Sunday, February 10, 2008
All-rounderness
The statistical judging of all-rounders is usually not done in what I would consider a satisfactory way. I'm not really going to remedy this problem in this post, though I will present some ranked lists. It's more a case of looking at the stats and seeing why it's hard to get them to agree well with common sense (without making some arbitrary decisions).
I'll only be considering batsman-bowler all-rounders. If you want to comment about wicket-keepers, it should be about Tim Zoehrer.
The base of this analysis will be the bowling averages with wickets weighted by the batting averages of the batsmen dismissed, and the batting averages with runs weighted by the strength of the bowling attack. This gives a comparison across all eras, and rewards those players who performed well against stronger sides. Both the averages I use in this post are normalised to 31,48, which is the overall batting average for all Tests. All references to averages below are these weighted averages.
My main ranking tool will be the batting average divided by the bowling average. I prefer this to the difference, which is more commonly used, because I think it gets closer to a definition of "all-rounder-ness". So, for instance, a batting average of 60 and a bowling average of 30 gives a ratio of 2. A batting average of 40 and a bowling average of 20 also gives a ratio of 2. I think this is fair — in the first case, you have an all-time great batsman who was a good bowler, and in the second you have an all-time great bowler who was a good batsman. You might think that one is a better player than the other, but I'm trying to get at the all-rounder-ness. I hope that's clear.
So, let's think of what qualities we'd like and qualifications we'll use in ranking the best genuine all-rounders of all time.
1. 20 Test innings
2. At least 2 wickets per Test (I don't use weighted wickets here; I just want to make sure that they bowled regularly)
3. A batting average above average (i.e., higher than 31,48)
4. A bowling average below average (i.e., lower than 31,48)
The top seven all-rounders of all time are then as follows. (Runs and wickets are the regular runs and wickets; wpm is wickets per match; ratio is the ratio of batting average to bowling average).
Why only seven? Because that's all there is. No other players satisfy those four conditions above.
I'm actually pretty happy with that list. It's obviously not the list of the best all-rounders ever, but as a list of the most all-rounder of all-rounders, I think it works. Keith Miller just beats Imran Khan as the best ever.
Now let's remove requirements 3 and 4 above and see what we get.
Now Sobers returns to number one, which is where most judges would put him. You can see why he missed out on the previous list — his bowling wasn't that good. Despite an average in the mid-30's (both weighted and regular), he was actually a very economical bowler. A high average and low economy rate (2,22) means that his strike rate was appallingly bad, over 90. Not the go-to man if you need a wicket! But he's generally considered the second-greatest ever player because no other great batsman could bowl so well. Even if "so well" is not so well.
The cut-off of 2 wickets per Test is pretty arbitrary, and it would be unfair to stop here, because it would exclude Jacques Kallis. For my last table, I've lowered the bar to just 1 wicket per Test. This means that a bunch of part-timers are included. While it would be silly to consider them as being as good as the more regular wicket-takers given here, the stats must tell some story — perhaps it suggests that they were underbowled, or perhaps they were just lucky and dismissed a few good batsmen from time to time.
And Kallis actually slots in at number one! Bob Cowper, with his part-time offies, will probably suprise most of you (it surprised me, even though I was vaguely aware of his handy bowling). Andrew Symonds' career is definitely on the improve. His regular bowling average is now under 35. That his weighted bowling average is just over 28 tells us that he's dismissing some good batsmen.
So there you go. I don't know what features you'd want in an ideal ranking of all-rounders. You could set boundary of 2 wickets per Test, and penalise players (such as Kallis) who take less wickets, but setting the boundary would be arbitrary.
Charles Davis, when rating bowlers, actually gives equal weighting to wickets per Test and bowling average. While I see the arguments for doing so (and it would eliminate the problem of setting that boundary), I still like to fall back on the average, so as not to unduly reward bowlers with no support.
I'll only be considering batsman-bowler all-rounders. If you want to comment about wicket-keepers, it should be about Tim Zoehrer.
