Shot Matrix II: Pass Type and Shot Type, or, Heading is super hard

In Tottenham Hotspur's most recent match against Newcastle United, we were judged by Opta's stringers to have created (and missed) four big chances. Two of the missed big chances had fallen to Roberto Soldado, while the other two went to Younes Kaboul and Christian Eriksen. Soldado's were most likely his free header from a central position on a corner in the first half that he sent over the bar, and his header from the side of the six-yard box of a rebound in the second half that Tim Krul saved easily. Younes Kaboul's was his failed bundling of a rebound over the line, and Christian Eriksen's was his shot from the center off Andros Townsend's pass that Krul blocked with his foot in a true wonder save. It will be my contention is this article that not all these shots were created equal. In particular, that first Soldado header, while a shot you hope your striker will bury, is not a particularly high expectation chance on average.

(The shot locations mentioned above refer to zones 3, 2, 1, and 3 again in my Shot Matrix diagram, posted to the right.)

I have Soldado's first "big chance" coded as a relatively low quality chance because it was a header assisted by a cross. My Shot Matrix data logs a bunch of information on every shot in a really big table (thus the name), and I've noticed an intriguing connection between crosses and headers. Of course, a whole lot of headed shots are assisted by crosses. In my database, roughly 73% of all shots from crosses are headers, and roughly 84% of headers are assisted by crosses. So to analyze crossing and headers, the two categories must be combined. This gives me four basic categories of shots to consider for this analysis: headers off crosses, other headers, other shots off crosses, and other shots not off crosses.

I'm further breaking those shots down by zones. The vast majority of headers off crosses (over 95%) are attempted in Zones 1-3. Headed shots off crosses from outside Zones 1-3 are pretty much useless, as you would expect.

In important news of importance, thanks to commenter darrylzero, I now have name I like for these high-expectation areas inside the box. The Danger Zone.

Notably, though of course a good number of goals are scored on headed crosses from within the Danger Zone, these are on average much lower expectation chances than the usual attempt from these key areas of the pitch. (A slight exception is Zone 2, as I'll get to shortly.)

So let's take a look at the data. I'll go three each of the individual Zones 1-3 first, then consider the combined Danger Zone as well as other areas of the pitch.

Expected Returns from Headers and Crosses by Location

For each zone, I've broken down the shots into four types. "Cross-Head" are headed shots assisted by crosses. "Oth Head" are headed shots not assisted by crosses. "Oth Cross" are non-headed shots assisted by crosses. And "Other Shot" are just regular shots.

• Number: Just the total number of shots of this type from this zone in my database
• %On Target: The percentage of shots of this type taken in the zone on target.
• %Goal: The percentage of goals from shots of this type taken in the zone.
• G/SoT: The percentage of goals from shots on target of this type taken in the zone.

If you remember the numbers from my previous piece (or just look down at the data for Zones 2 and 3), you'll see that 28% goal conversion is a tremendously high rate compared to the typical shot. Nonetheless, it's slightly less than half the rate of goal conversion for regular shots taken in the central area of the six-yard box. Headed shots off crosses are extremely difficult to maneuver on target, even from the goalmouth area over half of headed shots fail to hit the target. You can see that the main driver of the different %Goal numbers here is the difficulty of hitting the target. If a ball falls to a player in Zone 1 from a normal pass or some other means, he can get it to the goal 75% of the time, and 75% of those shots will be goals. If he gets a cross that he has to play with his head, he'll only put the shot on goal 45% of the time and that shot, when on target, will hit the back of the net 65% of the time. The decrease in on-target rate is significantly larger than the decrease in SoT conversion.

You can also see the multiplicative effect of crosses and headers. Headers not off crosses, perhaps from rebounds of shots or the occasional lofted pass, are better than headers off crosses but not as easy to convert as regular shots. Likewise with crosses—a cross played into feet in the six-yard box, if the player can manage to turn it goalward, will be a score nearly half the time. But it's still harder to redirect that cross than to play a regular shot. This makes sense, of course. Getting a clean strike on a cross is hard, getting a clean strike using only your head is hard. Trying to do both at the same time, really hard. (Thus the title of the piece.)

Now, this multiplicative effect of headers and crosses doesn't apply equally all over the pitch. From long distance or wide in the box, headers and crosses produce such poor opportunities that it's barely worth listing them. More interestingly, in Zone 2, the wide areas of the six-yard box, there appears to be much less of a "penalty" for playing crosses. Here's the data:

In the wide areas of the six-yard box, the returns on crosses and headers are better than elsewhere, compared to the average shot. In particular, at least over the 260 shot sample I have, it appears that crosses into feet in Zone 2 have a slightly higher rate of conversion than normal shots from this area. I can imagine why this might be. In the wide areas of the box, if the keeper is positioned correctly, he should be able to block the goal. On a low cross through the box, either played early before the keeper expects or late after the ball has run past him, there should be a much more open goal to shoot for. And indeed that is what you see in the numbers, that it's relatively difficult to put a shot on target off a cross into wide areas (not surprising), but once you do put the shot on target, you have a 50/50 chance of scoring because there's a good possibility the keeper isn't in position.

