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%
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|
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.