The base of this analysis will be the bowling averages with wickets weighted by the batting averages of the batsmen dismissed, and the batting averages with runs weighted by the strength of the bowling attack. This gives a comparison across all eras, and rewards those players who performed well against stronger sides. Both the averages I use in this post are normalised to 31,48, which is the overall batting average for all Tests. All references to averages below are these weighted averages.
My main ranking tool will be the batting average divided by the bowling average. I prefer this to the difference, which is more commonly used, because I think it gets closer to a definition of "all-rounder-ness". So, for instance, a batting average of 60 and a bowling average of 30 gives a ratio of 2. A batting average of 40 and a bowling average of 20 also gives a ratio of 2. I think this is fair — in the first case, you have an all-time great batsman who was a good bowler, and in the second you have an all-time great bowler who was a good batsman. You might think that one is a better player than the other, but I'm trying to get at the all-rounder-ness. I hope that's clear.
So, let's think of what qualities we'd like and qualifications we'll use in ranking the best genuine all-rounders of all time.
1. 20 Test innings
2. At least 2 wickets per Test (I don't use weighted wickets here; I just want to make sure that they bowled regularly)
3. A batting average above average (i.e., higher than 31,48)
4. A bowling average below average (i.e., lower than 31,48)
The top seven all-rounders of all time are then as follows. (Runs and wickets are the regular runs and wickets; wpm is wickets per match; ratio is the ratio of batting average to bowling average).
name mat runs avg wkts avg wpm ratio
KR Miller 55 2958 35,37 170 23,20 3,09 1,52
Imran Khan 88 3807 36,07 362 24,01 4,11 1,50
W Bates 15 656 36,05 50 26,96 3,33 1,34
TL Goddard 41 2516 35,60 123 27,06 3,00 1,32
IT Botham 102 5200 33,43 383 30,51 3,75 1,10
TE Bailey 61 2290 32,23 132 30,33 2,16 1,06
JM Gregory 24 1146 32,89 85 31,24 3,54 1,05
Why only seven? Because that's all there is. No other players satisfy those four conditions above.
I'm actually pretty happy with that list. It's obviously not the list of the best all-rounders ever, but as a list of the most all-rounder of all-rounders, I think it works. Keith Miller just beats Imran Khan as the best ever.
Now let's remove requirements 3 and 4 above and see what we get.
name mat runs avg wkts avg wpm ratio
GStA Sobers 93 8032 54,62 235 34,63 2,53 1,58
KR Miller 55 2958 35,37 170 23,20 3,09 1,52
Imran Khan 88 3807 36,07 362 24,01 4,11 1,50
AG Steel 13 600 48,93 29 35,16 2,23 1,39
W Bates 15 656 36,05 50 26,96 3,33 1,34
TL Goddard 41 2516 35,60 123 27,06 3,00 1,32
AK Davidson 44 1328 27,75 186 21,51 4,23 1,29
GA Faulkner 25 1754 45,89 82 36,35 3,28 1,26
SM Pollock 108 3781 30,31 421 24,18 3,90 1,25
AW Greig 58 3599 39,76 141 33,45 2,43 1,19
RJ Hadlee 86 3124 26,09 431 23,76 5,01 1,10
IT Botham 102 5200 33,43 383 30,51 3,75 1,10
TE Bailey 61 2290 32,23 132 30,33 2,16 1,06
W Barnes 21 725 30,57 51 28,81 2,43 1,06
JM Gregory 24 1146 32,89 85 31,24 3,54 1,05
A Flintoff 66 3331 31,06 190 29,89 2,88 1,04
MA Noble 42 1997 33,12 121 32,61 2,88 1,02
CL Cairns 62 3320 32,53 218 32,07 3,52 1,01
G Ulyett 25 949 32,25 50 31,93 2,00 1,01
C Kelleway 26 1422 37,08 52 37,45 2,00 0,99
Now Sobers returns to number one, which is where most judges would put him. You can see why he missed out on the previous list — his bowling wasn't that good. Despite an average in the mid-30's (both weighted and regular), he was actually a very economical bowler. A high average and low economy rate (2,22) means that his strike rate was appallingly bad, over 90. Not the go-to man if you need a wicket! But he's generally considered the second-greatest ever player because no other great batsman could bowl so well. Even if "so well" is not so well.
