# The Weighted Batting Average (WBA) in Tests

The batting average favours batsmen with many not-outs, while the Runs-per-Innings metric penalises batsmen for low not-out scores. The WBA is the middle ground that is fair to all

The Batting Average is an obviously flawed metric. To demonstrate this, I will compare the career numbers of six batsmen. These are batsmen with widely varying 'not out %' values.
Batting Average data for selected batsmen
BatsmanInningsNot outsNO %RunsAverage
Brian Lara 232 6 2.6%1195352.89
Saeed Anwar 91 2 2.2% 405245.53
Sachin Tendulkar3293310.0%1592153.79
Herbert Sutcliffe 84 910.7% 455560.73
Steve Waugh 2604617.7%1092751.06
Andy Flower 1121917.0% 479451.55
Steve Waugh and Andy Flower have way-too-high averages. Brian Lara and Saeed Anwar have way-too-low averages. Sachin Tendulkar and Herbert Sutcliffe have acceptable values. Since these are base numbers, contextual factors do not come into the picture.
The Batting Average metric is intrinsically unfair to batsmen with low 'not out %' values. The alternative plain-vanilla RpI (Runs per Innings) would swing the pendulum the other way - It would be grossly unfair to Steve Waugh and Andy Flower - 16* and 8* 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, 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 Don Bradman's career. He played 80 innings and was undefeated 10 times - 30*, 37*, 56*, 57*, 102*, 103*, 127*, 144*, 173* and 299*. His career RpI is 87.45 (=6996/80). The last six innings are above the RpI and are considered as completed innings. Only the italicised first four innings are to be prorated. The Weighted Batting Average is 89.62 (=6996/78.06). To explain, 78.06 = 70(Dismissed inns) + 6(Above RpI) + 2.06(Pro-rated: 180/87.45).
Nothing can be fairer. Bradman does not lose in unbeaten innings such as 270* since that is counted only as 1.0. He does not lose out on innings such as 30* since that innings count is taken as 0.343, which is very fair. Of course, when he was dismissed at 12, 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 99.6% for Tamim Iqbal (0.9% not outs) to 78.8% for Shaun Pollock (25.5% 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 very 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 outs %" and "WBA-Average %" values. Those with high number of not outs do not lose out - rather, they do not gain in an undeserved manner, as happened earlier. The WBA value is always lower than the Batting Average. The relevent factor is the extent of drop.

Anantha Narayanan has written for ESPNcricinfo and CastrolCricket and worked with a number of companies on their cricket performance ratings-related systems