Peshawar Zalmi lost the first qualifying final of the 2017 Pakistan Super League against Quetta Gladiators by one run. Thanks to Kevin Pietersen's 40 off 22 and Ahmed Shehzad's 71 off 38, Quetta had made an even 200 batting first, despite having struggled in the final third of their innings. Pietersen and Shehzad added 90 together in seven overs.

The run chase followed a similar pattern. After two early wickets, Mohammad Hafeez and Dawid Malan added 139 in 12 overs before Hafeez was out. Malan was at the wicket for the first 91 legal deliveries of the run chase. Of these, he faced 30, and made 56 runs. Hafeez was out to the fifth ball of the 14th over, having faced 47 of 72 balls bowled while he was at the wicket.

Despite Shahid Afridi's 34 in 13 balls, Peshawar lost by one run. From a cricketing point of view, this game is easily read. The conclusion is that despite Hafeez's brilliant 77, and support from Malan (56) and Afridi (34), Peshawar lost a game they ought to have won.

Does this reading hold in T20, though? There is some evidence to suggest otherwise. This evidence also points to a logic of the T20 run chase that is distinct from that of the ODI run chase.

Theories about how chases should be approached in limited-overs cricket abound. Given that boundary shots produce four and six runs off one ball, the predominant theory in the early days of ODI cricket was that chasing teams should keep wickets in hand even at the cost of falling behind the required rate, and then make one concerted push over a small number of overs at the end to win. Imran Khan and Javed Miandad were arguably the most famous proponents of this theory. The thinking here was that in the early overs of a chase, the game could not be won, but it could definitely be lost. This theory worked well when the overall asking rate was under five runs per over, and falling behind the rate meant needing about 7.5 to 8.0 runs per over for the last 10-15 overs.

"The logic of the T20 run chase is distinct from that of the ODI run chase"

ODI teams were constructed to adopt this theory. India did this famously well under Sunil Gavaskar's leadership in Australia 1985-86. Ravi Shastri was promoted to open the batting and provide solid, albeit slow, starts in that tournament. Desmond Haynes and Gordon Greenidge played this way for West Indies throughout the 1980s.

But soon teams began to see that using an attacking opener would help. From Mark Greatbatch in the 1992 World Cup to Brendon McCullum in the 2015 one, New Zealand and every other side have adopted this tactic. This became so popular that the ICC then had a so-called "middle-overs problem" and changed the rules to restrict field settings during this phase to reward risk-taking similar to that found at the beginning and end of limited-overs innings.

Hafeez's innings in the PSL game was not dissimilar to Virat Kohli's innings in the 2016 IPL final. Like Kohli, Hafeez did not attack from the word go. And just like Kohli, his approach will be widely considered through the lens of the well-understood ODI logic.

Consider how Hafeez's innings would translate into a 50-over innings. Going by the frequency with which a target of at least 200 is set in a T20 game, the equivalent asking rate in an ODI first innings in the T20 era (June 13, 2003 onwards) is 6.8 runs per over, or 340. Both are set 7% of the time by teams batting first.

Virat Kohli is distraught after returning to the dug out AFP

Hafeez played 47 balls out of a possible 120, and scored 77 chasing a target of 201. In other words, he used 39% of the deliveries available to his team and scored at a rate that was just under the required rate. The equivalent ODI innings in the equivalent ODI run chase of 340 is 132 in 117 balls (scoring at the minimum required rate for 39% of the possible 300 deliveries).

This is equivalency considered from the batsman's point of view. From the team's standpoint, the equivalency does not quite work this way. The units of scoring available in the 20-over and 50-over chase are the same. Sixes, fours, singles, twos, threes, wides, no-balls, leg-byes and byes are all counted in exactly the same way in both chases. The cricket ball and the boundary are also the same, as are the bats, as is the quota per bowler (20% of the total balls bowled per bowler). All the ingredients of run production are the same. In the 50-over chase, 132 off 117 in a 340 target would leave the other ten batsmen needing to get 208 in 183 balls. In the 20-over chase, 77 off 47 in a 201 target would leave the other batsmen needing to get 124 in 73.