The cut-off of 2 wickets per Test is pretty arbitrary, and it would be unfair to stop here, because it would exclude Jacques Kallis. For my last table, I've lowered the bar to just 1 wicket per Test. This means that a bunch of part-timers are included. While it would be silly to consider them as being as good as the more regular wicket-takers given here, the stats must tell some story — perhaps it suggests that they were underbowled, or perhaps they were just lucky and dismissed a few good batsmen from time to time.
name mat runs avg wkts avg wpm ratio
JH Kallis 113 9331 50,52 223 31,50 1,97 1,60
RM Cowper 27 2061 44,43 36 28,14 1,33 1,58
GStA Sobers 93 8032 54,62 235 34,63 2,53 1,58
FS Jackson 20 1415 55,40 24 35,89 1,20 1,54
KR Miller 55 2958 35,37 170 23,20 3,09 1,52
Imran Khan 88 3807 36,07 362 24,01 4,11 1,50
CG Macartney 35 2131 44,52 45 30,30 1,29 1,47
AG Steel 13 600 48,93 29 35,16 2,23 1,39
A Symonds 19 1031 38,34 22 28,16 1,16 1,36
W Bates 15 656 36,05 50 26,96 3,33 1,34
TL Goddard 41 2516 35,60 123 27,06 3,00 1,32
AK Davidson 44 1328 27,75 186 21,51 4,23 1,29
EJ Barlow 30 2516 40,24 40 31,36 1,33 1,28
GA Faulkner 25 1754 45,89 82 36,35 3,28 1,26
SM Pollock 108 3781 30,31 421 24,18 3,90 1,25
BM McMillan 38 1968 37,59 75 30,46 1,97 1,23
ER Dexter 62 4502 43,58 66 35,48 1,06 1,23
FMM Worrell 51 3860 49,45 69 40,78 1,35 1,21
AW Greig 58 3599 39,76 141 33,45 2,43 1,19
JDP Oram 25 1380 37,47 49 33,21 1,96 1,13
RJ Hadlee 86 3124 26,09 431 23,76 5,01 1,10
IT Botham 102 5200 33,43 383 30,51 3,75 1,10
TE Bailey 61 2290 32,23 132 30,33 2,16 1,06
W Barnes 21 725 30,57 51 28,81 2,43 1,06
JM Gregory 24 1146 32,89 85 31,24 3,54 1,05
NWD Yardley 20 812 23,53 21 22,63 1,05 1,04
A Flintoff 66 3331 31,06 190 29,89 2,88 1,04
Mushtaq Mohammad 57 3643 37,45 79 36,35 1,39 1,03
MA Noble 42 1997 33,12 121 32,61 2,88 1,02
CL Cairns 62 3320 32,53 218 32,07 3,52 1,01
And Kallis actually slots in at number one! Bob Cowper, with his part-time offies, will probably suprise most of you (it surprised me, even though I was vaguely aware of his handy bowling). Andrew Symonds' career is definitely on the improve. His regular bowling average is now under 35. That his weighted bowling average is just over 28 tells us that he's dismissing some good batsmen.
So there you go. I don't know what features you'd want in an ideal ranking of all-rounders. You could set boundary of 2 wickets per Test, and penalise players (such as Kallis) who take less wickets, but setting the boundary would be arbitrary.
Charles Davis, when rating bowlers, actually gives equal weighting to wickets per Test and bowling average. While I see the arguments for doing so (and it would eliminate the problem of setting that boundary), I still like to fall back on the average, so as not to unduly reward bowlers with no support.
# posted by David Barry : 22:12
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Very interesting, as usual - I would've expected Imran to be near the top, and definitely the top among the "Fab Four" of the 80s.
About Kallis' bowling - he clearly started bowling less as his batting became more important to the side, and of course also because of fitness issues.
I wonder how things would change if you used the overall batting and bowling averages of people considered to be allrounders (well, maybe by the 31.48 criterion here) - or, say, of the top 50 according to your criterion.
