Does it matter what order you send players to take penalties?

Updated: Thursday, 8:45am (fancy chart added)

In light of another bout of Ronaldo playing to the cameras with a face full of restrained aggro at not getting the chance to take Portugal’s fifth penalty, it’s worth looking at this idea of whether the order matters and if it does, which order gives you the best chance of winning.

There was great, and of course immediate, discussion of this on Twitter today with some very respected analysts in the form of Jason deVos and Bobby McMahon coming down on the side of saving your best player until the last shot with deVos, post game on TSN, alluding to research that advocates for starting with the worst of your five shooting first and working down towards your best player shooting last. Here’s that research (as summarized from McMahon’s post on Forbes today):

This paper employs computer simulation, probability theory and mathematical modelling to explore the effectiveness of different penalty shoot-out strategies. Their analyses suggests that there is an advantage in placing the team’s fifth best penalty taker on the first kick, the fourth best on the second kick, the third best on the third, the second best on the fourth, and the team’s best penalty taker on the fifth kick. If the competition goes to sudden death, the sixth best penalty taker should take the sixth kick and so on.

McGarry, T. and Franks, I. M. (2000) On winning the penalty shoot-out in soccer. Journal of Sports Sciences, 18, 401-409.

As mentioned, McMahon, in his Forbes article, presented  the same research, co-authored by UBC’s own Ian Franks to buttress his argument. Also quoted was another article from The Journal of Sports Science. This, detailing what percentage of penalties is scored by order, is perhaps the most telling:

  • First kick 86.6%
  • Second kick 81.7%
  • Third kick 79.3%
  • Fourth kick 72.5%
  • Fifth kick 80%
  • ‘Sudden death’ kicks 64.3%
 Jordet, G., Hartman, E., Visscher, C. and Lemmink, K. A. P. M. (2006) Kicks from the penalty mark in soccer: The roles of stress, skill, and fatigue for kick outcomes. Journal of Sports Sciences, 1-9, Preview article.

These numbers are based on penalty shootouts at World Cups, Euros and Copa Americas. There’s no detail as to how many it’s based on or which years (in the portions quoted in McMahon’s article). There’s two significant points I think you can draw from these numbers. The first is that either teams are deliberating picking their best penalty taker to go first (which is obviously contrary to the point that deVos and McMahon are drawing from the research) or there is significantly less stress and anxiety that players feel shooting first compared to later on and that is why a higher percentage of them score. Here’s the researchers take on their numbers:

These results highlight the increasing pressure as the competition progresses and may also highlight the ‘best player should go first’ fallacy. The idea of ‘getting off to a good start’ by putting the best penalty taker first appears wrong as there is least pressure on this kick.

That may be true or perhaps it’s just that teams are more likely to have their best penalty taker shoot first and that’s why more of the first shots go in. Alonso missed today but he is clearly one of the best options for Spain on penalties. Same with Balotelli for Italy who supposedly has not missed a penalty in a competitive game since 2008. Further if there is indeed ‘increasing pressure as the competition progresses’ why is there an uptick on the fifth penalties? Surely these carry with them more pressure than the second, third and fourth rounds?

The most cogent point you can make besides the fact that success on the first kick is significantly higher than all others is that the differences between the second, third and fifth are statistically insignificant. The variation between the percentages is too small to be meaningful.

In fact the most statistically significant statistic I’ve read today was on Bobby McMahon’s Twitter feed saying that 20% of penalty shootouts don’t make it to the fifth round. This, for me, is the most compelling reason to not have your best shooter go last. If you choose to put that player last you are conceding that there is a one in five chance he or she may not even get a chance to shoot.

There’s a double jeopardy there. By placing your best shooter last you, by definition, put a player more likely to miss in a position where they will have to shoot. If they fulfill that statistical likelihood not only do they miss more often than the top pk taker would but they help create the scenario that deprives that top pk taker of even getting to shoot as they improve the odds of the other team wrapping up the game before the tenth shot is taken.

Based on that, I would always choose to have the player I perceive to have the best chance of scoring on the day take one of the first three penalties and generally the first one. If, as a coach, you believe they have the best chance to score, you have to give them that platform to be able to do so.

