Thank you so much it proves what I always suspected: Inzi with such a team consistently won more then he should have.

I did not see Wadekar on your list. He led India in the West Indies with what seemed to be a weaker team and won resoundingly. Was he included in your computations?

Minimum qualification is 20 tests as captain. Wadekar = 16

I'm not sure that this analysis is particularly useful. It doesn't sit well with me. It seems a bit silly to try and evaluate expected results, there is too many variables to do it accurately.

@Aaron
Agreed.
Haven't really gone through the detailed analysis but your comment seems valid.
It is like "expecting", say Tendulkar or Lara to score a hundred and win the match single handedly everytime they go out to bat.....
If they don't they aren't so good after all!

yes, interesting analysis. the point, aaron , is to attempt to extract pure captaincy skill (i'd imagine) the ability for someone to inspire a group of cricketers to perform beyond expectation. the value of the whole being more than the sum of the parts etc. if the leader can be the catalyst for this, that's indeed what i would call "good captaincy"

I suspect you can get an indication (at least) of the effect of the longevity of a captain in a couple of ways. (1) The simplest would be to plot ratio against tests for all captains on your list. If the result is a scatterplot then there probably isn't an effect. If on the otherhand the results are grouped more tightly around 1 for prolific captains then there is an effect. To quantify this more you could look at the standard deviation of the ratio as a function of Tests as captain. (2) Another way might be to look at a couple of individual captains with positive ratios. Plot their ratio after 20 tests, 25 tests, 30 tests, etc. Now, you would expect a captain to get better with time in charge. If this doesn't occur then your hypothesis is likely to be true.

Another potential problem is that if you lead a very good team, that is expected to win nearly everything, you're only going to be able to a little better than 1. Example to follow:

The analysis ignores a very important factor, the opponents. Its hardly meanful to have won most of the matches against relatively weaker teams. Should we break Inzi's record to see how many matches did he win against Aus, SouthAfrica or even India for that matter we'd get a better picture.

I agree, I think it's odd that Ponting rate higher than both Border and Waugh, when he inherited the superstar team. Border lay the foundations for the team, Taylor built the walls and Waugh put a roof on it. All Ponting had to do was check the mail occasionally.

Example: Let's say I lead the best team in history against consistently weak opposition. I am expected to win 78.5% of the time, draw 18.5% of the time and presumably lose 3% of the time. My 'exp' is therefore (0.785/0.785+0.03) = 0.963. Now let's say I lead such a team to 20 wins from 20 games (the best I can do), my 'act' is (20/20) = 1 (I can never do better than an 'act' of 1, no matter how many more games than 20 I play). My ratio therefore is (1/0.963) = 1.04. I have Ponting syndrome; I can't prove I am a good Captain (disclaimer: I'm not saying Ponting is a good captain). In fact, interestingly Ponting's ratio is 1.03.

Maybe it would be slightly better if the 'exp' and 'act' values were actually w/(w+l+d), but still the best I can do is (1/0.785) = 1.27. No matter how many games I win I can never beat the captains at the top of the list. My team is just too good.

I'm sure there is a solution to this but I haven't had enough time to think about it, perhaps you can think of one.

I dont think its fair to say that just because you have a great team to lead, your job as a captain becomes any more simpler. Yes, it helps, but then you also get the situation where there are too many egos in the dressing room. You dont have to look further than the England team. You need someone who is calm and has the respect of everyone. Its unfair to the likes of Clive LLoyd and Ricky Ponting

It seems a bit silly to have drawn matches be this influential.
What about this! Captain A had 10 test, drew 9 and lost 1. Captain B had 10 test, won 5 and lost 5. Which is the better captain?
With your system I'm inclined to believe that with this system, Captain A would be rated better even though he never won a test.
When you draw matches you are contributing to nothing and weaker sides will see this as a victory but it should never be better than actually winning matches.

I disagree with Aaron's comment - I absolutely love this analysis. I think that David has put the appropriate caveats in so that we all know how much salt we should be adding to our conclusions.

A couple of things that immediately struck me (in additon to those that David already mentioned):

1. No Zimbabwe captain with a ratio above 1. It seems that no one was able to get this team to perform to the best of their abilities.

2. The high ranking of Gooch. I didn't ever consider him to be a great England captain but it seems that he did a pretty good job (no doubt helped by the mountain of runs he scored himself when captain.)

3, Vaughan & Hussain ranking so high - the "Fletcher factor"?

And one question...

...would it be better to compare absolute difference in W(W+L) rather than ratio?

I feel that it's a better achievement by Howarth to "improve" from an expected 0.4 to 0.61 than for Hafeez to improve from 0.32 to 0.5 (and Brearley's is probably the best of all.)

it clears that what inzi did is something out of the world...i mean the way he led was amazing i cant forget the 2004&2005 in my whole life..that is was the greatest season in the whole decade.

Any chance you could do the math to figure out what a statistically significant difference would be? Or shoot me the numbers and I'll figure it out :-)

Also, it looks like Mike Brearley emerges as one of the best, in accordance with his reputation. 80% wins with teams that would have been expected to only win 60%. Very impressive.

David, this is certainly a good analysis but our Indian friends will not agree with your efforts because they are in a habit to put Indians at the top in their statistically manipulated articles that appear on Crininfo almost every day. Secondly, how they can digest having a couple of captains in top 5 from their neighboring country???

You must change your criteria to please Indians because that’s what ICC and all other cricket boards are actually doing these days !!

I admire the effort, but some of the figures don't seem to be logical. For instance from your figures, Mike Smith 'turned' 4.6 potential wins into draws, but only 3.1 potential losses into draws, yet he scores over 1. I can see how this comes from your method, but it doesn't seem entirely logical.
I'm also not quite clear which averages you took. Was it the batting and bowling averages for that match, or for career to date, or overall career? if, as it seems, that it was for that match only, it doesn't seem entirely logical. To take an extreme example: suppose a team scored 401, and then bowled out the opponents for 200 twice. This would be an overwhelming victory, but the captain (if I understand correctly) would get no credit, because his team's bowling and batting averages would be far superior to the opponents', yet this could be a case of an underdog team crushing stronger opponents, for which the captain should get some credit, surely.

DVC: I'll have a think about that long captains stuff. My only guess at a way of letting captains of great sides do equally well would be to take into account winning margins somehow. But that would require more thought than I'm willing to give it at the moment.

Jeff: using difference rather than ratio shuffles the results around a little bit. Much of a muchness really. Gooch had that series draw with the Windies in 1991 or so.

Adam: I think the way to test significance would be to start by splitting up the odd and even matches for each captain and then see what the correlation is between the two halves of his captaincy. But I don't really want to do this until I sort out the long-captaincy-reign problem.

Pete: I used overall career averages.

Pete, just on the Mike Smith example: I think it's perfectly logical the way it works. According to the expected figures, he led a team that should have won about 3 times for every two losses.

Now, average draw rates change across eras, as attitudes, pitches, bats, etc. change. So the method essentially assumes that however many draws a captain has, they are scattered randomly across his results. So, if all Tests were played to completion, then Smith would end up with roughly 3 wins for every 2 losses. By randomly turning some results into draws, you expect that 1.5 times more wins will be turned into draws than losses.

I hope that makes sense.

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!

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..

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.

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

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.

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?

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).

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!

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.

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.