About Kallis' bowling - he clearly started bowling less as his batting became more important to the side, and of course also because of fitness issues.
I wonder how things would change if you used the overall batting and bowling averages of people considered to be allrounders (well, maybe by the 31.48 criterion here) - or, say, of the top 50 according to your criterion.
Hmm. Do you mean what would happen if I scaled each of the averages given here to match the overall averages of all-rounders? (Overall weighted averages of the top 50, qualification of 1 wicket per match: batting 35.87, bowling 29.83.)
If you do that, the ratios will change, but the order of the players won't. If a/b > c/d, then scaling a and c by the same factor (or b and d by the same factor) won't change the direction of the inequality.
And yes, you're quite right about Kallis and fitness. I did mean to mention fitness issues, but I forgot when writing up.
If you do that, the ratios will change, but the order of the players won't. If a/b > c/d, then scaling a and c by the same factor (or b and d by the same factor) won't change the direction of the inequality.
And yes, you're quite right about Kallis and fitness. I did mean to mention fitness issues, but I forgot when writing up.
Yes, of course the order wouldn't change, but I'd be interested in seeing whether any people moved nearer or further apart, etc. - but more to the point, I wanted to see the difference (6.04 runs).
The difference is also an interesting way to look at the contribution of allrounders, but of course it gives a bit of an advantage to people like Sobers and Kallis.
Long ago, I'd read an analysis where each wicket was considered equivalent to 20 (or 25?) runs, and each catch also got some points/runs (10?). Made for interesting reading. I think Botham in particular got a lot of points for catches. Fielding was an aspect where Botham and Kapil were quite ahead of Imran and Hadlee.
The difference is also an interesting way to look at the contribution of allrounders, but of course it gives a bit of an advantage to people like Sobers and Kallis.
Long ago, I'd read an analysis where each wicket was considered equivalent to 20 (or 25?) runs, and each catch also got some points/runs (10?). Made for interesting reading. I think Botham in particular got a lot of points for catches. Fielding was an aspect where Botham and Kapil were quite ahead of Imran and Hadlee.
The difference of 6.04 is exaggerated by me setting the bar at 1 wicket per match, so that lots of batsmen who bowled were included. If you require 2 wpm, the difference drops dramatically: overall weighted batting average for the top 50 is 30.47, overall weighted bowling average is 28.79.
Rating catches is a tough one. Giving 10 runs per catch seems to be a bit high to me. In his overall player ratings, Charles Davis ignores a player's catches unless he catches more than 1 per match, on the grounds that anything less and you're just a regular fieldsman who takes catches when they come to you, and that most fieldsmen who take more than one catch per match are regarded as excellent fieldsmen. This seems pretty reasonable to me, though I'd probably lower the bar a bit below 1.
It's impossible to rate fielding satisfactorily until we have stats on average throwing accuracy (both infield and outfield), misfields, dropped catches, runs saved by diving, etc. And even that latter would require subjective judgement.
Rating catches is a tough one. Giving 10 runs per catch seems to be a bit high to me. In his overall player ratings, Charles Davis ignores a player's catches unless he catches more than 1 per match, on the grounds that anything less and you're just a regular fieldsman who takes catches when they come to you, and that most fieldsmen who take more than one catch per match are regarded as excellent fieldsmen. This seems pretty reasonable to me, though I'd probably lower the bar a bit below 1.
It's impossible to rate fielding satisfactorily until we have stats on average throwing accuracy (both infield and outfield), misfields, dropped catches, runs saved by diving, etc. And even that latter would require subjective judgement.
David,
Very interesting analysis. I'm still waiting for a truly exceptional (a "Bradmanesque") allrounder to show up. One who would hold his place in a test side by virtue of his batting or bowling alone. Statistically, I'd set the bar for that all-rounder very high: 8000 runs and 400 wickets in 100 tests. A batting average of over 45 and a bowling average somewhere in the 25-30 range.
Interestingly, Kapil Dev, made it to neither of your lists. Just goes to show!
