# How many boundaries should a T20 team attempt in an innings? More than you might think

Why fours and sixes are the primary grammar of the format. And will increasingly be so

Himanish Ganjoo

09-Dec-2020

Is it fair to view T20 through the same lens as we do cricket? Yes, the bat and ball are present in T20, but the fact that ten wickets are available to be spent in 120 balls fundamentally alters the calculus of risk and reward, arguably making it an entirely different game. In this condensed world, boundaries are the real currency, representing the maximal use of each precious delivery of the 120 you get to face. Adopting a mentality that pushes boundary-hitting to the forefront of batting strategy involves shelving a key tenet of batting as it is taught: the aversion to risk. The need to preserve one's wicket dominates the psyche of players, almost all of whom begin learning from a red-ball point of view. Success in T20 demands unlearning this and embracing the high-risk, high-reward strategy of trying to hit as many balls as possible.

If we model the chances of winning a T20 game as a result of the difference in fours, sixes, runs (ones and twos) and dots between the two teams, we can fit data from actual matches to pin numbers on the exact importance of each of these events. The way we express this is the odds factor. As an example, an odds factor of 2.0 for sixes means that each six you hit more than the opposition doubles your odds of winning the game. Using data from 1331 T20s in the IPL, PSL, BBL, CPL and the T20 Blast over the last five years, we find the odds factor corresponding to each outcome.

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While each additional dot ball compared to the other team reduces your odds by a factor of 0.71, the payoff for boundaries is much greater. Each additional four hit inflates your odds of winning 1.9 times, and each six improves them by a whopping 2.9 times. Singles and doubles have a comparatively insignificant influence on the chances of winning.

These numbers not only concretely illustrate the obvious truth that boundaries matter much more than dots, they also quantify their relative importance: to maintain the same odds of winning, you can afford to play 3.2 more dots as long as you hit one more six, and you can afford to play 1.9 more dots per extra four you hit. In summary, a six is worth 3.2 dot balls on average.

The relative importance of boundaries and dots varies between different competitions, owing to variations in conditions and playing philosophies. A six is worth 4.28 dot balls in the IPL, 3.52 dot balls in the BBL, 3.04 dot balls in the PSL, and 2.78 dots in the CPL. However, across these analyses of individual leagues, there is consistently no statistically significant relationship between the odds of winning and the difference in the number of ones and twos run by a team. The data speaks conclusively: running between the wickets is overrated in T20, dot balls are not a crime, and boundary-hitting is the real driver of success.

This philosophy has been adopted by the elite white-ball sides of the world: the World Cup-winning West Indies teams, the post-2015 attacking avatar of the English white-ball side, and most recently by the Mumbai Indians in their victorious 2020 IPL campaign.

The most prominent exponent of this ideology is Chris Gayle. In the IPL, Gayle has a boundary percentage of 23% from 3179 balls faced, placing him fifth out of the 99 batsmen who have faced 500 balls or more. More surprisingly, he has a dot ball percentage of 41.5%, the 13th highest out of the 99; and the fourth-lowest percentage of ones and twos taken. And yet he has maintained a strike rate of 150 over 131 innings. His approach is simple: pay little heed to running, try to make every scoring shot a boundary, and if you fail, concede a dot. Gayle trusts his skill to get the ball over the ropes, and realises that, given his ability, staying at the crease has a greater net payoff than turning the strike over.

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Gayle's West Indies team-mates Kieron Pollard, Sunil Narine and Andre Russell employ a similar strategy of boundary or dot to great success. As the plot above shows, there is no correlation between dot and boundary percentage. Since boundaries are the major source of strike rate, we can establish that there is little relation between dot balls and a batsman's strike rate.

Players and teams who are ahead of the curve in terms of strategy place increased emphasis on attacking through the innings. In the most recent IPL season, Quinton de Kock of the Mumbai Indians had the role of a powerplay boundary hitter, lofting or hoicking the ball over the infield to maximise impact. His team-mate Ishan Kishan matched him in trying to clear the fence as often as possible, and Suryakumar Yadav attacked in the middle overs. Mumbai had the best powerplay boundary percentage, 20.83%, and the best middle-overs boundary percentage, 15.59%. Attacking consistently regardless of wickets brought them success as a batting unit.

The occurrence of boundaries is a product of intent and execution. While the execution depends on the pitch, the ball and the field, the intent to attack is a controllable for the batting side. This intent, represented by the frequency with which a batsman seeks to hit a boundary, can be increased at will to try and score faster. The advantage is dependent on the payoff.

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The question of payoff was central to the NBA's three-point revolution. Although three-pointers are less likely to be successful than two-pointers, analysts found that the average returns from an attempted three-pointer were significantly higher than those from two-pointers. This has led to a steady increase in the number of attempted three-pointers in the NBA in the last ten years. A high-risk shot was identified as one with a better payoff despite the lower odds of success, and strategy evolved accordingly.

The payoff from attacking in T20 has another dimension: balancing the heightened chances of getting out against the scarcity of wickets. Attempted boundaries can bring you higher returns, but how much likelier are you to lose wickets as a result? And how many boundary attempts could be too many? To answer this, we must study the distribution of outcomes when a batsman attempts a boundary.

The analytics company CricViz collects data on the type of shot hit, the trajectory of a shot, and the result. According to their database, the following eight shots have the highest boundary percentage: slog-sweep, upper cut, scoop, switch hit, pull, slog, hook, and reverse sweep. Classifying all such shots (and all aerial shots) as boundary attempts, we can approximately quantify how a boundary attempt is different from non-attempts. This definition covers 85% of boundaries actually hit, making it a decent proxy for boundary attempts.

