Analysis

# The Weighted Batting Average (WBA) in Tests - updated

The batting average favours batters 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 batters. There are batters 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
Waugh and Flower have way-too-high averages. Lara and Anwar have way-too-low averages. Tendulkar and 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 batters 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 Waugh and 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 batters, the WBA is calculated as explained below. For the past few years, I have used Runs per Innings to determine the WBA. However, I have now reverted back to the most accurate way of working out the WBA - Runs per Dismissal is a 100% accurate measure. To calculate this measure, I exclude the unbeaten innings and calculate the runs per dismissal from the remaining innings.
• All dismissals, irrespective of the score, have an innings count of 1.0
• All not-out innings above the average Runs per Dismissal have an innings count of 1.0
• All not-out innings below the average Runs per Dismissal 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 ten times. 30*, 37*, 56*, 57*, 102*, 103*, 127*, 144*, 173* and 299*. His career Runs per Dismissal is 83.83 (=5868/70). 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 89.55 (=6996/78.15). To explain, 78.15 = 70 (dismissed inns) + 6 (Above RpD) + 2.15 (Prorated: (30+37+56+57=180/83.83)).
Nothing can be fairer. Bradman does not lose in unbeaten innings such as 299* or 173* since those are counted only as 1.0. He does not lose out on innings such as 30* since that innings count is taken as 0.358, 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 100.0% for Marnus Labuschagne/Kaushal Silva with zero not-outs to 78.3% for Shaun Pollock (25.5% not-outs).
Going back to our examples, let us see how the WBA works out for the selected batters.
Batting Average / WBA Comparisons for selected batsmen
BatsmanBatting AverageW B AWBA-Ave %NO %
Brian Lara 52.8951.8698.0%2.6%
Saeed Anwar 45.5344.5397.8%2.2%
Sachin Tendulkar53.7949.5192.0%10.0%
Herbert Sutcliffe 60.7356.2192.6%10.7%
Steve Waugh 51.0643.4785.1%17.7%
Andy Flower 51.5544.1885.7%17.0%
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-Ave %" values. Those with high number of not-outs do not lose out. Rather, they do not gain in an undeserved manner, as was happening with Batting Average. The WBA value is always lower than the Batting Average. The relevant 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