Pappus' plane - cricket stats

Homer broke down Michael Clarke's innings to see what happened when he came in with the score less than 150, and when he came in with the score greater than or equal to 150. Clarke does much better when the going's easy. But that's not a proof that Clarke is special — we would expect that batsmen do better when the bowlers have been struggling to take wickets.

So ran the numbers for all batsmen at 5 or 6. I grouped the innings into those worse than 3/150 or 4/200 (these seem reasonably equivalent), and those better. Then I took the difference of the averages. Then, to get some mileage out of this old monstrosity post of mine, I got an estimate of the probability that the "going's easy" average would arise by chance, given the "going's not easy" average, and the number of innings in each category. To give an example, Michael Clarke below gets a p-value of 0,20 — only about one in five batsmen would have such a rise in average. If there's an asterisk, then it means that the difference was too large for my estimation algorithm, and I got a senseless result.

(In The Best of the Best, Charles Davis defines a 'pressure average', which takes into account the state of the match — 4/50 in the second innings isn't a pressure situation if you've got a lead of 250 on the first innings. I can't be bothered going into this much detail.)

Note that many of the batsmen below spent much of their career higher up the order. Also note that my stats are a couple of months out of date.

Qualification of at least 10 easy innings and at least 10 not-easy innings:

             worse than 3/150    better than 3/150
name          inns  runs  avg     inns  runs  avg   diff    p
SC Ganguly    77    2285  32,2    43    2069  54,4  -22,3   *
MJ Clarke     24    854   37,1    17    1037  74,1  -36,9   0,20
MV Boucher    12    342   28,5    11    599   66,6  -38,1   0,26
DR Martyn     23    619   31,0    14    787   60,5  -29,6   0,35
PH Parfitt    18    632   39,5    11    696   87,0  -47,5   0,37
DB Vengsarkar 16    439   33,8    11    581   72,6  -38,9   0,37
TE Bailey     25    653   29,7    13    543   60,3  -30,7   0,38
DI Gower      35    1262  39,4    16    926   71,2  -31,8   0,45
KR Miller     32    978   34,9    19    1000  55,6  -20,6   0,49
RP Arnold     13    215   16,5    11    331   30,1  -13,6   0,50

Clarke really has been pretty bad (well, sort of — 37,1 is below average). In terms of the raw difference, he's fifth worst (Les Ames is just off this table, difference of -37,3.).

And now those rare batsmen who do worse when the pressure's off:

             worse than 3/150    better than 3/150
name          inns  runs  avg     inns  runs  avg   diff    p
A Flower      80    3761  57,9    10    310   31,0  26,9    *
CH Lloyd      78    3700  52,1    30    987   35,3  16,9    *
ND McKenzie   29    1056  40,6    16    438   27,4  13,2    0,30
A Symonds     10    389   43,2    10    233   29,1  14,1    0,44
SJ McCabe     19    830   48,8    12    397   33,1  15,7    0,46
SE Gregory    37    1015  28,2    12    205   18,6  9,6     0,56
IVA Richards  45    2051  51,3    22    852   40,6  10,7    0,77
RT Ponting    33    1604  51,7    17    570   40,7  11,0    0,81
KD Walters    60    2653  51,0    28    1113  42,8  8,2     0,87
KF Barrington 21    878   43,9    14    409   37,2  6,7     0,90

When the p-value is higher than 0,5, it means that such a 'slump' would occur in the career of one in two batsmen — pretty unremarkable. Clive Lloyd's record is probably the most remarkable of these, given the relatively large number of innings.

In the set of 83 players, 52 have better averages in easy situations, and 31 in not-easy situations.

Sorry for the no-post last weekend. The problem with devoting only one day a week to cricket stats is that if I don't get something working, then it doesn't get done for a while. I will try to return to IPL analysis next weekend.