Toni Kroos stood over the football on the edge of the Swedish penalty area. The angle was acute. Team-mate Marco Reus pointed out to Kroos that it might be better if he went for goal, since the Swedish defense had a height advantage over the German attack. Kroos did, playing a very short pass to Reus, who lined up a drive for Kroos around the nominal Swedish wall. Kroos' drive curled around the wall with pace and nestled in the far corner of the Swedish goal.

Kroos had come through when it mattered. Germany's world-champion midfield maestro had just produced that holy grail in elite professional sport - the clutch performance.

The standard narratives of sporting contests suggest that there are some parts of games that are more important than others. There are key moments, and key players who specialise in these key moments. The great tennis players, we are told, excel especially when the game is on the line. The great footballers are the ones who finish (or defend) that one crucial chance late in the game. Great basketball players specialise in the last few dozen seconds of games. They take their game to a higher level. The great batsmen are the ones who score when it matters.

The idea that some parts of sporting contests matter more than others follows from these notions. Identifying these key moments and winning them is a skill some players have and others don't. Fans praise or condemn players based on their perceived achievements in these big moments. Sport is cast in a gladiatorial light in which there are winners and champions, and losers and cowards.

This model of sport and its contestants is a fantasy. History provides little evidence to support the idea that sporting contests are made up of big moments and smaller moments, key moments and average moments. Limited-overs cricket provides a great example of this model of sport because it involves run chases. The pursuit of a clearly defined target in a definite number of deliveries is considered perfect ground for "separating the men from the boys", as the curiously infantile expression of choice goes.

The "finisher" is a specialist in run chases, imagined as a player who is at the crease at the "business end" of the chase and sees the team home. Players who frequently finish undefeated in run chases are considered to be pressure performers. This reputation is acquired by a high success rate.

And yet, this definition is inaccurate. Every player who ever achieved a reputation as a finisher just happens to have played in very strong teams that had very strong batting line-ups. Michael Bevan and MS Dhoni, two of the greatest finishers in limited-overs cricket, score slower in chases than their team-mates do. What's more, in a large number of chases, they are not required at all. Dhoni, for instance, has played in 166 chases, of which India have won 104 and lost 62. He has batted in only 131 of these chases, of which India have won 69 and lost 62. Dhoni averages 50 in these games and scores at 81 runs per 100 balls. At the other end, India's batsmen average 31 and score at 89 runs per 100 balls.

Dhoni's reputation as a cold-blooded finisher was greatly enhanced in Australia in 2012. India's record against Australia away has historically been modest. On February 12, 2012, the two teams met at the Adelaide Oval. Australia batted first and made 269. India had reached 178 for 3 after 34 overs, and required 92 in the remaining 16 overs (96 balls). Gautam Gambhir was out on the first ball of the 35th over and Dhoni came to the crease. India eventually won by four wickets with two balls to spare. But they needed 13 from the last over, and 12 off the last four balls. Dhoni hit a six and finished 44 not out off 58 balls. The reviews of the game referred to an "ice-cool" Dhoni, but there was also the feeling that the game should not have been in the balance for as long as it had been. Sidharth Monga's account of India's chase puts Dhoni's effort in context. India had not batted well on the tour. Dhoni was under pressure. And he made sure that India got over the line.

The facts reveal a different picture. Dhoni could bide his time because the other end produced 46 in 34 for the loss of two wickets. Overall, Dhoni made 44 in 58; the other end produced 48 in 37. Dhoni's caution was subsidised by successful aggression at the other end. Had the other end produced only a run a ball, India would have found themselves needing 24 from the final over (in the worst case), and not 13.

So why was our attention drawn to Dhoni's caution and not to the successful aggression at the other end? Perhaps it is because we notice that Dhoni is there at the end of the game. Finishers who "see their team home" are the ones who are still there "when it matters".

This is generally true not only about Dhoni but about finishers in general. The table below shows a list of the most prolific finishers in ODI history (openers excluded). Twenty of these 30 batsmen score slower than their average partner in run chases. Among the exceptions, all but three score less than one-fifth of a run faster than the players at the other end. Over the full 50 overs, this amounts to ten runs. Virat Kohli, who has a brilliant record in chases, scores 69 (off 72) in the average chase; 66 runs are scored every 72 balls at the other end in these chases.

