One of the less reported trends in one day international cricket nowadays is the decline of the sixth bowler. Not only are part timers being used less often, but when used they are being used less.

To quantify the number of bowlers used by a team, we need to go into the principles of microeconomics and the “Herfindahl Hirschman Index” (HHI). The HHI is used to measure the degree of competition in an industry, and is calculated as the sum of squares of market share of each firm in the industry. The beauty of the HHI is that the inverse of the HHI can be used as a proxy for the effective number of firms in the industry.

In the context of electoral politics, the inverse of HHI can be considered as the “effective number of parties” in an election. We can use it in the concept of cricket as well, to look at the “effective number of bowlers” used in an innings.

If 5 bowlers each bowl 10 overs in an innings, each has a “20% share” of the overs in the innings, and the HHI comes out to be 5 x 0.2 x 0.2 = 0.2. Taking the inverse, we find there are effectively 5 bowlers.

If 4 bowlers bowl 10 overs each, a fifth bowler bowls 9 overs and a sixth bowler bowls 1 over, the HHI comes out to be 4 x 0.2 x 0.2 + 0.18 x 0.18 + 0.02 x 0.02 = 0.16 + 0.0324 + 0.0004 = 0.1928, effectively giving 5.2 bowlers. If the fifth and sixth bowlers, instead of bowling 9 and 1 overs respectively, had bowled 5 overs each then the effective number of bowlers would be 5.55. So this measure takes care of both the actual number of bowlers used and how much each bowled.

Since the beginning of the century until around 2015, teams were effectively using about 5.6 to 5.7 bowlers per innings. Since 2015, however, this number has dropped sharply to 5.5.

While this drop doesn’t seem particularly steep, it is interesting to note that two teams are primarily responsible for this steep drop - Afghanistan and India.

In the 2011-13 period, Afghanistan regularly used at least seven bowlers in each innings. This started changing in 2014, when they used only six bowlers in a quarter of their innings, and in 2015, they used six bowlers in half their innings. In a quarter of their innings in each of the last three years, they’ve used “only” five bowlers, perhaps reflecting the rise of specialists such as Rashid Khan and Mujeeb ur Rehman.

I sometimes joke that through the 2000s, India had a formidable bowling lineup in its batting order - Sehwag bowled off spin, Yuvraj was a pretty good left arm spinner, Ganguly was a pretty competent medium pacer (especially when the ball swung) and there was Sachin Tendulkar who could bowl off spin, leg spin and medium pace.

Once that generation retired, though, India has had a massive paucity of batsmen who can bowl, and this is reflected in the drop in number of effective bowlers. Among the current crop, only Kedar Jadhav can bowl, and it appears of late that he’s been “found out”. This is possibly one reason why Vijay Shankar has made it to the Indian squad despite limited experience at the highest level. In over a third of the games in 2018, India only used five bowlers. This hasn’t happened in 2019, though this could be attributed to Hardik Pandya’s unavailability which has forced India to share its fifth bowlers duties.

England, since their revival following the 2015 World Cup debacle have gone the other way. Since 2017, they’ve very rarely used just five bowlers, and in at least 25% of the games, used 7 bowlers. The presence of Ben Stokes, Moeen Ali and even Joe Root in their top 7 affords them this luxury.

Flat pitches are expected at this World Cup, and that might mean that teams might need to use a sixth bowler (since at least one regular bowler is likely to get hit badly). It will be interesting to see how the likes of Afghanistan and India adapt to this.