January 19, 2009

Another take at the best Test captains

A stats piece that takes a fresh look at Test captains and results

To evaluate how good a captain's results are, you need to know how good they would have been with an average captain. We all know that Ricky Ponting has a stupendously high number of wins as captain, but for much of his captaincy he's had one of the all-time great teams under him. So we should expect that he'd have a lot more wins than losses. The problem is now to quantify what we would expect. Though Ananth has tried to account for differences in team strength in his latest post, I don't think it works well enough.

I've taken each Test and calculated the overall batting average and the overall bowling average for each team. The latter was done by weighting each bowler's average according to the number of balls bowled in each innings. If there were two innings, I took the average of the two innings. That's a bit lazy of me, but it shouldn't make too much difference. (All averages are adjusted using the methods explained in this post.)

Then you take (home bat - away bat - home bowl + away bowl) and you have a measure of the relative strength of the home side to the away side. I calculated this for all Tests, noted the result of each Test, and then saw how the fraction of wins, losses and draws changed as the strength of the home team varies. The results are shown in Figure 1.

The fractions of wins does basically what we'd expect – it starts out flat and very low for teams that are outclassed, before rising steadily before plateauing. There are always going to be some draws (because of rain), so the fraction of wins won't hit zero or one. Even the weakest of home teams can achieve a draw rate of about 30% (well, maybe not Bangladesh), whereas very weak teams away can only draw about 20% of Tests.

The trend in draws is a bit different. It seems to go gently upwards until the teams are evenly matched, and then more sharply downwards as the home team becomes stronger.

I approximated these curves with piecewise linear functions. For the draws, it's flat for x less than -27, then upwards so that it hits the y-axis at y = 0.424, then downwards until x = 17, and then flat, at a value of 0.185.

For the wins, it's flat at 0.031 below x = -13.7, then upwards until x = 17.2, and then flat at a value of 0.785.

So now, for each Test, I calculate the difference in strength. Then I plug that number into the fitted graphs to get a fraction of a win, draw, and loss. For example, suppose that the teams are evenly matched. Then the home side gets 0.366 wins, 0.424 draws, 0.21 losses. The wins and losses for the away side are flipped: 0.21 wins and 0.366 losses.

You do this for each Test that a captain plays, and add up the expected wins, draws, and losses. Now we can compare to the actual record.

There's a question here about how to deal with draws. I decided to ignore them, for a couple of reasons. The first is that teams which score runs faster should have less draws, but I didn't take strike rate into account when doing the regressions above (I don't have strike rate data for all Test batsmen). Also, all Tests in Australia (as well as some elsewhere) were played to a finish between 1882/3 and World War II – no draws in a major cricketing country for over sixty years!

So while I'm happy that draws became almost extinct under Steve Waugh's captaincy as his batsmen increased average scoring rates, he's not going to benefit from this in this analysis.

Instead I calculated the fraction of wins out of matches that ended in a result, that is: wins / (wins + losses). Do this for the actual value, divide by the expected value, and you get a ratio saying how much better or worse the captain's record is compared to what would be expected.

Whether or not it is reasonable to ascribe all the difference to the captain is certainly debatable, but let's look at the results anyway. The table below shows the number of matches captained, the expected results, the actual results, the expected and actual values of wins/(wins + losses), and the ratio of the latter two. Qualification of 20 Tests.

