Is a batsman wicket-keeper worth more to the team than the best wicket keeper? - How to calculate the comparison.
The first step is subtracting byes from runs scored before calculating the batting average.
A more important step is making a deduction for each dropped straightforward catch. Of course, classifying a catch as a genuine dropped chance is a matter of judgement, but then so is lbw.
I believe that umpires should signal to the scorer to record dropped straightforward chances by the wicket keeper.
Each dropped catch is penalized by 1/10 of the innings score of the batting team. This seems fair because the bowling team need to take an extra wicket, and the (average) cost of each wicket for that particular innings is 1/10 of that innings total.
In other words, each dropped catch is penalized at the cost of a wicket, adjusted for the innings score. So that a dropped catch in a high scoring game (ie. a large total from the batting side for that innings) is penalized more severely than a dropped catch in a low scoring game (ie. a low score for that particular innings).
So a wicket-keeper's career batting average would be:
Total number of runs scored in career minus byes conceded in career minus extra runs conceded from straightforward dropped catches in career.
Divided by total number of times given out in career.
Note: Straightforward dropped catches are signalled as such by the umpire. Extra runs conceded from dropped catches are each calculated at 10 percent of the opposition's score during the innings in which the catch was dropped. One dropped catch is worth 10 percent of the opposition's score per innings, two dropped catches at 20 percent, etc.
If a keeper dropped a straightforward catch in an innings where the opposition scored 200 runs, the wicket keeper would have 20 runs deducted from the runs he has scored with the bat when his batting average is being calculated.
But if the opposition scored 600 in that innings of the dropped catch then the average cost of runs per wicket taken would be 60 - so that the keeper would have 60 runs deducted from his total of runs before batting average was calculated.
This analysis should settle once and for all the argument over whether it is better for a team to field their best wicket keeper, or their best batsman who is an adequate wicket keeper.
At present the batting average is a relatively precise and quantitative measure of batting ability, while the benefits of wicket keeping (*such as reliable catching) are subjective and impressionistic. This intrinsically benefits the batsman wicket keeper.
But the consequences of a droped catch are more severe than generally acknowledged - each dropped catch means another wicket must be taken, and this usually requires tens of runs to be conceded.
This proposed analysis would enable an objective comparison of two keepers - one of whom is a better batsman but drops more chances, and the inferior batter being a better keeper who holds more chances.