Adjusted Averages – or what do Vinod Kambli and Mick Hucknall out of Simply Red have in common?

This feature was suggested following discussions in the CW Forum, when forum member watson posted a thread discussing American evolutionary biologist Stephen Jay Gould’s theories on baseball batting averages and its applicability to Don Bradman’s outlying average.

There were two discussions which arose in this thread largely involving myself, watson, Red Hill and, appropriately, the big bambino, which I’d like to look at in more detail; one discussion concerned a 60-average in batting and it’s continued achievement as compared to baseball’s 400-hitters, which have largely disappeared – that was dealt with in my earlier piece here.

The other discussion was elicited by my posting of adjusted averages from a book by Surjit S Bhalla, Between the Wickets, which was published in 1986. Mr Bhalla’s adjustments were based on both opposition and scoring (as affected by conditions) which brought down Harold Larwood’s average by 13 points – this seemed inappropriate when taken in context and as a result I decided to run my own adjustments. Though these are based only on opposition strength and not conditions, nonetheless I think they are informative – I have posted Mr Bhalla’s adjusted averages below, as they form the basis of this feature.

The forum member’s concerns with Mr Bhalla’s adjusted averages notwithstanding, Between the Wickets is a great book and years ahead of its time. The author’s intention was to rate and rank all Test players up to that point, based on something he calls the WIN rating (short for Weighted Indices), these being made up of (for batsmen) adjusted averages, player’s worth to a team, consistency of performance, milestone scores and speed of scoring. The adjusted averages are based on standardization of the pitch and rating of opposition strength; the former is ingeniously calculated from the changing numbers of balls bowled (in the first two innings only), while the latter, which pre-dates the ICC ratings, is based on ordinal rankings (i.e. if A beats B and B beats C, A is better than B and C). The upshot is that all performances are normalised as if they were played at Lord’s against a moderate attack.

Although they only account for a part of Mr Bhalla’s overall player ratings, our discussion here will be restricted to the adjusted averages as I originally posted on the forum – here they are again:-

Batsmen (revised average >50, with actual average also shown)

82.90 Don Bradman (99.94)
62.40 George Headley (60.83)
60.25 Graeme Pollock (60.97)
58.76 Jack Hobbs (56.95)
55.76 Viv Richards (52.62)
54.33 Garry (57.78)
53.23 Everton Weekes (58.62)
52.64 Dudley Nourse (53.82)
52.24 Gordon Greenidge (48.32)
51.40 Aubrey Faulkner (40.79)
51.55 Greg Chappell (53.86)
51.40 Len Hutton (56.57)
50.82 Herbert Sutcliffe (60.73)
50.56 Allan Border (52.80)
50.55 Walter Hammond (58.46)
50.40 Ken Barrington (58.67)

Bowlers (revised average <20)

15.59 Harold Larwood (28.36)
16.13 Allan Davidson (20.53)
16.29 Clarrie Grimmett (24.22)
16.77 Bill O’Reilly (22.60)
17.02 Maurice Tate (26.16)
17.04 Neil Adcock (21.11)
17.68 Jim Laker (21.25)
18.16 Fred Trueman (21.58)
18.16 Hedley Verity (24.38)
19.06 Keith Miller (22.98)
19.28 Peter Pollock (24.19)
19.60 Alec Bedser (24.90)
19.65 David Allen (30.98)
19.91 Ray Lindwall (23.03)

It’s important to remember that the book was written in the mid-1980s so some players had not reached the end of their career, such as Richards and Greenidge. Also, as well as the Larwood adjusted improvement it’s interesting to note that Sydney Barnes adjusts from 16.43 all the way up to 25.94, meaning that Barnes adjusts to eight points worse than e.g. South Africa’s Neil Adcock.

Though certain respected forum members will be delighted to see Larwood rated as the best bowler of all time, it was Larwood’s adjusted average which raised the most eyebrows. I did mention that there is some account taken of the varying conditions, while also noting that Larwood played with some success against a very strong Aussie side during the 1932-33 “Bodyline” tour, but nonetheless a downward adjustment of 13 points did seem to be generous to say the least.

So I decided to run my own adjustments. I had put together a large database for my previous impact study which would enable this to be done, as it also included opposition strength ratings which were incorporated into those ratings. The opposition strengths are basically the ICC team rating, which I had previously calculated back to 1877 based on the algorithm given on their website. Those opposition strength values were used to modify the players performances based on a match-specific opposition value and their averages recalculated – sounds simple enough, but nonetheless it’s taken a few weeks to derive and make sense of the final numbers.

Initially I used an overall average opposition rating for all Test sides as a basis for modifying the performances, however I subsequently realised that, as the very low ratings of Bangladesh and Zimbabwe reduce the average quite significantly in later years, then the median value (108) should be used instead. So basically all performances are modified as compared to an opposition strength of 108, meaning a century against Australia in 2004 is worth significantly more than a century against Bangladesh during their first year in Test cricket.