Standard cricketing wisdom states that compared to a new batsman, a set batsman will find it easier to score quickly. This wisdom has developed in the context of batting - the art of accumulating as many runs as possible with as much certainty as possible. The art of batting involves recommendations about relying on timing, hitting the ball along the ground, playing with a straight bat, not playing across the line when the ball is on the stumps, and waiting for the bad ball. This wisdom is often transferred wholly to the T20 context.

Halfway through his innings, Hafeez had scored 31 off 24; the second half produced 46 off 23. This split suggests that the conventional wisdom about batting is true. Using the first few overs to "get in" seems to have helped Hafeez score more quickly in the second half. At 31 off 24, Hafeez had used up 20% of the deliveries available to his team to be nine runs behind the minimum required rate. Later, when he was on 32 off 27, they were 13 runs behind the required scoring rate. In the second half of his innings, he did eight runs better than the minimum required rate.

"In T20, a batsman choosing to use 20 balls to get his eye in is taking an enormous risk by essentially conceding one-sixth of the total available deliveries to the opposition without contest"

It is here that the cricketing logic breaks down. One batsman using up nearly 40% of the total deliveries to get set and end up at the minimum required rate means the other batsmen have a great challenge on hand to achieve more than the required rate for 60% of the total deliveries.

Suppose those remaining 124 runs are scored by five batsmen among themselves. Let us say (conservatively) that each batsman takes two balls to get set. Let us say four of them get out. That's 14 balls out of the remaining 73. If we assume that those 14 balls produce 14 runs (let us assume this even though four of those 14 deliveries result in dismissals), then 110 runs remain to be scored from the remaining 59 deliveries without a single dismissal. In other words, Hafeez's 77 in 47 still left Peshawar one innings of 110 off 59 short of victory.

Consider the same calculation for the equivalent 50-over chase: 208 are required from 183 balls. Let's say that five batsmen are available for this, and that each of them takes an average of six balls to get set, and during those six balls, score, on average, three runs each. Four of them are dismissed. This means that them getting set uses up 34 balls, during which 15 runs are scored. What remains is 193 in 149 balls.

Still very difficult. But compare the requirement of 193 in 149 balls (or 7.8 runs per over), to the requirement of 110 in 59 balls (11.2 runs per over). The comparison is valid because the units of scoring and all other factors are equal in both cases. The latter is significantly more difficult.

When we consider these chases, we usually remember the last over, or the last couple of overs. We have a tendency to think that it was those two overs that determined the outcome of the game, and that earlier events are of little consequence. Perhaps this is why we are likely to describe Peshawar's chase as the players at the end undoing Hafeez's great work.

Yet, in T20, a batsman choosing to use 20 balls to get his eye in is taking an enormous risk by essentially conceding one-sixth of the total available deliveries to the opposition without contest. This concession arguably makes a bigger contribution to the result than anything that happens in the last two overs of the match.

A target of ten runs per over (rounded)* has been set 422 times in T20 games in ESPNcricinfo's database. Of these, 390 chases have lasted into the 16th over and 75 chasing teams have won. A further nine were won before the 16th over. Of the 390 chasing teams that took the match into the last five overs of the chase, 68 did it with seven or more wickets in hand and a required rate of ten runs per over (rounded) or more; 26 of these teams won. Meanwhile, 13 teams did it with six or fewer wickets in hand and a required rate of less than ten runs per over; 11 won. Compare 11 wins in 13, to 26 wins in 68. More significantly, compare 13 to 68.

The history of T20 thus suggests that teams are far more willing to use cricketing wisdom and keep wickets in hand rather than go hell for leather early. But history also shows that the latter approach is decisively more successful. This because of a paradoxical point: while it is probably better for the batsman to launch an assault on the bowling later rather than sooner, it is worse for the team when the batsman does that. This is because all the deliveries used up to get set are essentially conceded without contest to the opposition. With so few deliveries available as a whole, this concession is unaffordable, according to the arithmetic.