What’s a dropped catch worth in ODI Cricket?

Jason Roy dropped the ball today. I didn’t see it, but apparently it was rather an easy catch. Pakistan went on from 135-2 (24 overs) to finish 348-8, a score just out of England’s reach. The final winning margin was 14 runs.

What did that drop do to Pakistan’s expected score? Here’s the simulations for the two scenarios: 136-2 (24.1) and 135-3 (24.1)

Fig 1: Two scenarios for the 145th ball of Pakistan’s Innings: Out or one run scored.

If Hafeez had been out, the mean score was 350, while the dropped catch increased the mean score to 377. That’s a 27 run impact.

Can we break that down?

  • Firstly, the runs scored on that ball. Value = one run. Easy.
  • Secondly, the reduced run rate as a new batsman plays themselves in. According to some analysis I’ve done on how batsmen play themselves in, that’s worth four runs (Hafeez had faced 12 balls by this point, so would have been just starting to accelerate).
  • The rest of the impact (22 runs) comes from two factors: more conservative batting as Pakistan from having fewer wickets in hand, and the increased chance of getting bowled out (and thus not using all their overs).

To generalise, the cost of a dropped catch would be a function of:

  • Runs scored on that ball
  • Whether the surviving batsman is set
  • How long left in the innings (the wicket affects the value of future deliveries. Thus the later in the innings a wicket falls, the lower the value of that wicket)
  • How many wickets the batting team has in hand (does the wicket cause more defensive batting)? In this case, being three wickets down after half the innings still leaves plenty of scope for aggressive batting so doesn’t have as big an impact as it could.
  • Strike Rate and Average of the reprieved batsman relative to the rest of the team (dropping Wahab Riaz is better than dropping Babar Azam).

Interesting topic. I might come back to this when other people drop sitters.

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