Kartikeya Date

There are exceptions. AB de Villiers, Suresh Raina, Aravinda de Silva and Andrew Symonds all score appreciably quicker than their partners. They are also more consistent than their partners. Yet, these four players would not feature on most lists of reliable finishers. They would figure in many people's lists of adventurous stroke-makers, great players even. But, especially in the case of de Villiers, there has been criticism of his inability to "take his team home", especially during the 2015 World Cup.

The over-wise record of three batsmen - de Villiers, Kohli and Dhoni - in chases will illustrate the difference between them. The chart below shows a five-over rolling scoring rate for the player and for their average partner by over in an ODI. The grey bars show the number of instances in which a player has been at the wicket in a given over in an ODI.

Kartikeya Date / © Kartikeya Date

De Villiers consistently scores quicker than the players at the other end. Kohli scores as quickly as the players at the other end, and then, on the rare occasions when it is still necessary, he can explode after the 40th over. Dhoni, on the other hand, consistently scores slower than his partners in chases, except towards the very end.

Kartikeya Date / © Kartikeya Date

Kartikeya Date / © Kartikeya Date

Unsurprisingly, Kohli and Dhoni are more successful than de Villiers in chases. They have to do relatively less heavy lifting. Kohli usually has a partner who maintains a steady scoring tempo and can match his scoring rate. Dhoni has partners who ensure that the required rate stays within reach.

The 100 most prolific run chasers in the world are shown in the chart below. The horizontal axis represents the number of runs scored at the other end per delivery for each run scored by the player per delivery. If this ratio is less than one, it means the player scores quicker than his team-mates; if greater than one, it means the player scores slower than his team-mates. The vertical axis shows the number of dismissals at the other end per dismissal for the player. If this figure is more than one, it means that the player is more consistent than his team-mates, and vice versa.

Kartikeya Date / © Kartikeya Date

Players fall into four categories - anchors, quick scorers, superior players, and liabilities. Anchors are more consistent but score slower than their team-mates. Quick scorers are less consistent but score quicker. Superior players are better on both parameters, and liabilities worse on both.

As the chart shows, most of the most prolific chasers are anchors. Superior players are typically marginally superior. For example, for every run scored by Kohli, 0.97 runs are scored at the other end. Liabilities are expectedly extremely rare. Most of them either keep wicket or bowl. If they do neither, they tend to be dropped, and thus don't figure in the list of the most prolific run chasers.

Only one "superior" player in ODI history has scored at least 10% faster than his team-mates and been at least 10% more consistent than them - Sachin Tendulkar between 1994 and 2004. Viv Richards scored 22% faster than his team-mates while maintaining about 9% superior consistency.

From 1994 to 2004, a period spanning three World Cups, Tendulkar played primarily (though not exclusively) as an opener, and made 6039 runs in chases, more than any middle-order batsman has batting second over an entire career. Tendulkar's career as a whole lasted a quarter of a century, and that longevity justifies the consideration of a decade of his career in isolation. The year he began opening the batting was 1994, and that's a good point at which to begin this period; 2004 is a good place to end it, as 2005 and 2006 were injury-ridden for Tendulkar and transitional for the Indian team. When he returned, it was in a different, significantly stronger, Indian side.

Tendulkar, Richards or de Villiers are not typically classed as great finishers. They are simply classed as great ODI batsmen.

The finisher, as most people imagine the creature, does not exist. There are players who have the luxury of biding their time because a lot of heavy lifting is being done very ably at the other end for about 80-90% of the duration of the chase. Those players at the other end may not get the not-out, but they contribute at least as much, if not more to the chase than the finisher does.

The trope about "being there when it matters" is a powerful one. Perhaps the question is: when do we think it matters? In professional tennis, for instance, it is widely accepted among fans that there are important points and unimportant points, because, in theory, it is possible to win a tennis match despite winning fewer points than the opponent. An informal Twitter poll I took showed that three out of four respondents thought that the top players win important points at a higher rate than unimportant points. Important points are those where the game is either in the balance or on the line.

The table below, using data from Tennis Abstract gives win percentages for four players - Rafael Nadal, Roger Federer, Novak Djokovic and Andy Murray - in each of six point categories (that are not mutually exclusive).

Breakpoints: 0-40, 15-40, 30-40, 40-AD

Behind: 0-15, 0-30, 15-30

Ahead: 15-0, 30-0, 30-15

Gamepoints: 40-0, 40-15, 40-30, AD-40 Even: 0-0, 15-15, 30-30, 40-40

Close: 30-30, 40-30, 30-40, 40-40, 40-AD, AD-40

Kartikeya Date / © Kartikeya Date

Tennis Abstract provides a measure known as the Dominance Ratio, which gives the number of points won by a player off the opponent's serve divided by the number of points conceded by a player while serving. This measure - on which Nadal scores 1.29, Federer 1.31, Djokovic 1.27 and Murray 1.20 - shows that the best players are better at winning points in general. The table above shows that they are not significantly better or worse at winning any particular type of points. They don't perform better on "important points" than on others.

