Read part one of this two-part series examining structural limits to batting and bowling in T20 here.

The single is the most peculiar event in a limited-overs match. It is peculiar because most singles signify a unique stalemate. In baseball, the hitter has to attempt to reach first base if a fair hit is made. In cricket, the batsman is expected to make a judgement as to whether it is possible to complete a run safely, and then decide whether or not to run. In limited-overs cricket, the point is to score as many runs as possible in a predetermined number of overs. So a delivery from which no run is scored can be considered a win for the bowler. A delivery hit to the boundary can be considered a win for the batsman. Given average scoring rates, twos or threes (which are rare events as shown below) could be considered wins for the batting side. This leaves us with the single.

In a game in which the scoring rate is faster than a run a ball, the single is the narrowest possible loss for the batting side on that delivery. In a game in which the scoring rate in slower than a run a ball , the single is the narrowest possible win for the batting side. The former situation described T20 games, while the latter describes ODI games.

In the T20 era (starting in June 2003), 79% of all ODI first innings have involved a scoring rate of under six an over and 95% under seven. In the same period, 12% of all T20 games have had a scoring rate of under six. Since the 2015 ODI World Cup, 9% of all T20 games and 73% of all ODI games have had a scoring rate of under six.

It is therefore reasonable to say that on the average delivery in an ODI, the single is the narrowest possible win for the batting side, while on the average delivery in T20, it is the narrowest possible defeat for the batting side.

Based on ball-by-ball data from 102 IPL and BBL games and 120 ODI games from 2017 and 2018, the most common run outcomes for each delivery in ODIs and T20s are 0,1,4,2 and 6, in that order. This ball-by-ball data also records the batsman's control of each delivery.

Control % by run outcome in each match type Match type 0 1 2 3 4 6 BBL 51 86 83 77 88 95 IPL 49 86 82 81 89 96 ODI 72 90 86 92 89 96

Share of each run outcome in each match type Match type 0 1 2 3 4 6 BBL 38.5% 37.5% 8.6% 0.6% 10.3% 4.5% IPL 37.9% 38.9% 6.2% 0.3% 11.6% 5.1% ODI 51.9% 33.1% 5.0% 0.5% 7.9% 1.6%

Dot balls and singles are the most frequent events in limited-overs cricket. They account for 85% of all deliveries in ODIs and 76% of all deliveries in T20. In both T20 and ODIs, about one in ten fours is a mishit and one in 20 sixes in a mishit. On the dots and singles side of things, matters are interestingly different. Half of all dot balls in T20 occur with the batsman not in control of the delivery, while 72% of all dot balls in ODIs occurs with the batsman not in control of the delivery. One in ten singles in ODIs occurs with the batsman not in control of the delivery, while in T20s, one in eight singles occurs this way.

Another way to think about this is that in the average T20 innings (120 deliveries), 46 deliveries are dot balls and 46 are singles. Of the 46 dots, 23 occur with the batsman not in control. Of the 46 singles, six occur with the batsman not in control. There are 40 in control singles in the average T20 innings - one every three deliveries. In the average ODI (300 deliveries), 156 deliveries are dot balls and 100 are singles. Of the 156 dots, 44 occur with the batsman not in control. Of the 100 singles, ten occur with the batsman not in control. There are 90 in control singles in the average T20 innings.

Thirty-three per cent deliveries in the average T20 innings go for an intended single, compared to 30% in the average ODI innings; 15% of dot balls in the average T20 innings occur when the batsman is not in control, compared to 19% in ODIs. When the batsman is in control, the figures are 19% in T20s and 37% in ODIs. Batsmen choose to (or are forced to) defend twice as often in ODIs as they do in T20s.

Kartikeya Date

Kartikeya Date

If we consider the over-wise frequencies of dot balls and singles, separated by control, then the so-called "middle-over-problem" from ODI cricket is immediately evident. From overs 11 to 40, the number of in-control dot balls and singles per over holds steady between 2 and 2.5 each. In T20 innings, there is no corresponding pattern. The number of in-control singles per over rises to about 2.5 in the seventh over (as soon as the Powerplay ends) and remains steadily between 2.5 and 2 until the 16th over. The in-control dots, on the other hand, steadily declines from overs 1 to over 20. From overs 7 to 14, it declines gently going from just above one dot ball per over to just below one dot ball per over.

In one sense then, the T20 format has solved the middle-overs problem. If one accepts the idea that taking a single is a way "to keep the scoreboard moving" and advancing the team's cause, then T20 maintains this feature, while halving the number of dot balls (from 37% in ODIs to 19% in T20). But unlike in ODIs, in T20 the batting side falls further behind after the single than it was before the single. Bowling sides contest the single less vigorously in T20 than they do in ODIs. Fields are often set with all the required infielders on one side of the wicket (usually the off side) and all the available boundary fielders on the other side. In such fields, the infielders stand as deep as possible, on the very edge of the circle, essentially conceding one run every ball.

We are conditioned by decades of ODI-watching to think of the single in a certain way. It signifies progress for the batting side in the ODI innings. It rotates the strike, forces the bowler to face a new batsman and the fielders into a new field setting. Given the average scoring rate in ODIs, the single is progress. This is also how we seem to see the single in T20. Yet, in T20, fielding sides contest the single less frequently than they do in ODIs. This is why in-control dots occur twice as often in ODIs than they do in T20s. The average scoring rate in T20 is comfortably greater than a run a ball. Far from signifying progress, the single is a setback for the batting side, in much the same way that a dot ball is a setback for the batting side in ODIs. When you see a single in a T20 innings, what you are watching is more like a dot ball in an ODI innings. It has very little in common with the single as we have come to know it from the ODI game.

Teams that score more boundary runs, but fewer non-boundary runs than their opponents have won 77% of T20 games and 68% of ODI games. Boundary runs account for 55% of all T20 runs and 42% of all ODI runs. Boundaries influence the T20 game more than they influence the ODI game. Evidence from the control numbers suggests that singles in T20 are a concession by the batting side to the bowling side, in much the same way that dot balls are a concession by the batting side in ODIs. Even though the control figures for singles are similar in both formats, the control figures for dots suggest that fielding sides in T20 contest singles less vigorously than they do in ODIs.

This idea could be clarified further by recording attempted boundaries. If bowling sides do not contest singles, then the attention should shift to attempts to score boundaries. This is where the contest in T20 is concentrated. The single is just filler.