# On “Penalties under pressure”

This tweet has been making the rounds:

The statistic itself was based on a BBC study of all World Cup penalty kicks, and it certainly piqued my interest. A psychological effect based on the kick’s pressure, and one with this effect size – 93% vs. 44% – is enough to have a drastic impact on games.  Further, it could potentially impact how coaches would select their players. Lastly, the linkage of this type of finding would no doubt tie into other sports, for example in the shootouts that end regular season hockey games, and potentially into other walks of life.

While I don’t have access to the BBC’s data, I did have a spare moment to dig deeper.

(1) While the BBC study looked at every World Cup game decided by PK’s, “every World Cup game decided by PK’s” amounted to just 22 games.

(2) By looking at the exact percentages shown (e.g., only a limited number of fractions yield percentages of 44% and 93%), I’m pretty sure that the fractions being compared are 13/14 (93%) and 7/16 (44%).

Here’s why: Using those fractions, the 13 successful kicks to win the PK and the 9 failures to extend the PK are both events that end the game, and of course, 13 + 9 = 22 total games. The 1 failure to close out a win, and the 7 successful attempts in the face of elimination, would have caused the PK to go on.

(3) The difference between 13/14 and 7/16 is notable, but that’s about all I’d call it.  That’s a pretty small sample of kicks.

(4) There’s one more interesting aspect to this statistic. Let’s operate under the assumption that some teams (either because of field players, goalies, or both) might be slightly better at PK’s than others. While I don’t know this for sure, (i) I’ve argued that hockey shootouts aren’t random and (ii) I checked the “Live Betting” line during the Brazil Chile game, and the implied lines of online sportsbooks had Brazil as a 54% shootout favorite.

If some teams are better at the shootout than others, then we might have a bit of selection bias in these numbers. Teams with opportunities to close out the game with a successful kick might be just better than those who have to make a kick just to keep their team’s chances alive.

Of course, I wouldn’t argue that team-to-team differences in PK’s are enough to account for a difference between 93% and 44%, but that could be part of it.

(5) When in doubt, go to Google Scholar. Not surprisingly, PK outcomes have been analyzed before. Here are some findings.

Collectivist nations performed better on shootouts than individualistic ones. This one I need to save and read at a later date.

Younger players are better at converting PK’s than older players. Interesting, because I would’ve expected the opposite to be the case

-In the same article linked above, the author’s found that World Cup conversion (71% success rate) were lower than those in other competitions with less pressure (European Championships, Copa Americana)

-Same article: here’s the success rate by attempt, using the larger sample size of games

• First kick 86.6%
• Second kick 81.7%
• Third kick 79.3%
• Fourth kick 72.5%
• Fifth kick 80%
• ‘Sudden death’ kicks 64.3%

Behavior on the walk up to the kick- called a player’s “valor” – was associated with a kick’s success

If coaches were smart, they’d consider using one of their substitutes on a back-up goalie who was better at stopping PK’s than the starter

-In hockey, home teams performed worse than expected on shootouts. This result is difficult to verify using World Cup data, of course, but I thought it was relevant.