A note of caution

Though I think they’re interesting in and off themselves, we shouldn’t place too much emphasis on the actual numbers derived – it’s more important to see how mine differ in magnitude as compared to the actual averages, taking into account the ICC team ratings, and also as compared to those of Mr Bhalla, while keeping in mind that I have made no adjustment for pitch quality.

Adjusted averages – the Wilson factor

Chasing the Don

One thing to keep in mind when looking at the following adjusted averages is that they are determined by how well a player performs against teams of varying quality, as measured by the ICC Test team rating system. I haven’t simply taken a single average based on the strength of each team he played against and modified his career average, I’ve modified each innings score based on the opposition rating for that match so as to take into account how well he fared against them, then totalled his adjusted runs, or adjusted wickets/conceded runs for bowlers, and recalculated the overall career averages based on each modified performance.

Here are the top adjusted batting averages, minimum ten Test innings played, showing all players who maintained an adjusted career batting average of at least 60 (adjusted average, adjustment, player, innings, actual average):-

That’s 19 with an adjusted average of over 60, whereas Mr Bhalla’s list contains just three; there were others who averaged over 60 using my system but with fewer than ten Test innings to their name, including Barry Richards who notched up an adjusted average of 82.79 in seven Test innings. As I mentioned earlier, there is no pitch correction in my list, however I’m of the opinion that the main difference between the two adjustments is that the ICC Test team ratings show the increasing strength of teams over time. Great players will have an increased average if they have succeeded against tougher opposition.

Some of those included in the list above warrant further discussion. Bradman is clearly worthy of his lofty average even when opposition strength is taken into account, while perhaps unsurprisingly Voges has come down somewhat, though significantly he is still in the number two spot. Pollock and Sobers both increase dramatically, suggesting great success against good teams, as have Lara and Nourse. David Steele? Steele’s average of 42.06 is a statistical travesty – he played in only eight Tests, but faced the likes of Lille, Thomson and Walker in three Tests, then Holding, Holder, Roberts and Daniel in the other five. Likewise Milburn – he faced Hall, Griffith, Sobers and Gibbs and averaged 52.66 against them before adjustment. Finally, while Tendulkar adjusts upwards slightly more than Kallis, it’s not quite enough to overtake the South African all-rounder.

Not all of the above can be categorised as all-time great batsmen, however this is mainly due to the small number of innings used as the cut-off – let’s try increasing this to 40 innings.

That’s 13 Australians, eight West Indians, five Indians, four representing England, three South Africans and one each from Pakistan and Sri Lanka. After Lara and Pollock, Seymour Nurse has the next highest adjustment of this group. Nurse is famous for his 258 against New Zealand in his final Test innings, though given New Zealand’s rating at that time this performance adjusts downwards, however it’s his performances against England and Australia, with six tons and nine fifties in 23 Tests, which adjust his average to almost 60. Sangakkara was a surprise to me, as his adjustment, though positive, is significantly smaller than e.g. Tendulkar, Kallis and Dravid.

The highest for New Zealand, Zimbabwe and Bangladesh were respectively Mark Richardson (53.42 – Stewie Dempster appears in the first list but had less than 40 innings), Andy Flower (55.72) and Monimul Haque (43.79).

What difference does it make?

Let’s now look at the differences in batting adjustments at either extreme, again with the qualifiers of first ten innings then 40. Here are the batsmen with the highest downward adjustments (showing adjustment, player, actual avg, adjusted avg) :-

As can be seen, Voges in fact has the highest downward adjustment of any player with at least ten Test innings. Notably Douglas Jardine drops to below 40 (you win some, you lose some, Mr Fertang), but that may be reasonable for a batsman who managed just one century in 33 Test innings – but what a century it was, as he showed the world how to handle Bodyline bowling as served up by Learie Constantine and Manny Martindale, crafting 128* during a five-hour bombardment. Also Vinod Kambli, whose career track paralleled Mick Hucknall out of Simply Red in his brief sojourn for Fulchester United, sees his average drop to well below 50.

Increasing the threshold to 40 Test innings:-

George Headley is worthy of further discussion; Mr Bhalla shows Headley’s average increasing to over 62, however my take on the quality of opposition he faced suggests that a downgrade is warranted. For example, for his 223 against England at Kingston in 1930 the opposition attack, other than Bill Voce, featured Nigel Haig, Ewart Astill and a 52-year old Wilfred Rhodes. Similarly, his famous 270* at the same venue five years later featured an England attack of George Paine, Eric Hollies, Ken Farnes and Jim Smith. Aubrey Faulkner’s average is similarly impacted, whereas Mr Bhalla sees Faulkner’s average increasing to over 50; I’m not convinced a pitch adjustment could account for a difference of almost 16. Though there are other early players listed, this is not, as stated earlier, due to a difference in pitch offset, rather it is the generally lower quality of opposition faced in those times.