----expected----  --actual--  exp   act
captain          mat w     d     l     w   d   l    w/(w+l)    ratio
Abdul Hafeez     23  5.1   7.1   10.8  6   11  6   0.32  0.50  1.56
GP Howarth       30  7.6   11.0  11.4  11  12  7   0.40  0.61  1.52
Inzamam-ul-Haq   31  6.8   11.3  12.9  11  9   11  0.35  0.50  1.44
J Darling        21  6.0   7.8   7.2   7   10  4   0.46  0.64  1.39
JM Brearley      31  11.5  12.0  7.5   18  9   4   0.60  0.82  1.35
GA Gooch         34  8.0   12.5  13.5  10  12  12  0.37  0.45  1.22
RB Richardson    24  8.4   8.2   7.4   11  7   6   0.53  0.65  1.22
MP Vaughan       51  19.0  18.2  13.7  26  14  11  0.58  0.70  1.21
CA Walsh         22  5.7   7.6   8.7   6   9   7   0.40  0.46  1.16
DG Bradman       24  11.7  7.7   4.6   15  6   3   0.72  0.83  1.16
SP Fleming       80  23.3  27.2  29.5  28  25  27  0.44  0.51  1.15
DPMD Jayawardene 26  10.2  8.8   7.0   15  4   7   0.60  0.68  1.14
Nawab of Pataudi 40  7.3   14.6  18.1  9   12  19  0.29  0.32  1.12
IVA Richards     50  22.0  18.1  9.9   27  15  8   0.69  0.77  1.12
N Hussain        45  14.1  15.5  15.5  17  13  15  0.48  0.53  1.12
RB Simpson       39  11.1  14.2  13.7  12  15  12  0.45  0.50  1.11
SM Gavaskar      47  13.9  17.9  15.2  9   30  8   0.48  0.53  1.11
IM Chappell      30  13.0  11.0  6.0   15  10  5   0.69  0.75  1.09
CH Lloyd         74  32.4  26.9  14.8  36  26  12  0.69  0.75  1.09
L Hutton         23  9.9   8.3   4.8   11  8   4   0.67  0.73  1.09
Wasim Akram      25  9.5   7.9   7.6   12  5   8   0.56  0.60  1.08
SM Pollock       26  11.9  8.7   5.4   14  7   5   0.69  0.74  1.07
Imran Khan       48  18.0  18.0  12.0  14  26  8   0.60  0.64  1.06
R Benaud         28  12.5  10.5  5.0   12  12  4   0.71  0.75  1.05
AL Hassett       24  11.7  8.1   4.1   14  6   4   0.74  0.78  1.05
MC Cowdrey       27  10.8  10.0  6.1   8   15  4   0.64  0.67  1.04
RT Ponting       52  28.1  16.4  7.4   35  9   8   0.79  0.81  1.03
SC Ganguly       49  19.7  16.1  13.1  21  15  13  0.60  0.62  1.03
MJK Smith        25  9.6   9.3   6.1   5   17  3   0.61  0.63  1.03
R Illingworth    31  13.7  11.1  6.2   12  14  5   0.69  0.71  1.02
WM Lawry         25  8.5   8.9   7.6   9   8   8   0.53  0.53  1.00
ST Jayasuriya    38  15.1  12.9  10.0  18  8   12  0.60  0.60  1.00
Javed Miandad    34  16.1  11.1  6.8   14  14  6   0.70  0.70  0.99
GC Smith         66  28.6  22.3  15.1  33  15  18  0.65  0.65  0.99
PBH May          41  17.8  14.7  8.5   20  11  10  0.68  0.67  0.98
WJ Cronje        53  25.3  18.1  9.6   27  15  11  0.73  0.71  0.98
GS Chappell      48  19.3  17.8  10.9  21  14  13  0.64  0.62  0.97
RS Dravid        25  9.2   9.4   6.4   8   11  6   0.59  0.57  0.97
AR Border        93  36.4  34.5  22.1  32  39  22  0.62  0.59  0.95
SR Waugh         57  33.3  18.3  5.4   41  7   9   0.86  0.82  0.95
JDC Goddard      22  7.7   8.3   6.0   8   7   7   0.56  0.53  0.95
MA Atherton      54  14.1  19.4  20.4  13  20  21  0.41  0.38  0.94
MA Taylor        50  23.7  17.5  8.8   26  11  13  0.73  0.67  0.91
ER Dexter        30  11.8  11.3  6.9   9   14  7   0.63  0.56  0.89
A Ranatunga      56  16.5  18.6  20.9  12  25  19  0.44  0.39  0.88
ADR Campbell     21  2.4   6.2   12.4  2   7   12  0.16  0.14  0.88
WM Woodfull      25  13.1  7.8   4.1   14  4   7   0.76  0.67  0.87
Kapil Dev        34  9.1   12.1  12.8  4   23  7   0.42  0.36  0.87
WR Hammond       20  8.7   6.9   4.4   4   13  3   0.66  0.57  0.86
HH Streak        21  4.7   6.0   10.3  4   6   11  0.31  0.27  0.85
SR Tendulkar     25  5.9   8.7   10.4  4   12  9   0.36  0.31  0.85
MW Gatting       23  4.9   8.8   9.3   2   16  5   0.35  0.29  0.83
BC Lara          47  10.5  16.1  20.4  10  11  26  0.34  0.28  0.82
M Azharuddin     47  18.6  17.2  11.2  14  19  14  0.62  0.50  0.80
GS Sobers        39  14.4  14.9  9.7   9   20  10  0.60  0.47  0.79
CL Hooper        22  5.1   7.8   9.2   4   7   11  0.36  0.27  0.75
BS Bedi          22  7.0   7.8   7.3   6   5   11  0.49  0.35  0.72
DI Gower         32  6.6   12.0  13.5  5   9   18  0.33  0.22  0.66
JR Reid          34  5.2   11.1  17.8  3   13  18  0.23  0.14  0.63
AC MacLaren      22  6.4   7.9   7.7   4   7   11  0.46  0.27  0.59
KJ Hughes        28  7.4   10.3  10.3  4   11  13  0.42  0.24  0.56
A Flower         20  3.4   6.3   10.2  1   9   10  0.25  0.09  0.36

The results are (of course) far from perfect. Nevertheless, there is plenty to be gleaned from the table. Gavaskar is placed relatively highly, because his teams turned more losses into draws than wins into draws. Thirty draws in 47 Tests is not exciting or something I would encourage captains to aim for, but it helped India's win/loss during that period.

Abdul Hafeez Kardar, Pakistan's first captain, comes out on top by virtue of turning about half of the losses he "should" have had into draws.

Mark Taylor comes out worse than his immediate predecessor and successors, which is at odds with most observers' opinions of his captaincy. Taylor's sides were notorious for losing dead rubbers; if these are excluded then his ratio moves up to around 1.

The one major problem with this analysis occurs with captains with very long reigns. In these cases, the good (or bad) field placings and so forth feed into his bowlers' averages for much (or all) of their careers. This has the effect of making the captain's expected results closer to what they actually were. I don't know how big this effect is. But captains like Border, Fleming, and Lloyd should probably have their ratios moved further away from 1.

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