Much has been written recently about the importance of bowling in T20 in general statistical terms and with reference to specific bowlers and their technical proficiency with yorkers and variations of pace. There is great interest in the apparent renewal of wristspin. It is far from clear if any of this is based on insights into the structural logic of the T20 contest. It's nice to see spinners beating the swinging bat in T20 games, but how significant is their contribution, or, for that matter, how significant is the contribution of any player?

This article is part one of a two-part series examining the structural limits of batting and bowling in T20. Bowling is considered in part one. Batting is considered in part two with special attention to the single.

A bowler's contribution is limited to 24 balls or fewer in T20. A batsman's contribution has no equivalent hard limit. How do these limits shape the bowler's role? While individual bowlers might offer novel contributions, are these really significant in T20? Evidence suggests that there is a structural limit to the value of bowling in T20, and even if it currently seems as though "batting wins matches, bowling wins tournaments", this may not be due to quality of the bowling.

Ball-by-ball commentary is available for nearly two-thirds of the approximately 7000 T20 games played since 2003. Based on these records, an over-wise scoring performance can be determined for each batsman and bowler. A batting and bowling rating can be calculated for each player based on these records. This is illustrated below using the examples of Chris Gayle and Sunil Narine.

In the graphs above, the black lines indicate the overall average scoring rate in each T20 over, from the first to the 20th. The black blobs indicate the player's scoring rate. For a batsman, a higher scoring rate is better, while for a bowler, a lower scoring rate is better. The black bars show the over-wise distribution of the player's participation.

While bowlers bowl the entire over, batsmen can face anywhere between zero and six legal deliveries in an over. The over-wise distribution takes into account the number of legal deliveries the batsman faced in each over, and not just how often a batsman was at a crease during a particular over of the 20.

Suppose a T20 batsman comes in on ball 4.2 (the second ball of the fifth over) and is dismissed on 8.5. Suppose this player faced three balls in the fifth over and made one run off them, made four off two in the sixth, ten off five in the seventh, two off two in the eighth, and three off two in the ninth. The average scoring rates for these overs are 7.55, 7.60, 6.17, 6.46 and 6.78. For each over, the player's scoring rate (per six balls faced) can be calculated. For each over, the player's net scoring rate per ball can be calculated from this. A weighted average of this net scoring rate per ball (weighted by the number of balls the player faced in each over), will give you the player's batting rating for this innings. This way, the difference between scoring 20 (off 14) between overs three and nine can be differentiated from scoring 20 off 14 between overs 14 and 19. A similar process can be used for bowlers, except that in their case, the bowler delivers the entire over in each case, except if there's an injury, or the match or innings is complete before the over is completed.

Gayle has batted in 292 innings and bowled in 116. He faces 24.9 balls per innings on average, and bowls 14.9 balls. The batting and bowling rating is the weighted average of the net over-wise performance. The weight is the over-wise distribution. So, Gayle's batting is worth +8.3 runs per innings. His bowling is worth -0.3 runs per innings. A smaller (i.e. negative) rating is better for a bowler, while a larger (i.e. positive) rating is better for a batsman.

Similarly, Narine has bowled in 278 innings and batted in 111. In the first half of his career, he batted in the tail, while in recent seasons he has been opening the batting. This is evident from his over-wise batting distribution, which shows higher concentration towards the two ends. Narine's batting is worth +2.3 runs per innings, while his bowling is worth -7.2 runs per innings. Narine bowls 23.3 balls per innings and faces 7.4 balls per innings on average.

Narine and Gayle are the top rated bowler and batsman according to this method of calculation. They are exceptional performers. Virat Kohli has a batting rating of +3.6 runs per innings, and faces 26 deliveries per innings on average. AB de Villiers' batting is rated at +5.5 runs per innings, and he faces 20.4 deliveries per innings.

If we consider all T20 batsmen who have batted at least 50 times and all bowlers who have bowled at least 50 times, then their records are distributed as shown below. The batting and bowling charts have been scaled identically, and each shows the number of deliveries per innings plotted against the batting or bowling rating. There are 336 batsmen and 294 bowlers. The average batting and bowling rating is 0.0, represented by the vertical axis.

A comparison of the two graphs above begins to suggest the structural logic of the contest. Nine per cent of all batsmen participate in more than 24 deliveries on average; the average contribution of 97 (29%) of these 336 batsmen is worse than the average performance (i.e. their batting rating is less than 0), while 147 (50%) of the 294 bowlers make contributions that are worse than average (i.e. their bowling rating is greater than 0).

The comparison between batsmen and bowlers who are better than average is given below. Note that "better than" means +1, +2 and so on for batsmen, and -1, -2 and so on for bowlers.

Instead of considering career summaries which give us average batting and bowling ratings, and average numbers of balls faced, we can consider the record at the level of the individual innings. The graphs below are the same as the two above, but instead of providing career summaries of players who have batted in 50 matches or bowled in 50 matches, all innings are represented (there are roughly 64,000 individual batting innings, and 52,000 bowling innings). This chart demonstrates the difference in scope available to the bowler and batsman.

Nineteen per cent of all individual T20 batting innings last longer than 24 balls. This is a small measure of the value of batsmen. The best individual bowling performance included above is Chris Morris' 2 for 2 in 4 overs against Cape Cobras in 2014, which has a bowling rating of -31.5 runs per innings. Narine's highest-rated bowling effort came for Guyana Amazon Warriors against Antigua Hawksbills in 2014. Narine bowled four overs for three runs; his rating was -28.5. Gayle's 175 in 66 balls has a batting rating of +95.2. Alex Hales' 95 in 30 balls in last year's T20 Blast has a rating of +60.7.

