Test Cricket’s greatest all-rounders

Back in the 1980s four all-rounders dominated the world test cricket scene: Ian Botham from England, Kapil Dev from India, Imran Khan (now a very prominent politician) from Pakistan, and Richard Hadlee from New Zealand. Much ink was spilled in the debate on who was the best, and how they compared with great all-rounders from the past such as Australia’s Keith Miller and Garfield Sobers from the West Indies. Many years ago I came up with a good way of evaluating all-rounders based on their statistics, and finally I have been able to crunch the numbers and come up with the results.

I should clarify a few things. This whole article relates only to men’s test cricket, though it would also apply to any other format. More importantly, the whole idea of rating players based on statistics is obviously flawed, as stats don’t capture everything about a player. But as long as we allow for that and don’t try to be too precise, I think we can gain some useful and interesting insights.

Rating players

One of the most-used ways of scoring all-rounders was simply batting average minus bowling average, but there are at least two major problems with this. First, it favours batting over bowling. The global average for batting and bowling are both about 30. Now, bowling averages almost never go lower than about 20, but batting averages over 50 are numerous. As a result, Sobers scores very highly on this scale on the strength of his batting, even though his bowling was decidedly mediocre.

The root of this problem is that the scale doesn’t actually measure anything sensible. Batting average is just runs scored / dismissals, and bowling average is runs conceded / wickets. So batting average minus bowling average equals (I hope you’re sitting down):

(runs scored × wickets – runs conceded × dismissals) / (dismissals × wickets)

It should be fairly obvious that this is completely bonkers: it doesn’t measure anything even remotely meaningful.

The second problem with this measure is common to other measures such as the batting average: it fails to take into account the quality of the opposition. For example, people have suggested that Jacques Kallis’s impressive averages come from his playing so many matches against weak Zimbabwe teams. (I don’t think the stats actually bear this out — it’s just an example.)

I always thought that the two problems could be solved separately, but as it happened, my solution to the first problem also solved the second. So now not only can we decide who, according to statistics, was the best all-rounder in the 1980s, we can decide who was best overall. We can even decide other questions such as who was the best bowler of all time, whether Don Bradman really is as much of a statistical outlier as he seems, and even whether Ricky Ponting (as a batsman) was as good as Glenn McGrath (as a bowler).

My plan was to come up with measures for batting and bowling that have the following qualities:

• They should point in the same direction. With the current batting average, higher is better, but bowling averages work the other way.
• They should be comparable, so a batting score of (say) 25 should indicate the same level of ability as a bowling score of 25.

The bowling rating

My initial idea was to leave the batting average as it was, but change the bowling average by taking its reciprocal with respect to the global overall bowling average. For example, suppose the global bowling average for all bowlers is 30. Then suppose a given bowler has an average of 20. That’s 2/3 of the average. So to get his bowling score, just invert that fraction and multiply it by the global average. So that would be 3/2 × 30, giving a bowling score of 45. Such a bowler would then be as good a player as a batsman with an average of 45.

The hard part then becomes: how do we calculate the global bowling average? We can’t just calculate the average over all test matches for the last 130-odd years, because bowling averages vary over the years: they were lower last century when many matches were played on bowler-friendly uncovered pitches. So when calculating a player’s bowling score, I use the global bowling average during the period of that player’s career. This makes sense because we are essentially measuring where our bowler sits amongst his contemporaries.

This also takes into account the other variable, which is the quality of batsmen our bowler has to bowl at. If there are a lot of good batsmen around, then the global bowling average over that period will be worse. Our bowler’s score will not be unfairly reduced by the fact that he has to bowl against superior batsmen — because all the other bowlers at that time had to also.

So this gives us a superior measure of bowling, which goes in a sensible direction (higher is better) and takes into account the quality of the opposition. To make it easy to evaluate, I thought it would be better to normalise it so that, say, an average bowler would have a score of 100. Then a poor part-time bowler might have a score of 50, while Murali would probably be up around 150. It’s easy to use this to compare two bowlers, even if they played in different centuries.

