 World Cup – one England goal in that match would have seen them facing Ghana in the last sixteen instead of Germany.

But remember I said “if Crouch’s goals only come against weak teams”. I don’t think that this is the case, and here’s some number crunching that backs me up:

Below is the mean rank of the opposition that each striker has netted against. The higher the red line the stronger the opponents they tend to score against.

From this it seems that Crouch’s critics have a point. Although far from the weakest, his goals come against weaker opposition than all but Rooney’s and Defoe’s. But before we jump to any conclusions we should really take into account the average quality of opposition that each player has played against. Had a player only ever featured in matches against 232nd ranked Palau we could hardly blame them for only ever finding the net against 232nd ranked Palau. The blue line shows mean opponent rank weighted by minutes played:

Now the real picture is starting to emerge. The countries that Crouch scores against are admittedly on the weaker side, but the countries that he plays against are also on the weaker side. Only Jermain Defoe is pitted against weaker opposition than Crouch and only by an average ranking position of one. If you choose to take the difference between opponent rank by minutes played and goals scored as your indicator of a quality marksman (i.e. the smaller the distance between the red and blue lines the better) Crouch comes out better than Shearer, Heskey, Rooney, Defoe and Bent.

However, I don’t think simply averaging out the opponent rank of a player’s goals is a very fair measure – and I think that it’s unfair on Peter Crouch. That’s right: I think that Crouch’s record should be seen as even better than the above graph suggests.

Had Peter Crouch not scored the three goals he has scored against Andorra (and I don’t mean scored three goals against Brazil or Spain instead, I mean just not scored them at all) he would have a still very good record of 0.79 goals per 90 minutes but his average opponent ranking for goals scored, instead of 61.6, would be a stunning 43.3 – making him the only player to have scored against a better average quality of opponent than he’s played against. Scoring goals, even against the weakest opposition, should never make your record look worse, only be less of an improvement than if you had scored against stronger opposition.

To get a less constricted picture we could plot goals and games like this:

Each dot is a match that the player appeared in. The higher a dot is placed, the better the opponent’s rank (horizontal scattering is random to avoid overlapping). A dot is blue if the player did not score in that match and it is red if the player did score in that match. One or two red rings around a red dot signifies the second and third goal that the player scored in the match.

We can see that Crouch has failed to score in the eight most testing matches he has appeared in: Argentina ranked 6, Portugal 4, Brazil 1, Germany 6, France 4, Germany 5, Spain 1, Brazil 1; the highest he has scored against being 8th ranked Mexico. However, what the graph does not show is that Crouch only played ten minutes or more in three of these matches: he played 9, 55, 7, 7, 45, 2, 45 and 8 minutes respectively. In these eight fixtures he played a total of 178 minutes, so it is fair to say that Crouch has failed to score in 1.98 matches worth of time against the top six teams in the world – not eight matches worth.

Wayne Rooney has played 9 matches and scored 2 goals against teams ranked 6th or higher, playing 76, 61, 90, 62, 90, 45, 58, 90 and 90 minutes for a total of 662 minutes, or 7.35 full matches. Against the world’s top teams Rooney has scored 2 goals in 7.35 matches and Crouch has scored 0 goals in 1.98 matches  – inferior, but hardly damning, figures for the Spurs player.

I will next look at the numbers using a fairer, but slightly more complicated, calculation; one that requires rank to be converted into something more practical.

Working with a system where 1 is best and 232 is worst is not very helpful for doing maths so from now on I will be using a converted form of the rankings – that I’m calling simply ‘quality’ – where the top ranked team in the world is worth 1.00 and the bottom is worth close to zero. Ranks are squared as part of the conversion to make the numbers more representative of real gaps in quality. Had I used a linear scale, a goal against 1st ranked Brazil would only worth 3.3 times as much as a goal scored against 176th ranked Andorra; on this scale it is 11 times as much. The latter seems a better weighting by my judgement. This shows how rank and quality relate:

We can now multiply each goal a player has scored by the quality of the opposition it was scored against, add them all up and divide by their total appearances to get a player’s quality goals scored per cap:

A quality goals scored per cap of 1.00 could mean that the player has scored one goal against the best team in the world for every appearance they’ve made. A quality goals scored per cap of 0.25 could mean that they have scored a goal every other game against, on average, sides of quality 0.5.

We also need to take into account the quality of the teams that the player has been playing against. A player can only score quality goals if they get the chance to play against quality teams. For each appearance I multiply the proportion of ninety minutes that the striker in question played (this could be greater than 1 if extra time was played) by the quality of opposition faced. These are also added up and divided by the number of appearance to get a player’s opportunity to score quality goals per cap:

If a player plays 72 minutes per match against teams of 0.8 quality he will have an opportunity to score quality goals per cap of 0.64 (0.8 x 0.8).

Here are the two new measures for each player:

The relatively low quality of Crouch’s goals lets him down here and he falls below Lineker and Shearer if looking solely at quality goals per cap, but his low opportunity to score quality goals per cap comes to his rescue. We can see how much it comes to his rescue by calculating the following:

Which is charted here:

Once the limited nature of his opportunities has been taken into account, Peter Crouch’s excellent goals per minute record sustains being weighted by quality to still be far and away the best of all the players studied. Peter Crouch is the most prolific England striker of the era and his perceived disproportionate reliance on scoring against football’s weak nations is a myth.


World Football Elo Ratings and its primary source, Advanced Satellite Consulting

England Football Online