Malinga’s missed delivery – what could it have been?

In the just played 5th match of the CB Series between India and Sri Lanka, Lasith Malinga bowled just 5 deliveries instead of the usual 6 in the 30th over of the match. Apparently the umpire Nigel Llong had difficulty counting up to six, and even the third umpire, with all the paraphernalia available at his disposal, could not correct the mistake. However, the match ended up in a tie. Which means that the missed 6th delivery of the 30th over could have been decisive, had it been bowled. If that had happened, Malinga would have been bowling to Gambhir. The question is, what is the most likely outcome of such a scenario?

Let us first look at Malinga’s bowling profile. In the year 2011, Malinga bowled a total of 1221 deliveries (this includes wides and byes), and the outcome of these 1221 deliveries is as follows:

Dot balls: 752
Singles: 307
Doubles: 53
Triples: 8
Boundary: 99
Six: 2
Wickets: 50 (48 by Malinga, 2 run outs)
Wides: 74 (including byes)
No-ball: 13
Byes: 11
Legbye: 29

Based on this information, the most likely outcome of an average Malinga delivery is a dot ball. However, the average number of runs scored off a Malinga delivery is 0.7961, and the probability of scoring at least one run is 55%. The probability of a wicket on a random Malinga delivery is 4%. So the odds clearly are in India’s favor if Malinga bowls the last ball of the 30th over. On the top of that, Malinga had already leaked 9 runs in the over, and now you can get the picture of what it might have been.

Let us also take into account that Malinga was not bowling to any random guy, but he was bowling to Gambhir (and Gambhir was the top scorer in the match). Again, let us look at 2011 data. In 2011 data, Malinga bowled a total of 21 balls to Gambhir, and here is the outcome: 14 runs by Gambhir (including 2 boundaries), 1 wide and no wickets. Here too, the odds clearly favor India.

So one can as well say that the reason India did not win the game is because Nigel Llong just couldn’t count. Maybe he should have been awarded the man of the match.