January 19, 2009

Another take at the best Test captains

David Barry
Mark Taylor behind the microphone, Sydney, January 22, 2004
The tendency of Mark Taylor's team to lose dead rubbers cost his captaincy numbers  © Getty Images
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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.

The graph for wins and draws, January 19, 2009
 © ESPNcricinfo Ltd
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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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Keywords: Captaincy, Stats

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Posted by Vinod Dhar on (March 13, 2009, 15:53 GMT)

Well in my opinion, a captain is only as good as his team. Many of us say that guys like Tendulkar, Lara were not great captains because they did not have results to show. At the same time, it is said that Taylor, Steve Waugh, Cronje etal were the greatest. But one must not forget that Captains are only as good as their teams. Could Steve Waugh have even half the results going his way had he been in charge of Bangladesh or the modern day Zimbabwe. In my opinion, a captain cannot contribute to more than say 10% to the results, rest 90% has to be contributed by 11 guys on the field.

Posted by Russ on (January 30, 2009, 8:39 GMT)

David, interesting analysis, along the lines of what I thought after reading the earlier post.

DVC's point on the percentage ratio is relevant. You could get round that in several ways (points for wins/draws for example) but doesn't substantially affect the result.

I see two problems. The lesser one relates to players over the course of their career. Career averages fluctuate both randomly and by age and experience. Taylor's captaincy, for example, was transitional from the Border era to the Waugh one, and the young and old players were probably worse (though he had the best of the Waughs, Warne and Slater). It might be worthwhile to adjust for age and experience, though it may not make a difference.

The other problem is any individual captain is also affected by the opposition captain. The way around the longevity problem is to iterate over the expectations, adjusting each time around for the opposing captain. Assuming your method is robust, there should be a convergence.

Posted by InterestingMan on (January 23, 2009, 19:07 GMT)

That is an interesting piece of analysis. Unfortunately IntelligentMan does not make an intelligent comment. So far, there has not been a single comment by anyone (other than him) even from Indians suggesting that the analysis is faulty because Hafeez and Inzi figure so high in the analysis. Analysis is analysis - and to suggest that somehow cricinfo distorts analysis to show a specific bias is downright ridiculous!

Posted by David Barry on (January 23, 2009, 11:56 GMT)

Sumit, it's mostly because of the poor attacks Inzamam has had to work with (though the Pakistani batting also tended to be weaker than their oppositions'). Mohammad Sami is probably the main culprit.

On Fleming, my interpretation would be that because of his long reign, he deserves to be yet higher!

In victories, his team averaged 36.2 with the bat and 20.7 with the ball. In losses those figures were 21.9 and 38.6. So it's not as though he had close wins and big losses. He had four innings losses, and four innings victories (eleven including Bangladesh and Zimbabwe).

Posted by Sumit on (January 23, 2009, 4:51 GMT)

Hello Dave, Can you confirm why the predictions for Inzamam's team were so skewed towards losses? Is it that he had a poor bowling attack or a poor batting lineup or that he played against vastly superior teams? Also, although you mention that long reigns can cause the ratio to be closer to 1, S Fleming has a very high ratio. Could it be that NZ during Fleming's reign lost a lot of matches badly, but also won some by not too big a margin?

Posted by D.V.C. on (January 20, 2009, 10:01 GMT)

David: I guess the simplest method of taking into account margin of victory would be just to add wins/losses by an innings or more. This would be biased against captains who choose not to enforce the follow-on though. Perhaps the way around that would be to count it as an innings victory if the losing teams total of their two innings is less than the winning team's 1st innings total. Then you could add the expected number of 'innings victories' and actual number of innings victories to the analysis. Perhaps that would help.

Posted by bradluen on (January 20, 2009, 2:42 GMT)

Trying a simplified version of this using a multinomial only changes things a little bit, so maybe you need a MOV thingie after all.

Top ten: 5 JM Brearley 97.07 2 GP Howarth 96.34 8 MP Vaughan 92.02 1 Abdul Hafeez 91.26 3 Inzamam ul-Haq 89.80 4 J Darling 89.76 10 DG Bradman 83.46 11 SP Fleming 83.40 14 IVA Richards 83.11 19 CH Lloyd 81.29

Bottom ten: 43 MA Taylor 19.03 59 JR Reid 16.53 47 WM Woodfull 15.42 58 DI Gower 14.49 57 BS Bedi 14.24 55 GS Sobers 10.38 62 A Flower 8.95 60 AC MacLaren 7.49 54 M Azharuddin 6.44 61 KJ Hughes 5.23

Posted by bradluen on (January 20, 2009, 2:23 GMT)

One way of taking into account longevity:

1. For each captain, simulate the result of each match of his reign independently. 2. Calculate the score of this simulated reign. 3. Repeat simulation 10000 times. 4. Find the percentage of simulated reigns for which the simulated score was less than the captain's true score. Higher percentage = better captain maybe.

Standard disclaimers about whether statistical significance actually means anything here apply.

Posted by Stumped on (January 20, 2009, 2:21 GMT)

David, how can you decide that it was the captain who changed a losing match into a draw or a win? Usually individual or team brilliance would be the outcome of the wins or draws not a captain moving a point to silly point and takes a catch. I feel a captains worth in a team is seen behind the scenes not neccessarily on the field by way of actions, but a word to a player in his ear/ a vote of confidence giving a young player the opening over instead of first change..

Posted by Marcus on (January 20, 2009, 0:00 GMT)

I tried something similar, though using a pretty esoteric and quite silly way of predicting wins, influenced by baseball stats. This way is almost certainly better, though I'm fairly certain that determining captaincy ability statistically, given the tiny sample sizes we deal with in cricket, is impossible. Great graph!

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