The potential upside for the batsman is greater than the potential upside for the bowler. Even if we consider innings that lasted less than 24 balls, Yusuf Pathan's 72 in 22 balls for Kolkata Knight Riders in 2014 (the highest-rated such innings) has a rating of +46.1 runs.

The fact that ten wickets are available to the batting side over just 120 deliveries forms only one part of the advantage available to the batting side. The rest of the batsmen's structural advantage comes from the total *flexibility* available only to batsmen.

Barring injury or the completion of a match, a bowler can bowl either six, 12, 18 or 24 deliveries. A batsman has no such limitations. A batsman who is stuck has the luxury of getting out. Given the generous resources available to batting sides, this is not a trivial advantage. For instance, if a bowler concedes 0, one, two or three runs in the first half of the over, then the second half of the over goes for at least seven runs 19% of the time. But if a bowler concedes at least seven runs in the first half of the over, then there's a 27% chance that the second half of the over will go for at least seven runs. If the first half of an over goes for ten runs or more, then there's a one in three chance that the second half of the over will go for at least seven runs.

Losing wickets should slow things down for the batting side, and to some extent, this does happen. If the batting side does not lose a wicket in the first half of an over, then at least seven runs are scored in the second half of the over 41% of the time. If a batting side loses one wicket in the first half of an over, this drops to 34%. However, 40% of all wickets in a T20 innings fall after the 14th over. In 75% of all T20 first innings, the team batting first has lost four wickets or fewer at the start of the 15th over.

In T20, losing a wicket is not always a setback, unlike in other forms of cricket. Rather, it is an indicator of the extra flexibility available exclusively to the batting side. If a batsman gets stuck, the obvious option is to take a single. The second option is to get out trying to hit the ball out of the ground. The resource equation is such that there are occasions in a T20 game when of the three options - hit a boundary, take a single, and dismissal, the third is better for the batting side than the single.

The bowling side does not have this luxury. A bowler cannot be withdrawn halfway through an over for tactical reasons. If, say, a batsman has the measure of a bowler, the fielding side has no option but to take the punishment for the rest of the over - significant because an over accounts for 5% of the total innings. Compare this to Test cricket, where the average Test innings lasts about 100 overs. A bad over in Test cricket means punishment for 1% of the proceedings before the fielding captain and make a change. In a T20 game, this single over accounts for five times as much of the game.

The inflexibility for the bowling side is further exacerbated by the fact that each bowler can deliver only four overs. The charts below demonstrate the consequences of this. The only bowlers who are net- positive contributors to their sides in T20 tend to be those who bowl their full quota in every game as a rule. The bit-part bowlers who deliver one, two or three overs per innings, tend to be net-negative contributors.

As many readers will have observed by now, this problem of inflexibility should also be evident in the 50-over game, where 30 balls are available on average per wicket, as opposed to 12 balls per wicket in T20. However, the acuteness is significantly greater in T20. The average T20 bowler bowls 18 balls in an innings, while the average T20 batsman faces 14 balls in an innings. In ODIs the corresponding figures are 44 balls and 30 balls. (Note that this is a simple balls- per-innings calculation, considering all players who batted or bowled in an innings, excluding did-not-bats and did-not-bowls, and ignoring how the innings ended.)

A ten-over quota in an ODI is larger than the average spell by a bowler in Test cricket, while a four-over quota is smaller. If the spell is taken to be an empirical limit on the bowler's capacity to be effective without a break, this distinction seems to be significant. The difference in the degree of inflexibility can also be seen by considering that one over is 10% of the bowler's possible contribution and 2% of the team's contribution in an ODI, while it is 25% of a bowler's contribution and 5% of a team's contribution in T20.

It is generally seen that batting sides tend to be more conservative than they need to be in T20, given the resources available. When the chasing team loses in ODIs, it is bowled out 74% of the time and loses at least eight wickets 90% of the time. In T20, the losing chasing team is bowled out only 37% the time and loses at least eight wickets only 68% of the time. This is the case though chases are successful more often in T20s (about 54% in recent years) than they are in ODIs (about 50% in recent years). In the 2018 IPL, of the 28 chasing teams that lost, 21 were not bowled out, and 14 lost six wickets or fewer.

Between the conservatism of the batting sides and the structural constraints the bowling sides operate under, the T20 contest faces an interesting vicious cycle. Batting sides feel the need to be conservative because they select too many specialist bowlers. They select too many bowlers because the rules give fielding sides little flexibility and they feel the need to have five or six bowling options, three (four if a team is lucky) of whom can also hit the ball hard. Given that there are only a handful of realistic opportunities for bowling changes, this means that at least two of the bowling options are underbowled. These players are also not trusted sufficiently as batsmen.

T20 could resolve this inflexibility by making one (or both) of the following two changes to the rules:

1. Eliminate the individual quota for bowlers

2. Allow captains to withdraw bowlers after three legal deliveries for tactical reasons

While individual bowlers bring innovation and variation to T20, the significance of their contribution is determined largely by the structural limits of the T20 contest. Bowlers have to contend with trigger-happy batsmen, but bowling teams have to contend with the inflexibility imposed by te format. Easing the latter will not only give bowling sides more teeth, it will also encourage teams to pick fewer bowlers and for batsmen to attack the bowling more than they currently do.