Next, those with the highest upward adjustments. First, ten innings or more:-

Ramnath Kenny managed three 50s in four Tests against Benaud’s Australians in 1959-60 and this is enough to see his average adjust to over 46. Milburn we dealt with earlier. Cammie Smith was a West Indian opener who debuted during the famous tour of Australia in 1960-61 which featured the first tied Test, but like Kenny played in only five Tests. Bob Woolmer managed just three tons in a 19-Test career, but he did it against the likes of Lillee, Thomson and Walker. Growing up a fan of Yorkshire, Phil Sharpe was one of my favourite players; Sharpe managed a couple of scores in the 80s against that great 1963 West Indian side led by Garfield Sobers, but up against the likes of Ken Barrington, Colin Cowdrey, Tom Graveney and Ted Dexter he was never able to nail down a permanent batting spot in the England side.

Here is the same list with the number of innings cut off at 40:-

Many of these were discussed at the start of the batting section, however Trevor Goddard is of particular interest, though I will leave that until the all-rounder section. Brian Booth is a relatively unsung Australian batsman, but his centuries typically came against good attacks like Trueman and Statham, Hall and Griffith.

Larwood and Co.

Now we’ll turn to the subject of the original concerns with the adjustments from the book. Here are the top adjusted bowling averages, minimum 30 wickets (all players who maintained an adjusted career bowling average of below 22):-

JJ Ferris is largely overlooked when discussing low Test averages, however as we can see his actual average of 12.70 is worthy of comparison with Lohmann’s more famous 10.76 – when adjusted, Ferris far outweighs Lohmann, 10.33 to 17.07. Yet Ferris was himself outplayed by Charlie Turner on the latter’s first visit to England, 314 wickets at 11.22 being scarcely believable to modern eyes. Mike Procter played just seven Tests but 41 wickets at 15.02 hint at what might have been – his adjusted average of 13.39 is the third-best ever. Lancashire’s Ken Higgs should have played more than 15 Tests considering the success he enjoyed, and my system sees him worth even more, fourth best ever. Pride of place here though must go to Curtley Ambrose, with over 400 Test wickets and an adjusted average of less than 19. Notably SF Barnes maintains an average of under 19 after adjustment, 18.28 as compared to 16.43 – this is much lower than Mr Bhalla’s adjustment of Barnes’ average to 25.94.

Again the above are not necessarily the greatest bowlers ever, so let’s limit to those with at least 200 Test wickets:-

What a mouthwatering collection of bowlers, though these are all pacemen – as spinners tend to have higher averages, let’s limit to 400 wickets:-

Murali and Warne join the list, and notably their adjustments are along similar lines to the pacemen. Speaking of adjustments, the sharper eyed among you will have noticed that the adjustments for bowlers seem to be significantly less than those of the top batsmen. However, though this is true when looking at the difference in runs, when percentage adjustments are considered batting and bowling adjust by a similar degree – Pollock, Sobers, Lara and Nourse all increase around 20%. while Ferris, Turner and Higgs all decrease around the same amount.

Now let’s look at each extreme – this is a little more complex than the batsmen, so we will limit the list to greater than 30 wickets, at least one wicket per match (wpm), and an actual or adjusted average of below 30 (we’re not really interested in a bowler who adjusts from e.g. 45 to 65):-

Goddard is the only player to feature in both batting and bowling positive adjustment lists, but as I said I’ll look at him in more detail when discussing all-rounders. Again this would not be considered a list of high-quality bowlers, so let’s try the same exercise for bowlers with at least 200 wickets:-

Odd that the top three are England bowlers, and no doubt Gough would be brassed off to see himself listed behind Caddick, though this is as ranked only on degree of adjustment, not on adjusted average. I actually think of most of these bowlers as being better than their actual average suggests so I’m quite happy to see these adjustments.

Here are the same two lists with the highest adjustments not in the bowler’s favour:-

With nearly 3,000 first-class wickets Scotsman Alex Kennedy really should have played more Tests, as evidenced by his high wickets per match, 31 in only five Tests.

As none of the above list took even 65 Test scalps, let’s look now at those with 100 Test wickets or more:-

As might be expected, the earlier bowlers, who generally faced lower quality opposition, find themselves worse off. It’s also likely that, if I had time to do a similar pitch correction to Mr Bhalla, plus an era correction for changing scoring patterns, they would fall even further. Steven Finn looks more like a 33+ bowler rather than 28, i.e. more Phil de Freitas than Ian Botham.