Taking data from all T20s since 2016 from the CricViz database, we find that batsmen attempt boundaries 25.5% of the time (including eventual wides) and are successful in hitting a four or six 36.8% of the time when they try. While the chances of a wicket are 3.2% on non-attempts, this rises to 11.8% on boundary attempts. The average runs from boundary attempts are 2.26, while the same figure is 0.97 for non-attempts. Although the chances of a wicket falling rise significantly, the payoff in terms of runs is 2.3 times higher, even with less-than-perfect efficiency of finding the boundary. Teams have acknowledged this - in keeping with the increasing focus on sustained hitting, the percentage of such attempted boundaries has steadily gone up over the past few years.

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We can also calculate the probabilities of various outcomes on boundary attempts and non-attempts. The bar graph below shows these. For simplicity, wides are excluded here.

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The first graph is for the average batsman, and the next two compare the same profiles for Virat Kohli and Andre Russell, highlighting the differences in their execution of boundaries. While the percentage of boundary attempts is vastly different because of the difference in their playing roles, these profiles tell us what happens when they

*do*decide to attack.Himanish Ganjoo/ESPNcricinfo Ltd

When Kohli looks for the boundary, he gets fours 24% of the time, and sixes 18% of the time; his dismissal rate shoots up to 10% on these attempts. Russell, on the other hand, gets mostly sixes compared to fours when looking for boundaries; he is also slightly more likely to get out. Russell is a more aggressive, primarily six-hitting batsman, while Kohli is more classical, with fours dominating his attacking output.

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These "profiles" can also be used to decide team strategy, dictating how much a team should attack. To mimic what a strategy think tank might do, we will run simulations of a match situation using the profile for an average player.

Assume that a team has five wickets in hand and needs 60 runs from 30 balls to win. What are their chances of victory if they attack 15 balls out of 30? It turns out that the chase is completed only 12% of the time. Can these chances be bettered if they attack more? There is a trade-off between losing wickets and hitting hard, so what is the ideal number of deliveries to attempt boundaries on, to maximise their chance of winning?

Running simulations of scenarios where the team attacks between ten and 30 balls, we see that there is no such thing as too much attack in this scenario: the more they attack, the higher the chances of winning. How the chances of success vary as the number of balls attacked increases is shown in the plot below.

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While all-out attack is the obvious strategy for a five-over target at the end of the chase, what about when a team needs, say, 100 from the last ten overs? If they have eight wickets remaining, they can afford to attack around 50 of the 60 balls to maximise their chances of winning. With batting resources in the shed, it makes sense that attacking more is the better option. On the other hand, if only six wickets remain, the possible loss of wickets starts balancing out the extra run output from attacking more balls. At around 46 balls attacked out of 60, the winning probability flatlines; there is no advantage from attacking more often than this.

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The larger the match span available, the greater the effect of losing wickets in determining the ideal percentage of boundary attempts. Running the simulations for a full chase, with 20 overs and ten wickets left, it is seen that there is an optimal number of balls to attempt boundaries on, after which the chances of winning start decreasing. For a target of 160, this number is between 60 and 70 balls, while it is 80 to 90 for a 200 target. The progression of winning chances is shown in the plot below, and it follows a general pattern of rising steeply until the optimal point and falling slowly after that as more boundaries are attempted.

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How would a chase of 200 pan out, depending on team construction? We will have a look at simulations comparing a team of high-risk high-reward players of the Russell archetype to a team of safer, four-hitting players in the mould of Kohli. As the plot below shows, a team of Kohli-style players have a slightly higher chance of winning compared to a team of Russells if they both attack more than about 60 balls in the full innings. Both Kohli and Russell are elite in different ways when they decide to attack, and Kohli's execution works slightly better over a full innings, even for a huge target. The actual is more effective in a tall chase because he attempts boundaries much more often than Kohli.

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Another question we can answer through these simulations is about the quandary of playing conservatively versus attacking while setting a total. Teams that lose a couple of wickets early on tend to retreat defensively, often misjudging when to up the scoring rate. Consider a team that is three wickets down after five overs. On how many balls out of the remaining 15 overs should they try to score boundaries to maximise their final total? Running simulations for a team comprised of the average batsman shows that the median runs scored increases steeply until about 60 boundary attempts out of 90, and then starts to fall gradually, as the team does not survive the full ten overs.

In contrast, for a team made up of Kohli-style or Russell-style players, who have a lower dismissal rate and higher run rate on account of being elite batsmen, more attack directly translates to more runs. They can afford to attack 75-80 balls in 15 overs before their returns hit a ceiling and they lose all seven wickets before the full quota of overs. In a batting order loaded with quality hitters who can execute shots well, it is most sensible to attack a majority of balls left, even with 15 overs remaining.

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While these are idealised simulations that assume a team of 11 batsmen of the same calibre, they demonstrate the importance of teams increasing their attack percentage to give themselves the best chances of winning. Calculating the optimal number of balls to target, teams can decide which match-ups to leverage and which bowlers to play out while still giving themselves the best chances of winning a game or of maximising their total.

As T20 becomes more specialised and players upgrade their skills to execute better, the success rate on boundary attempts will increase, and the optimum percentage of attempts will change to reflect that. A tactically evolving T20 will embrace a maximalist school of hitting, in which the primary maxim is attack, and the outlook of a batsman is to attempt boundaries on as many balls as possible. Wicket preservation will take a back seat, and line-ups will be designed to give the freedom to hit, undaunted by a wicket or two falling. Gayle's elite binary philosophy will be represented throughout the landscape of the game: batsmen thinking in terms of boundaries, and bowlers evolving to consider the ball staying in the field as a win. The boundary will become the primary grammar of T20, a sport independent of its parent and its notions.