Evidence of "clutch performances" has been elusive in other sports as well. In baseball the idea of the clutch hitter has existed for decades and has been studied at least since the 1970s, but there is no serious evidence to suggest that clutch hitting is actually a skill. Some studies have found the odd player who could be marginally considered to demonstrate "clutch capability", but these are not players who are typically considered clutch players.

So why does this idea persist? The idea of the "big moment" in sport is a classic example of an observer confusing the obvious with the significant. There are three reasons for this. The first two are well understood cognitive biases that humans have been shown to be prone to. And the third is a problem of standpoints.

The availability bias is our tendency to confuse the obvious with the significant. When evaluating a concept or an event, we tend to make use of those things that are most easily available to our minds. Memorable events during games are easier to remember and evaluate than other events in games. For example, not only did Dhoni stay till the end that day in Adelaide in 2012, he also hit a memorable six in the last over. However, that boundary was no more or less significant than any other delivery in the chase off which a boundary was hit or not hit. In that last over Dhoni had little option but to go for it, but the conditions that produced that desperate situation were as significant as the 13 runs scored in the final over.

The confirmation bias is our tendency to recall events in ways that confirm our pre-existing beliefs or ideas about those events. If we accept that big moments decide games, then we're likely to look for these big moments. Hence, when watching Federer play Nadal, we watch Nadal win an epic rally at 40-40, 5-5 in the fourth set, and start thinking to ourselves, "Wow, Nadal turns up in the big moments!"

What might a big moment actually be? As Kroos stood over the football in injury time, he knew the score like everybody else. He knew how much time was left. He knew that if they could score with that attack, they would almost certainly win. Everyone knew this. In that moment, just before he took the free kick, this was surely the biggest moment. It was the only moment. As it turned out, it was a moment that Kroos won. High-quality players are more likely to do this than average players because they're just basically better.

Afterwards, when one is evaluating the game as a whole, the only thing that can be said is that Germany scored a late winner. One has to shift standpoints from being in that 92nd minute with Kroos to standing apart and examining the game as a whole. The 92nd minute was the moment Germany grasped, after failing to grasp many others in the preceding 90 minutes. Germany had 76% of the possession and 18 shots on the Swedish goal. The game was shaped as much by each of those preceding 90 minutes as it was by that 92nd minute because Germany (or Sweden) failed to break the deadlock during those 90 minutes and 16 other opportunities, and several other plays which they failed to turn into opportunities.

Football consists of two teams, each trying to send the ball into the opposition goal. When a team has the ball, it tries to construct an attack. The defending team tries to break up the attack and win the ball. Typically the team that is more skilled at building attacks and breaking up opposing attacks wins. In Test cricket it is typically the team with the better bowlers - ones whose mastery of control and variation is superior to that of their peers - who end up on the winning side. In tennis the better players are just that little bit quicker; they anticipate better, move better, and have superior ball sense. These differences manifest themselves all the time in the contest. There are still some games - exceptions - where the less skilled player (or team) wins. These are known to us as upsets.

The idea of a clutch player - a player who is measurably superior in the big moments than at other times - ought not to exist in sport, because if such players did exist, it would mean that shortcuts exist in sport, that there are ways of winning without being excellent. "He's average most of the time, but that one time, when it mattered, he came through." This is a description of a fluke, not a skill.

To be fair, it is difficult to remember all 90 minutes of a game of football, or all points in a tennis match, or all deliveries in a cricket match. The problem occurs when we confuse what we can remember with what is significant. Excellence by individual players is common in sport. We hang on to big moments and clutch players because excellence is exhausting. It is exhausting to contemplate, difficult to describe, and until recently, the kinds of systematic measurements that would show excellence were beyond the reach of the average sports watcher (and indeed, the average sportswriter). Excellence was the domain of coaches and trainers who taught their wards methods and techniques. Methods and techniques are designed to produce good outcomes as a rule. The proliferation of measurements has made excellence accessible to spectators. As these become ubiquitous, perhaps we will learn to watch games differently.

Kroos is one of the world's best midfielders. He's also a specialist in dead-ball situations. He was on the ball that day in injury time because of these facts. Not because he is "clutch" in the big moments.