Ok, I’ve had a re-read of this so as to try to get to grips with it. I’m specifically avoiding pithy one-liner responses because it’s clear that a lot of effort has gone into this analysis and I respect anyone who puts in the hard yards to develop something like this, and it deserves a proper and considered response.
Obviously, the (scarcely believable) reduction in Bradman’s numbers is the striking headline, which I’ll come to but don’t want to focus on at the expense of everything else. Rather, I have questions generally about the methodology and what seem to be inconsistencies to me but which I may not have fully understood.
To start with, dead runs. Of course, I understand that we can find examples where a team has batted on and on beyond the point of really needing to, but is that really so common as to literally exclude all instances of particularly high scoring throughout the entirety of Test history? As cricket fans, we often lament the fact that players don’t go big when the opportunity presents itself, and yet here you have invented a criterion which seems specifically designed to do nothing except statistically punish players for doing so. To exclude all runs beyond 100/135/150 scored by any batsman in any innings they have played makes absolutely zero sense in a study literally focused on batting averages, and would do so only if you told me that Mark Waugh was a paid consultant on this exercise.
Let’s take just as one example Hanif Mohammad’s epic 337 against the West Indies in Bridgetown in 1958, which saved Pakistan from what seemed a certain heavy defeat. Pakistan had been rolled very cheaply in their first innings in the face of a huge West Indian total, and were forced to follow-on nearly 500 runs behind. If Hanif gets out for 150 there, Pakistan lose and lose huge. Why on earth should his last 187 runs be discounted as “dead”? In fact, I’d say that each run he scored beyond 150 was more valuable, not less.
Second, the dominance rating could do with more clarity (at least from my not-very-smart perspective). For starters, just the inclusion alone of certain players who have played so few innings is bound to skew the analysis. Barry Richards was surely a magnificent player, but seven Test innings can’t possibly be enough of a sample size for a study that presents itself as a statistical one. Graeme Pollock, it should be noted, played in that same series and scored more runs than Richards at a better average (albeit with one of those innings being a lot of “dead” runs according to your criteria). The inclusion of Taslim Arif is even more incongruous – he played only ten Test innings, and made 42% of his entire Test aggregate in just one of them! And yet there he is, looking down on almost everyone from fourth spot. If Richards and Taslim are included, why not Andy Ganteaume or Kurtis Patterson? And Lawrence Rowe must be kicking himself for not retiring after his first Test.
However, more than who is and is not included, what I don’t follow is how the dominance ratings are first applied and then adjusted. Notwithstanding the removal of dead runs which I have already discussed, I read your passage explaining the theory behind calculating the dominance rating, but can’t see any source numbers which show clearly why an individual batsman has a specific dominance rating and what his baseline 1.0 number is. Again I'd argue that the "dead runs" part of this analysis doesn't tally with the goal as we are looking at Test averages in the context of dominance over their peers, and yet are actively removing the huge scores which would indicate the kind of true dominance we are looking for.
Beyond even that though, is that I can’t see how or why the older batsmen have had their numbers reduced by so much in order to align with what their “equivalent” would be in the Present Era. To use an example that you note in your piece:
“A batsman who exhibits the same degree of dominance today as Bradman did in his own time would not require nearly such a high batting average as he achieved. Instead of an average of 91.0 (excluding dead runs), this reduces by 23%, to become 70.1 to allow for subsequent deflation in the level and spread of averages; and is further reduced by 4.5%, down to 66.9, to reflect the general increase in batting skills since Bradman’s playing days.”
Once again, I may have missed where this is clearly explained by why does Bradman (or someone like him) have his average reduced by 23% - what is the rationale for that specific number? It’s a colossal reduction, particularly given you are already removing “dead runs” (which Bradman made many, many more of than anyone else by proportion due to his almost inhuman ability to go big), and also applying the arbitrary “expertise” reduction (which I’ll come to later) as well. It seems like an excuse to apply reduction upon reduction for unclear reasons in order to reach a number you want it to.
You reference Charles Davis’ study during your piece, noting areas where he adjusted or downgraded Bradman and others in his standardisation that you haven’t, and have been “fairer” in your analysis. And yet Davis’ final conclusion – with Bradman’s standardised average of 84.5 – was that from a statistical point of view he really shouldn’t exist, being so many standard deviations from the mean, and that it would be reasonable to expect a player as statistically dominant as Bradman to emerge in the game of cricket approximately once in every 200,000 years. How has your exercise – which you suggest is fairer and more reasonable – reduced Bradman’s number by so much more than Davis did to the point that he’s not an outlier at all?
Third, the eras seem inconsistent. The Present Era as defined by the study encompasses a period of nearly 24 years, which is at odds with some previous eras being confined to a single decade. One of the core tenets of this study is that everything before 2000 is to be standardised to the baseline of what it would be in the Present Era, and yet this era is so broad in scope that I don’t see how that is meaningful or even possible. We’ve seen enough studies of standardised batting averages over the years to have concluded that Test batting conditions in recent times are very different to those of the early 2000s (nearly a quarter of a century ago!) but this exercise places it all in the same bucket.
