The third batting power play and game theory!

One of the interesting debates on the sidelines of the Cricket World Cup relates to the timing of when batting team captains should use their third power play (PP) of five overs. The third PP, to be availed at the request of the batting team, imposes a restriction that the fielding team can have only three fielders outside the thirty yard circle.

The dilemma for batting captains is to use it earlier, say in the 30-40 over period, or preserve it for the slog overs. Apart from the argument that since the ball is changed in the 34 th over (and since a harder ball is easier to hit), it may be effective to take PP early, there has not been much analysis of the issue. However, a simple balance sheet of the costs and benefits of both alternatives to each side reveals that the choice is not as hard as it appears.

The benefits for the batting side are several and significant

1. With or without field restrictions, slog overs are a form of PP in themselves, atleast from the mental frame of the batsmen. It may therefore be more effective to take an early PP and get more runs earlier than otherwise would have been the case. The batting team effectively gets two PPs! The batting team can also carry the momentum on to the slog overs - the bowling side will have to mentally recover after the PP.

2. The bowling side is forced to call on its best bowlers much earlier than they would have preferred. Typically, the best bowlers have three spells - opening burst, slog overs, and a containing or wicket searching spell in the middle. If the PP is taken in the slog overs, it coincides with the bowlers final planned spell. However, an early PP, especially if the bowler has already completed his middle spell, can wreck the best laid plans of the bowling captain. Forced into dividing their ten overs into four spells, the best bowlers will have less overs for the slog.

3. Even without field restrictions, slog overs generally yield more runs. The incremental benefit, in terms of runs scored, with PP restrictions are not likely to be substantial. However, in the earlier overs, without field restrictions, batting sides are likely to score only modestly (3-4 runs an over in an average scoring match and 5-6 runs an over in a high scoring one). The incremental benefit of early PP is therefore significant.

4. Finally, the harder the ball, the easier is it to strike. Since the ball is replaced in the 34 th over, it is surely more sensible to opt for an early PP.

The negative side of the equation for the batting side is the risk of losing wickets in the PP and being left with limited fire-power to take advantage of the slog overs. However, this is more a question of the batsman's judgement of the PP situation, an issue of mental orientation. An element of representativeness bias in the batsman's mind anchors the third PP to slog overs.

It needs to be borne in mind that batting PP are not slog overs. In slog overs, batsmen throw caution to the winds safely in the knowledge that the end of the innings is near. But early PPs are followed by more overs. The risks being taken need to be weighed accordingly.

Consider this 2X2 matrix of the two alternatives - early and slog overs PP - from the perspective of the batting and bowling sides.



As can be seen, the early PP is the dominant strategy for the batting side - for the batting side, its benefits are singificant while for the bowling side, the costs are just as high!