The pinch hitter's failures are recorded and his purpose is not

A promoted hitter who falls for six leaves a bad line in the book and a platform the next batter inherits unmeasured.

He is out for six off four and the scorecard has finished with him.

That entry will sit in his season average, drag it down, be quoted back at him, and possibly cost him the role. What the scorecard does not record is the field the opposition kept for the next eleven overs because of what he threatened to do, or the fact that the incoming batter walked in with the bowling plan already disturbed. The gamble is charged to the gambler. The winnings, if any, are paid to somebody else.

This is a counterfactual problem and cricket is stubbornly bad at counterfactuals. To value the promotion properly you need to compare what happened against what would have happened with the usual batter in that slot, and that innings does not exist. You get one run of the experiment and no control group.

Which does not mean nothing can be done. Team level modelling handles this reasonably well: simulate the innings forward from the promotion decision under both options and compare the distributions of final totals. The interesting output is not the mean. It is the shape. A pinch hitter typically widens the spread, raising both the chance of a very large total and the chance of a collapse, and whether that is good depends entirely on whether you need a large total or merely an adequate one.

That is a decision about variance, and individual batting averages have no vocabulary for variance at all. An average is a point estimate. It cannot express the idea that a player's value lies in changing the distribution rather than the expectation.

So we get an argument that repeats itself every tournament. The promotion fails twice, the numbers look terrible, the experiment ends, and the underlying logic, which may well have been sound, is never examined because the evidence was recorded in the wrong units.

I would want two things published alongside the individual figures. Team runs from the point of promotion to the end of the innings, compared against a baseline for the same match state. And the frequency with which the tactic produced a top decile total. That second one is where the case for pinch hitting actually lives.

Judging a variance play by its mean outcome is not analysis. It is a category error with a calculator attached.