The batting rating

From here, the obvious next step is simply to do the same thing for batting, yielding a batting score where 100 is average, less is worse and more is better. It seems odd that the batting score doesn’t directly relate to runs actually scored, but that’s not what it’s for. If you want to know how many runs the batsman scored, look at the old batting average. But that depends on the quality of bowling attack he has faced. So if you want to know how good the batsman is, the batting rating will tell you.

The all-round rating

Once we have batting and bowling ratings, normalised to the same scale, determining an all-round rating is simple. You do not try to take the average of the two. After all, if you’re an average bowler but a great batsman, then improving your batting doesn’t make you a better all-rounder: it just makes you a better batsman. This is why Viv Richards was not an all-rounder: his stupendous batting could never make up for his lacklustre bowling. You are only as strong as your weakest link, so the all-rounder rating is the minimum of the batting and bowling ratings.

Qualification

Almost done. We still have to set minimum limits for play, to avoid the Andy Ganteaume Problem (he scored 112 in his only test innings, so his average is higher than The Don’s). Let’s impose a minimum number of notional full matches. Five is not enough — that could be just a single series — so let’s say 10. Ten full matches means 20 innings, so we’ll say a batsman must have 20 innings to have a batting rating.

Bowling is a bit trickier — we can’t set a minimum number of innings since a bowler’s innings can be of any length. So let’s simply require our bowlers to have bowled in 20 full notional innings. I guess that on average, each proper bowler bowls 20 overs in an innings. (Actually, I just calculated this: ignoring insignificant 1-2 over contributions, which will largely be part-time bowlers having a go, bowlers average 19 overs per innings.) So our requirement to have a bowling rating is to have bowled 400 overs. (This seems a bit high, but if it’s reduced we can get some anomalies: Darren Lehmann end up being one of the top 5 all-rounders in history, on the strength of his quite good part-time bowling average.)

(I can’t remember if 8-ball overs were ever used in Test cricket, but I also don’t really care.)

Finally, how do we recognise a true all-rounder, rather than a bowler who can bat or vice versa? I say a player can’t be a true all-rounder if he’s below average in batting or bowling. So to qualify as an all-rounder, a player’s batting and bowling ratings must both be at least 100; in other words, his all-round rating must be at least 100. This doesn’t sound that hard, but I was surprised to discover that according to this standard, only 24 true all-rounders have ever played test cricket.

The All-round Hall of Fame

Based on all this, here’s the list of 24 test all-rounders up till the beginning of 2011. (My stats, from Idle Summers, are not up to date. I hope somebody will update them soon, because I don’t have time to.) I’ve also included a few notable players who didn’t qualify.

So Billy Bates, the English offspinner from the late 19th century, heads the list. His batting average seems unimpressive, but batting was harder back in those days of uncovered pitches. Second in the list is the great Australian Keith Miller, and third is the answer to my question as to who was the best of the 1980s super-allrounders: Imran Khan.

Sixth in the list is the best all-rounder of the 21st century: Australia’s Shane Watson. Further down are two South Africans with greatly contrasting stats: Jacques Kallis (brilliant batsman, very good bowler) and Shaun Pollock (vice versa).

Of the other ’80s super-allrounders, Ian Botham is in the top ten as expected. Kapil Dev only just makes the cut, but Richard Hadlee doesn’t quite count as an all-rounder. He’s one of the best test bowlers, but he tended to bat too far down the order to have any sustained impact with his batting.

Hadlee was always a great bowler who batted rather than a true all-rounder (at least in tests). But as a Kiwi, I am pleased to see two recent NZers are true all-rounders: Chris Cairns makes the top 10, and the underrated Jacob Oram is at #14. Some recent players don’t quite make it to the list, such as former NZ captain Daniel Vettori and dynamic Pakistani legspinner and big hitter Shahid Afridi.

As I always suspected, Gary Sobers wasn’t really an all-rounder. An excellent batsman but a below-average bowler, whose bowling aggregate is much more impressive than his bowling average.

I’m going to spend a little more time juggling all these numbers to find out similar information about batsmen and bowlers, and maybe some other interesting tidbits too. I will probably revisit the all-rounder calculations too, since I can already see a few ways they can be improved. It’s a shame there’s no Test cricket on at the moment — radio cricket commentary makes the perfect soundtrack for number-crunching.