My answer to: (To vote and comment on Quora, visit the link here.)
Thanks for asking me this question, because this gave me an opportunity to study this long-time idea of mine more closely, by creating an excel sheet.
I had thought of a concept of “most crucial innings average”. This is meant to filter out small innings that unnecessarily inflate the batting average of players just because they were not-out innings. The idea I had was: calculation of “most crucial innings average” should not include innings where the batsman stayed not out after scoring less than 25 runs (or another chosen limit – minimum respectable score, MRS).
- For a batsman who often finishes innings and remains not out, there is a criticism that not-out innings inflate their averages. But this system would filter out innings like 2*, 10*, 17*, etc. This is because the batsman didn’t even get a chance to convert these into a respectable score, and these innings may not be a true indicator of the batsman’s talent.
- However, it would still take into account innings such as 2, 20, 14 (i.e. innings where batsman got out), because the batsman got a chance to convert these into a respectable score, but still lost his wicket.
- It would still take into account innings such as 57*, 42*, 38*, etc., because these innings made significant contribution to the team and that the batsman stayed not out even after scoring this much must be awarded with inflated average.
- The general formula “runs/dismissals” gives undue advantage to batsmen who bat in the lower middle order or lower order, because their innings are often likely to be undismissed. For a top order batsman, an occasional score like 4* and 13* does not inflate the average much, but it is very likely to do so for lower order batsman. The concept of “most crucial innings average” would bring lower order batsmen at an equal level with top-order batsmen, because it helps in reduction of overall batting average.
- The limit minimum respectable score can be adjusted according to needs. Some people may consider 20 to be a respectable enough limit score for ODIs, while some may want a batsman to score at least 30 to show his talent. The idea is to choose a limit, below which an undismissed innings can be ignored (minimum respectable score).
(I also prepared averages by taking the MRS as 35 instead of 25: Sachin Tendulkar 44.41, Michael Bevan 50.02, Ricky Ponting 41.35, MS Dhoni 50.87, Jacques Kallis 44.24, K Sangakkara 39.82, Mike Hussey 44.16, Michael Clarke 43.42, Virat Kohli 51.73)
- The average of a top-order batsman like Sachin Tendulkar is not affected much.
- The average of MS Dhoni and Michael Bevan is still above 50 if the MRS is 25, while MS Dhoni’s average becomes higher than Bevan’s for MRS = 35. This means these batsmen should not be devalued by assuming that their high averages are due to lots of not-outs. They are more likely to be not out for a very important score like 45 than a minor 15. Any innings of 57* should be considered statistically superior to an innings of 57, irrespective of batting position. So, if it inflates the average, it should be okay.
- I am not sure if there’s much practical necessity of this statistic, but it may be a very good theoretical way to make batting average slightly more useful while comparing lower order batsmen with top order batsmen.
Update (27 September 2014): I read an article on ESPNCricinfo by Anantha Narayanan today. He has proposed a statistic similar in concept, but much more convincing because it is much more refined. Here’s the explanation:
A batsman with these innings: 67*, 45, 2, 10, 32, 23*, 20*, 13*, 78, 10 (10 innings, 4 not outs, 300 runs) has these two common kinds of averages, which are at two extremes: (a) Runs per dismissed innings: 300/6 = 50.00, (b) Runs per innings: 300/10 = 30.00. The number of innings in the denominator in the two cases are 6 and 10 respectively. The first favours the middle-order batsmen unfairly, and the second favours the top-order batsmen fairly.
To solve this, we need a divisor that is somewhere between 6 and 10: to be equally fair to both middle- and top-order batsmen. For this, the not-out innings shall be scaled down. An innings of 23* will be recorded as “23/30.00 of an innings”, instead of one full innings. Here 30.00 is the runs per innings. An innings of 13* is 13/30.00, the 20* is 20/30.00 of an innings and the innings of 67* would be a full innings. Now, the number of innings is 6 + 23/30 + 13/30 + 20/30 + 1 = 8.87 innings. Now, the adjusted average becomes 300/8.87 = 33.83.