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Penalties and the percentages that accompany them are a statistician's dream: take the colour of the goalkeeper's jersey, for example. Apparently Argentina went into Friday's shootout against the Netherlands with a 75% chance of winning as opposed to the Dutch's 54%, simply by dint of the fact that Emi Martinez was wearing a red shirt and Andries Noppert a green one.

The World Cup has now entered that stage where descriptions of the penalty are reduced to expressions like 'lottery' and 'luck' when in reality it is anything but – the single greatest determining factor in penalty-kick taking remains unchanged: it's about keeping one's nerve and allowing probability to guide you.

Put simply, Harry Kane didn't, neither did Marquinhos while Lautaro Martinez did.

Let's look at Kane's scenario first. The percentage likelihood for scoring a penalty stands at around 75% and, despite what the ex-pros would have you believe, it rises slightly to 76% for a successful outcome when the same player is presented with a second penalty to convert. But Kane's circumstances were slightly different in that was facing Hugo Lloris, the man who has been his clubmate for the past 10 years. The France goalkeeper has had a behind-the-taker view of every one of the 47 penalties Kane has taken for Tottenham and that's just in competitive matches. There's also the ones he's taken in every training session at the club's Bulls Cross training centre, too.

It explains why Kane, successful with his first kick against the France captain, altered trajectory and went for the top left corner when he had earlier stuck his first penalty into the middle left corner. A statistician will tell you that – by shooting for the top left corner – he had a 100% chance of success had he executed his high-risk, high-reward kick successfully. Of course, there is an operative word in that statement because the chances of him actually pulling off a kick of such accuracy and scoring is 76.9% based on historical records in previous European Championships and World Cups.

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It is, of course, stating the bleeding obvious to point out that it is not just technical ability that starts to play a part at this stage when it comes to taking a penalty at a major tournament.

The psychological impact can be witnessed clearly in some of the repeat trends that tend to throw themselves up in shootouts. But at these finals there is a case for disputing some of what science would have us believe. The figures will tell you that you have a 60% chance of winning on penalties if you win the toss and go first. In Qatar that figure is operating at 50% with Croatia losing the coin flip against Japan but winning it in their quarter-final match up with Brazil. The Croats have demonstrated the necessity of being well versed in the art of the penalty. They have reached the semi-finals by winning just one game at these finals and their nerve-jangling progress has mimicked their knockout stage of Russia 2018 – when they accounted for Denmark and the hosts on penalties – en route to the final. It seems certain that the experience they have gleaned from four years ago has provided them with a platform four years on. 

In the other two ties settled by penalties at these finals the Netherlands went first only to lose to Argentina, while Morocco took the opening kick in their last-16 win over Spain.

Another quirk of the shootout can be found in the high-pressure emphasis that is placed on the eighth taker. It stands to reason that this is a position in the shootout that can often prove decisive – and that is backed up by the figures. Prior to these finals a mere 60.7% of penalties taken eighth in a World Cup shootout have been converted (17 of 28). Meanwhile the ninth penalty taker tends to score marginally better at 62.5% of the time (15 of 24).

If ever numbers could be seen to provide the physical manifestation of something it is that of the stress felt by Marquinhos in missing Brazil's decisive spot kick in exiting to Croatia on Friday evening and the shank by Enzo Fernandez as he spurned the opportunity to safeguard Argentina's passage against Netherlands later that night. The Brazilian's miss proved decisive whereas Fernandez was bailed out by Martinez.

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