For previous eras, the amount of time designated as an “era” varies widely. In many cases, it is a simple calendar decade. But then we also have the period after WWII which when designating eras to include batsmen encompasses a full 21 years inclusive from 1946-66, but when deciding on expertise % is split in half. Why? The few years after the war saw an explosion in runscoring to an all time peak. The 1950s then, as we know, saw a concerted effort to make pitches in most of the world more bowler friendly with a corresponding drop in batting averages. Then the 1960s saw a rebalance between bat and ball that took global averages back up past the 30 mark where they have remained more or less ever since (barring a dip into the 29s during the 1990s).
The blokes batting in the mid-1960s aren’t the same guys who were batting in the late-1940s, nor were they batting in necessarily comparable conditions to all the guys in between, so what is the rationale behind a 46-66 era – or why the expertise splits it with quite a significant percentage difference in 1955? Why not stop it at the end of a decade? The next era is 13 years inclusive from 67-79, followed by simple calendar decades again for the ‘80s and ‘90s. If that shortening is because of the sheer increase in cricketing volume over time – more cricket was played by more cricketers in later decades – then I get that, but it subsequently renders completely senseless the idea of a “Present Era” encompassing a period nearly two and a half times longer than those immediately before! I don’t see how you can meaningfully baseline or compare when the parameters are seemingly so arbitrary and inconsistent.
Fourth, expertise advancement. This is one of my pet hates in regard to cricketing discussions generally, not just this particular piece, because it so often relies on the concept of teleporting a player from the past without warning decades into the future and then judging him on that. You make this point during your piece where you write:
“…if Bradman were to be transported to the Present Era with his demonstrated abilities unchanged, he would be somewhat less dominant in relation to present day players than he was in relation to his contemporaries because batting expertise in general has risen in the intervening period. (Hence my lower, fully standardised, average for him.) The same point applies to all batsmen of each previous era.”
Yes, cricket has evolved over time, because of course it has. In every field of human endeavour we are faster and stronger and know more than we used to, and if we don’t then something has gone seriously wrong. We have access to tools, knowledge and technology that previous generations didn’t have and in many cases couldn’t even dream of. However, this to me is a natural function our advancement, rather than an indication that we are today inherently “better” than those who had gone before. Every college physics professor in the world has more absolute physics knowledge than Einstein had, but that doesn’t mean they are greater than he was. Einstein himself also acknowledged the debt he owed to those who had gone before with his famous quote about “standing on the shoulders of giants.”
If we are acknowledge – as we should – that the game of cricket has evolved over the course of its history then we also need to acknowledge those things which impacted players of the past which today’s champions no longer have to deal with. Pitches weren’t covered from the elements, boundaries weren’t roped in 20 yards from the fence, protective equipment protected **** all, bats didn’t have sweet spots which turned a piece of willow into a cannon, and bowlers delivered the ball from further up the pitch due to no-balls being determined by the position of the back foot, not the front. If we are going to use the evolution of the game to rate players, then we need to adjust in both directions.
And that’s without even addressing the arbitrary percentages applied to downgrade players’ “expertise” from previous eras. Why are batsmen from the 1990s downgraded 2%, but players from the 1980s by more than double that at 4.5%? What is the rationale behind the percentage decreases applied at each time period? To my point above about time period inconsistencies, why are we saying that expertise has increased by a certain (inconsistent) percentage in virtually every decade, but then there has been absolutely no increase at all in batting expertise between 2000 and 2023?
When it comes to the application of these reductions for previous players, why aren’t they consistent with the figures you’d previously allocated for each era. For example, Ken Barrington played in an era which you have said was 7.5% lower in expertise than the Present Era. However, on your ranked table in the column “Allow for Advance in Expertise”, you have adjusted Barrington’s average by 3.8%. Why not 7.5% - has that adjustment already been factored in elsewhere in another number? It was hard to tell, and throughout the list the % reduction on the table was lower than the % reduction for era which you’d nominated earlier. I may well be missing something there which you’d already explained somewhere else, but it would be good to understand why it is different.
Finally, a sense check. I always think that will studies like this one of the most interesting parts is coming to the end of your analysis and discovering something that you wouldn’t have expected to find or that casts new light on previously accepted wisdom. However, I also strongly believe that any conclusion should be balanced by a sense check, a smell test if you will – basically, does this make sense based on everything I know of the subject at hand and what could reasonably be expected? I won’t even address the top of the list, and the inclusion in an all time top ten of blokes for whom the hashtag #samplesizelol could have been invented.
Rather, I’d look further down the list for my sense check. If you conducted a study to rank Test batsmen and found that Viv Richards and Len Hutton were placed one after the other on your list, then you’d probably think that’s a fair starting point that you may well be on the right track. However, if the two consecutive positions they held on the list were 53rd and 54th, I’d reckon you might cross-reference that against your knowledge and appreciation of cricketing history and have another look at your methodology.
While I appreciate the effort which went into this, and accepting fully that I may well have gotten the wrong end of the stick on literally everything, this study screams to me to be one which started with the controversial conclusion that it wanted to reach, and then introduced ever more extreme criteria in order to reach it.