Cheers,
Samir
Very interesting analysis. I'm still waiting for a truly exceptional (a "Bradmanesque") allrounder to show up. One who would hold his place in a test side by virtue of his batting or bowling alone. Statistically, I'd set the bar for that all-rounder very high: 8000 runs and 400 wickets in 100 tests. A batting average of over 45 and a bowling average somewhere in the 25-30 range.
Interestingly, Kapil Dev, made it to neither of your lists. Just goes to show!
Cheers,
Samir
Yeah, Kapil's batting was exceptional because of his strike rate (which at the time was well ahead of anyone else in history; these days we have Afridi and Gilchrist ahead of him), his average wasn't quite so great.
The popular perception that a true all-rounder could hold his place as either a batsman or a bowler is a strange one, given that it's hardly ever happened. (Someone like Sobers could do it for a while, but only because the Windies attack at the time was weak.) My suspicion (just a feeling, don't know if it's true for many people or not) is that we remember batsmen and bowlers by their whole careers, but we remember all-rounders by their great series. And in individual series, some all-rounders can definitely be as good or better than the specialists in each discipline.
The popular perception that a true all-rounder could hold his place as either a batsman or a bowler is a strange one, given that it's hardly ever happened. (Someone like Sobers could do it for a while, but only because the Windies attack at the time was weak.) My suspicion (just a feeling, don't know if it's true for many people or not) is that we remember batsmen and bowlers by their whole careers, but we remember all-rounders by their great series. And in individual series, some all-rounders can definitely be as good or better than the specialists in each discipline.
David,
I didn't mean to say that a "true all-rounder" (whatever that is) should be able to hold his place either as a batsman or as a bowler, just that a Bradmanesque one would be able to do so (with the stats I indicated setting him some standard deviations apart from the rest of the pack).
Also I agree with the point about Kapil. The tail-end of his career dragged on for too long and devastated his stats. In terms of impacts on series, his performances against Pakistan in 1979-80 were what really ensured his reputation for the rest of his career (and of course, those smashing innings he'd play!). His bowling also suffered from his being bowled into the ground by more than one Indian captain (the spin attack had faded away in his time).
Cheers,
Samir
I didn't mean to say that a "true all-rounder" (whatever that is) should be able to hold his place either as a batsman or as a bowler, just that a Bradmanesque one would be able to do so (with the stats I indicated setting him some standard deviations apart from the rest of the pack).
Also I agree with the point about Kapil. The tail-end of his career dragged on for too long and devastated his stats. In terms of impacts on series, his performances against Pakistan in 1979-80 were what really ensured his reputation for the rest of his career (and of course, those smashing innings he'd play!). His bowling also suffered from his being bowled into the ground by more than one Indian captain (the spin attack had faded away in his time).
Cheers,
Samir
Sorry, I didn't mean to suggest that that's what you'd said. It is a common perception in the public though.
Agree, rating catches is quite tough - but ignoring anything less than a catch per match is harsh, esp. if the guy isn't a close-in fielder. Slip fielders get the most, etc. ....... and of course other aspects of fielding, like runouts, runs saved etc., are even harder to evaluate.
As for an allrounder holding his place as a batsman or a bowler, I think it is fair to expect that he should be able to hold his place at least as a pure batsman or a pure bowler, while being competent in the other discipline - an approximation might be that his batting average should be more than his bowling average :-)
I think Kapil was an underachiever with the bat - he lacked application at the crease.
As for a guy ever living up to the standards that Samir has set for the "Bradmanesque" allrounder, with an output of 80 runs and 4 wickets per test (has anyone even maintained that for 10-20 tests, ever?), I wonder if his body could last 100 tests.
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As for an allrounder holding his place as a batsman or a bowler, I think it is fair to expect that he should be able to hold his place at least as a pure batsman or a pure bowler, while being competent in the other discipline - an approximation might be that his batting average should be more than his bowling average :-)
I think Kapil was an underachiever with the bat - he lacked application at the crease.
As for a guy ever living up to the standards that Samir has set for the "Bradmanesque" allrounder, with an output of 80 runs and 4 wickets per test (has anyone even maintained that for 10-20 tests, ever?), I wonder if his body could last 100 tests.
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