More succinctly, according to Castrol Edge Football, Ronaldo has scored on over 91% of the penalties he’s taken since 2008. If I’m picking the order, Ronaldo is put somewhere  where he has a 100% chance of getting to shoot.

If an odds maker was going to handicap the shooters, given the order they would shoot, they would not look just at their historical success rate. If the bet offered is “Will Ronaldo score in the shootout. Period” they will look at the chances of him getting to shoot.

If we use McMahon’s assertion that only 80% of shootouts reach the last round and assume a graduated progression from the seventh to the tenth shooter given the first six are 100% guaranteed to shoot, then the odds will look something like this.

Name Historical success rate Odds of shooting Chance of scoring
Alonso 86% 100% 86%
Moutinho 84% 100% 84%
Iniesta 82% 100% 82%
Pepe 80% 100% 80%
Pique 80% 100% 80%
Nani 84% 100% 84%
Ramos 81% 95% 76.90%
Alves 81% 90% 73%
Fabregas 85% 85% 72.25%
Ronaldo 91% 80% 72.30%

By using this order for the shooting (and all but Ronaldo’s historical success rate on penalties are estimates), we have reduced the chances of the best penalty taker of the ten by almost 20 percentage points.

Full disclosure: I’m useless at math. Those with a brain for it and welcome to pick this logic apart in the comments

OK, subject now beaten to death. Hoping that tomorrow’s semi-final is settled in 90 minutes.

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2 Responses to Does it matter what order you send players to take penalties?

  1. TM says:

    OK, I’ll bite, let’s have fun with math.

    First let’s be clear that you are assuming above that the players’ historical success rate represents a fair approximation of their likelihood of scoring a goal (ignoring factors like success rates against this individual keeper and order they take the PK) and that each player’s chance of scoring is an independent event. These are very big assumptions.

    In any case, the math above is somewhat spotty but I won’t bother calculating the actual numbers according to your methodology because there’s a fundamental flaw in its logic in that the names and order of the opposing players is only known after the coach has already picked up his PK takers. When the names of the 5 Portugal players were picked the best the coach could have known, even if he guessed the names of the 5 Spaniards, is their average success rate from the spot (82.8%). More importantly, he didn’t even know if his team is shooting first or second.

    Moreover, we should take into account that the main objective of this exercise is not player A taking the PK but rather the team not losing in the first round of PKs (since you can only control your players one cannot guarantee winning but merely not losing). Let’s assume, for instance, that you are going against perfect players (100% chance of scoring) and when the first of your players misses you’re gone, do you care if it’s no 1 or no 5 that misses? Chance of not dying is exactly the same..

    I ran the numbers and with these 5 Portugal players and the pre-pick best guess of Spain’s success rate, regardless of the order Ronaldo goes in, the coach could only know that they had a 30.6% chance of losing (and BTW a 34.3% chance of winning).

    To make things more realistic (too late for that) if we constrain the choice to only who should have gone fourth, Ronaldo or Alves, had Ronaldo taken it Portugal would have had a 10% greater chance of going to the 5th taker but when it came Ramos’ time they’d have a 10% lesser chance of not losing.

    As Bento said, if it had gone to Ronaldo 4-4 nobody would be talking about this….

  2. Greg Basham says:

    This site below has some interesting stuff including mentioning the study in the original post. There was also an interesting point about the GK moving in those articles and how shooters fared better. I like the view that the GK should just play big and get those he can versus diving for corners and missing.

    You want to score as many to start as possible and putting your best guy too late is not a good strategy. Not sure of the numbers but an early miss usually boosts confidence in opponents.

    If is about consistency and responding to the pressure of the situation. Those two factors alone are the most important considerations a coach should be using. While I hate watching players warm up (amateur) knocking dead balls at the net it is never a bad thing to take one of your practice sessions and finish up or include competitive shootouts to judge how your players are doing. In my experience the best penalty shooters weren’t always the top goal scorers.

    My last game as a coach we won the shootout in 5 by placing in the mix two left footed shooters (neither of which were goal scorers) but did well in training on these. One was a MF and the 5th shooter a DEF.

    I have known good coaches who would ask for volunteers and my experience watching that was always watching a train wreck. I have never done that but will let a player opt out if that day he is not at the top of his form or is bagged after the game and OT.

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