Ted McDonald is also worthy of further discussion, though his deleterious adjustment is largely because the England sides immediately following the war were probably not as strong as those per-war. McDonald’s strike partner Jack Gregory suffers the same fate, though not to the same degree – his adjustment is +5.63 but at 85 wickets he didn’t qualify for the above list.

All-rounders

Here are the top all-rounders, again with at least 1 wicket per match, showing difference between adjusted batting and bowling average, player, adjusted batting avg, adjusted bowling average, unadjusted differential:-

Sobers was amazing; his actual averages are eye-popping enough, but his adjusted averages are unbelievable – almost 70 batting and under 30 bowling. I mentioned earlier that Trevor Goddard is the only player mentioned in both positive adjustment lists, however that’s not true – Dwayne Bravo also features in both lists, and this is reflected by his massive increase in average differential from -8.41 to +13.51. Goddard though is the only player, meeting both the batting and bowling qualification criteria, with an adjusted batting average over 40 and an adjusted bowling average under 20.

Keith Miller is a surprise, as although he still features in our top 20 his adjusted differential is actually lower than his unadjusted differential. But Miller is a statistical anomaly, a player whose stats don’t do him justice – Miller’s adjusted bowling average is 20.67 against quality opposition, but over 28 against less than average opposition; Flying Officer Miller wasn’t interested unless there was a challenge.

Comparing Bhalla and Wilson

Finally, let’s look at the players that maintained an adjusted batting average of at least 50 or bowling under 20 in Mr Bhalla’s book – below are listed player’s actual Batting Average, Bhalla-adjusted average, Wilson-adjusted average, adjustment between Bhalla and average, adjustment between Wilson and average, Player’s name:-

These numbers are interesting; while there are a few where both adjustments are either adjusting in the same direction (Richards, Weekes, Greenidge, Hammond), or are around the original batting average (Hobbs), some are significantly different. More than half of those listed above differ by more than ten runs between my adjustment and Mr Bhalla’s.

This seems too high to be explained solely by pitch adjustments, and the fact that almost all of the adjustments are significantly more positive by my measure suggests it could be likely that this is related to a difference between how the ICC rating system rates opponents and how Mr Bhalla’s method rates them. This is highlighted by the fact that Aubrey Faulkner’s batting average drops by five runs using my method while increasing ten runs using Mr Bhalla’s. The fact that players of other times increase significantly with my measure but decrease with Mr Bhalla’s suggests that a rating of opposition strength based on an ordinal method would tend to over-emphasize some eras and under-estimate others. Either that or the ICC system is doing the same thing but in the opposite direction, though as the accepted rating system this seems less likely.

Below is the equivalent list for bowlers:-

In every case, Mr Bhalla’s adjustment is significantly more negative (or favouring the bowler) than mine. The overall difference betrween the two methods is most significant in regards to Larwood, Tate and Allen. I’m puzzled by Allen’s massive downward adjustment, as his actual average even against poorer opposition was about 26.5 – how he could adjust to below 20 in Mr Bhalla’s system is I admit beyond me. The difference between my adjustment and Mr Bhalla’s for Larwood and Tate represents almost 50% of their actual average. In the case of Larwood, it’s easy to forget that in the seven Ashes Tests preceding the Bodyline tour he was averaging over 67, so again an adjusted career average of 15 is very surprising. In the case of Tate, the ICC ratings see his average opponent as being well under the median (94 as opposed to 108), but as mentioned earlier Mr Bhalla would not have had access to these ratings and based his adjustments on ordinal won-loss records, so we should expect some difference.

Verity is interesting, as his adjustment is almost equal but opposite when comparing the two methods. A look at Verity’s figures suggest something of a Miller-like approach – his average against quality opposition was 21.67, whereas against below-average opposition it jumps to over 32.

A post in the ground – the half century

In Test cricket, there are currently 64 cricketers who have maintained a career average of over 50 (minimum 10 innings). By comparison, Mr Bhalla shows just 16 worthy of that milestone, however he has ranked and listed players based on his WIN index, so there may have been other players who averaged over 50 who are not mentioned in the book. Nonetheless my figures say 105 and this is a huge difference which can’t be explained away by pitch adjustment alone.

As regards bowlers, there are seven who have managed to average less than 20 (minimum 78 Test wickets, as Larwood has the fewest Test wickets of anyone listed), while Mr Bhalla lists 14. I show five.

It seems that my adjustments based on performances with opposition taken into account has had the general effect of increased scoring, whereas Mr Bhalla’s have had the opposite affect. This could be impacted by my using the median rather than average team rating – based on median opponent rating of 108, there are about 50.6% of opponents above the median, so it seems that’s not the case.

At some point I may find the time to perform the extra adjustments based on conditions (and era scoring), but it’s a lot of work – don’t hold me to it.