Soldado's weak header yesterday is classified as a Zone 2 "Other Header." These chances, probably a lot of them rebounds or deflected balls, are high-quality chances. 16% is good. But while it's not that hard to head on target from a close position when you're not dealing with a fizzing cross, it is difficult to get the kind of power and accuracy behind the ball that will beat the keeper. Soldado failed to do that, bopping the ball weakly into Krul's arms.

Once you get outside of the six-yard box, chances off crosses and headers lose a lot of their value. I like how the numbers on headers off crosses and other headers converge to an 8% conversion rate by quite different means. Hitting a cross ball with your head from twenty feet or more and putting on target is very difficult. If you do get it on target, there's at least a non-terrible chance that you got enough power and precision behind the ball to score. On other headers, where the ball is most likely coming in at a kinder speed and angle, directing it to goal is relatively easy. Beating the keeper, though, is incredibly difficult as you rarely get enough power on the header to trouble the keeper.

Soldado's first big chance was a header off a cross from Zone 3. It was relatively close in Zone 3, so the expectation was probably higher than the average above, but it's still a very difficult shot. "Free headers" that aren't right on top of the goal mouth are difficult shots, and when Opta classifies them as big chances, I think some important precision is lost.

I've only got about 200 headers and 400 crosses in my database from Zones 4 and 5, and these are just terrible chances. The headers run in the range of 1% goal conversion, the plays off crosses maybe 2-3%. These are no better, on average, than shots from outside the box entirely.

If you look back at the tables from my previous post, you'll see that the numbers here don't quite add up. I've left out one very important set of shots, that's for the next post. They're pretty cool. (Teaser!)

As I said above, headers and shots from crosses are very rarely taken from outside the Danger Zone. This leads to a fun little statistical oddity, that headers and shots from crosses rate, on average, as higher expectation than an average shot and nearly as good as an average shot from inside the box. This is not because headers and shots off crosses are higher-expectation shots, but rather because they are almost always taken from higher-expectation areas. A table:

Those ~10,000 headers and shots from crosses have high expectation compared to typical shots, but when you consider that over 95% of them are attempted from the Danger Zone, and disproportionately from within the six-yard box, you can see that compared to a similar shot from the same area, headers and shots of crosses have relatively lower expected value.

Stats and Tactics

This data clearly shows the superiority of chances created not from crosses or headers, but from playing the ball to feet through central positions. One easy conclusion to draw would be that, tactically, everyone should try to play more balls to feet in central positions. I want to caution against this sort of "mirror-reading" of the stats. All the numbers here show are the values of shots, not the cost of creating those shots. If your players are losing possession in dangerous areas because they're trying to play the ball into feet in traffic, that's a cost of the tactics. If your players are packing the center of the pitch and allowing the opposition defense to pack in as well to prevent your desired shots, that's a cost of the tactics. While everyone would like to just constantly play passes into the feet of the striker standing free in the center of the six-yard box, that's actually incredibly hard to do, and there are severe costs associated with focusing on that tactic.

So this questions of costs compared to benefits is the first important caution I have for anyone making easy tactical judgments based on the stats above.

An example: There was a working paper published earlier this year by the economist Jan Vecer, entitled "Crossing in Soccer has a Strong Negative Impact on Scoring: Evidence from the English Premier League." He concludes, "An average team is expected to score additional 0.57 goals per game if it reduced open crossing." There are few things I love more about football than its dynamism, the way, for example, a winger holding an advanced position can keep a fullback from joining the attack, which forces an attacking midfielder into a wide role, which reduces the number of men attacking the back post, which leads to a good cross going untouched and out for a goal kick. Everything on the pitch is interrelated. And the players matter. If that winger is Theo Walcott, the fullback has to track him, if it's Gylfi Sigurdsson, a pacey right back might join the attack under the assumption that he can make a sprint back if the play breaks down. So the situations based on tactics and roster which produce open-play crossing should not be reduced to a single regression formula. Vecer presumes based on his regressions that all clubs could in similar ways gain value from a reduction of open-play crossing, without considering the personnel involved or the reasons such tactics had been chosen.

I also hypothesize a pretty serious problem of correlation/causation, as I would expect that teams chasing a game will attempt more crosses as the opposition defense packs the center and prevents higher-value chances. So the correlation may not, in fact, show causation. This latter theory is something I can test with the Shot Matrix database. I have coded in time-stamps for each shot, and I am building a script to determine the game state for each shot as well. So hopefully in the next couple weeks I can test my theory and present some numbers on game state from the database. But that's in the future.

Coming up next, probably Monday: (III) The Magical Through-Ball and (IV) A comparison of EPL clubs in 2013 by shot type in the Danger Zone.