## Modified batting averages

Over at the Cricket Fans' Forum I saw this article, which describes some of the work of two economists, who have come up with a way of adjusting the batting average to take into account the consistency of the batsman and the importance of his scores in each individual innings. I don't think that the former adjustment is warranted at all. The latter adjustment has some merit, but I'm not convinced about it — a good batsman in a weak team would be unduly rewarded, and vice versa.

One modification to the batting average that does make sense is an adjustment for the bowling strength of the opposition. I've implemented this in a pretty simple way. For a given batsman's innings, I weight the runs scored by a average of the bowlers' bowling averages, where this latter average is weighted by how much each bowler bowled.

Perhaps an example would be useful. Suppose that a batsman from Team A scores 100, and in that innings Team B used three bowlers. Bowler A, whose bowling average is 25, bowled 20 overs. Bowler B, whose average is 25, bowled 10 overs. Bowler C, whose average is 30, also bowled 10 overs. The weighted bowling average would then be 0,5*20 + 0,25*25 + 0,25*30 = 23,75.

(Once again, I've used the career averages. This makes the numerics much more stable and easier to perform, but means that the modified averages can change when a batsman's not playing.)

This is similar in spirit to the modified bowling averages below, though somewhat less elegant — you'd expect that a captain would often give the most overs to whoever happens to be bowling the best that day, regardless of what his career average is. Still, it's a relatively simple idea and it seems pretty fair.

Here are the top 25 Test batsman according to this modified average (qual. 20 innings):

`name              matches inns  no  runs  avg     adj runs  adj avgBradman,Donald    52      80    10  6996  99,94   6321,22   90,30Hussey,Michael    18      29    7   1896  86,18   1639,18   74,51Headley,George    22      40    4   2190  60,83   2261,05   62,81Walcott,Clyde     44      74    7   3798  56,69   3903,64   58,26Weekes,Everton    48      81    5   4455  58,62   4243,46   55,84Jackson,Stanley   20      33    4   1415  48,79   1606,10   55,38Hobbs,Jack        61      102   7   5410  56,95   5218,26   54,93Sobers,Garry      93      160   21  8032  57,78   7590,09   54,61Hutton,Leonard    79      138   15  6971  56,68   6613,95   53,77Sutcliffe,Herbert 54      84    9   4555  60,73   4020,51   53,61Nourse,Dudley     34      62    7   2960  53,82   2932,81   53,32Barrington,Ken    82      131   15  6806  58,67   6096,42   52,56Chappell,Greg     87      151   19  7110  53,86   6899,34   52,27Tyldesley,Ernest  14      20    2   990   55,00   939,58    52,20Pollock,Graeme    23      41    4   2256  60,97   1924,28   52,01Ponting,Ricky     111     184   26  9408  59,54   8111,16   51,34Ranjitsinhji      15      26    4   989   44,96   1116,44   50,75Pietersen,Kevin   32      61    3   2993  51,60   2934,97   50,60Kallis,Jacques    110     187   30  9114  58,05   7917,01   50,43Lara,Brian        130     230   6   11912 53,18   11272,23  50,32Ryder,Jack        20      32    5   1394  51,63   1358,58   50,32Worrell,Frank     51      87    9   3860  49,49   3856,59   49,44Steel,Allan       13      20    3   600   35,29   831,70    48,92Harvey,Neil       79      137   10  6149  48,42   6193,82   48,77Compton,Denis     78      131   15  5807  50,06   5656,85   48,77`

(Includes all Tests up to Test 1852, the second between Sri Lanka and England in the current series.)

Most of the usual suspects at the top of the list take quite a hit, with Headley and Walcott the two exceptions. The biggest major falls are from Eddie Paynter and Wally Hammond, who come in 36th (47,27) and 37th (46,86) respectively. Stanley Jackson leads the charge of the 19th century brigade (though he also played in the early 20th century). Allan Steel, who played all of his Tests in the 1880's, has one of the biggest increases, going from 35,29 to 48,92. Steel is also pretty cool because he made nice round numbers: 600 Test runs, and 7000 first-class runs.

Some other notables (usual average in brackets): JJ Lyons 44,37 (27,07); WG Grace 42,91 (32,29); Arthur Shrewsbury 46,32 (35,47); Victor Trumper 41,73 (39,05); Chris Martin 1,97 (2,00).

Feel free to request any others.

Interesting David.

Have you read the blog on cricinfo regarding the extended batting average? It is a modified average and takes into account 'not out' innings with a different perspective. Here's the link:

Hi Q. Narayanan's extended batting average is seriously flawed. There are two underlying assumptions to it. The first is that the recent innings of a batsman give a good indication of what his next innings will be. This isn't all that true - I have some graphs on the topic here, which show that while it might be a good indication for some players, it isn't for others. And generally, any effect of "form" is quite weak.

The second problem is that it doesn't take into account the current score of the batsman. Once again I have graphs. :) They are here. Narayan's extended batting average can change with a score of nought not out! It's not realistic at all.

I completely agree ith your assessment David. Love your graphs.