The batting average is an obviously limited metric when it comes to measuring the value of a batsman. To demonstrate this, I will compare the ODI career numbers of six batsmen with widely varying not-out-percentage values.
The averages of MS Dhoni and Michael Bevan are way too high, while those of David Warner and Shikhar Dhawan are way too low. Javed Miandad and Jos Buttler have acceptable values. Since these are base numbers, contextual factors such as whether a batsman opened the batting, number of fielders within the circle, a player's finishing ability, number of overs left to play, etc, do not come into the picture.
The batting average metric is intrinsically unfair to batsmen with low not-out percentages. The alternative plain-vanilla RpI (Runs per Innings) would swing the pendulum the other way - it would be grossly unfair to Dhoni and Bevan - unbeaten innings of 11 and 23 would be taken as completed innings. What is needed is something in the middle - logical, fair and accurate.
Hence, I have developed a new metric - the Weighted Batting Average (WBA). In order to negate the huge disadvantage faced by top-order batsmen when it comes to not-outs, the WBA is calculated as explained below.
All dismissals, irrespective of the score, have an innings count of 1.0
All not-out innings above the average Runs per Innings (RpI) have an innings count of 1.0
All not-out innings below the average RpI are assigned proportionate innings values between 0.0 and 1.0
The WBA is then calculated using the derived Weighted Innings count
Let me illustrate this concept with Adam Gilchrist's career. He played 279 innings and was undefeated 11 times - 11*, 11*, 20*, 24*, 29*, 59*, 66*, 69*, 76*, 79*, 121*. His career RpI is 34.48 (9619 / 279). The last six innings in the sequence above are above the RpI and are considered as innings that ended in a dismissal. Only the italicised first five innings, which add up to 95, are to be prorated. The Weighted Batting Average is 34.75 (=9619/276.76). To explain, 276.76 = 268 (dismissed innings) + 6.00 (Above RpI) + 2.76 (Pro-rated: 95/34.48).
Nothing can be fairer. Gilchrist does not lose out on unbeaten innings such as 79 not out, since that is counted only as 1.0. He does not lose out on innings such as 11 not out since that innings count is taken as 0.319, which is accurate. Of course, when he was dismissed at 4, his innings count is taken as 1.0. That is how it should be since he was dismissed.
On an average, the WBA to Batting Average ratio ranges from 100% for Sherwin Campbell (no not outs) to 68.2% for Lance Kluesener (36.5% not outs).
Going back to our examples, let us see how the WBA works out for the selected batsmen.
It is clear that these numbers are fair and equitable. Look at how the maximum benefits accrue to those batsmen with fewer not outs. There seems to be a clear inverse correlation between not-out percentage and the value of WBA as a percentage of the average. Those with a high number of not-outs do not lose out - rather, they do not gain in an undeserved manner, as happens with the batting average.
An added benefit of the weighted innings concept is that it is possible to derive an accurate Balls per Weighted Innings measure. These are very useful in analysing batsmen's performances. Jos Buttler has a very low BpWI value (28.1) - not a surprise because he is among the most attacking batsmen ever, with a strike rate of nearly 120. To state what should be obvious by now, WBA = SR (per ball) x BpWI.