You say that there's little to choose from between the difference between (BQI - average) and (BQI / average).

For me, it's like this. Suppose batsman A averages 60 and batsman B averages 40. Bowler C can dismiss batsman A after conceding 30 runs. Bowler D can dismiss batsman B after conceding 20 runs.

In a sense, each bowler has cut the opposing batsman down by half. (Obviously this is a toy example, and there'd be other bowlers. But it makes my point.) So in my opinion, each bowler should get rewarded the same amount.

Taking the quotient does this, but taking the difference doesn't.

Also, taking the quotient is nicer when you compare across eras with large scoring differences. This is not so important with a qualification of 200 wickets, but it changes things if you want to let in Lohmann and Barnes, etc.

An observation on Table 4 - it seems that list can be divided into two halves with opening bowlers defining the top half. It seem to be due to the fact that opening bowlers get to bowl to two players (the openers) before they've scored, and subsequently the rest of the top order starting off their innings, thus increasing the likelihood of dismissing them below their career/current average. Spinners on the other hand are more likely to be bowling at batsmen with runs on the board, and are in a way penalised in this form of computation.
However, table 5 seems to compensate this to some extent by accounting for the spinners average.

I'd just like to thank you for you contributions, as someone who is a bit of a number nerd I'm really enjoying the different presentations of the statistics you're producing and the fact you take the time to respond to the comments.

I wondered if one possible extension to this might be the addition of what was statistically the best attack though I'm not sure how you could go about this in a simple way. Standouts would be Warne and McGrath, Lillee and Thompson, Wasim and Waqar, WI attacks of the 80s, all spin indian attacks. Cricket is afterall a team game and batsmen get statistics for highest partnerships, isn't it time the bowlers got an equivalent?

Dan (A bowler who often creates pressure at one end, allowing someone else to take the wickets!)

A good way of doing it is to actually consider the batsman's average in 12 months prior to and including that innings (that tells you the batsman's form). So getting Sachin Tendulkar out in a test match in 2002 (or in 2007-08) will weigh more than getting him out in 2005-06. Similarly getting Viv Richards out in 1976 would be more precious than getting him out in 1990. I know this is equally hard as considering a player's average at the start of the match. A good approximation to this is to consider only the player's average in the year of his dismissal. So you do consider Tendulkar's average for the whole 2002 for any dismissal in 2002. This, though not accurate, gives a fair approximation.

Another parameter that I would consider to rank "quality" wickets would be the match/pitch conditions. Obviously, a bowler taking 5/100 on a batting paradise has taken "higher quality" wickets than someone with, say, 6/80 on a green top in overcast conditions. One way to quantify this might just be to take into account the total runs scored in a test. So if a bowler has taken 10 wickets in a match where over 1500 runs were scored, those 10 wickets should be given more weight than a bowler with 10 wickets in an 800-run game.

Great analysis, which demonstrates who the top bowlers of all time are.

Q) Which batsmen have fared the best against the top bowlers listed above ie, Ambrose, Marshall, McGrath et al? That would be very revealing... would Gavaskar show up higher than Richards, who played along Marshall, Holding and Garner rather than against?

Hi Ananth - I did not understand the sentence "It works both ways and over a long career, these variations even out" when you refer to a bowler taking lower order wickets. Could you please clarify? My understanding is that to score high on this measure, Kumble should have stopped after taking five wickets in the match where he took ten. What evens out over his career, and how?

Also, it sounds a little hollow to me, personally, when you say that this list does not rate the bowlers at all. It seems to me that the implication is always there that the bowler who takes more top-order wickets is the better bowler.

I must protest against the removal of bowlers with fewer than 200 wickets.

It removes a number of luminous names. Indeed every bowler, with the sole exception of Grimmett, who bowled before WWII, and many other All Time Greats, such as Davidson, who finished before the escalation of Test matches around 1970.

Good follow up! However, I too like reading stats but I often wonder if the numbers alone tell the truth (lies, damned lies and statistics - Disraeli [not Twain]).
What is lacking is objective context - bowling the most dangerous batsmen out within the conditions on the day is NOT something that can be measured but would be the true value of a wicket. e.g. Getting a premier batsment out for les than his career average on conditions that usually favour him. Surely the capture of the wicket would rate more highly than say on a ground or facing bowling that causes this player to play below their normal standard.

HOW ABOUT THESE TWO SUGGESTIONS:
1. Rather than taking a career average, form is only temporary (class being permanent), how about a moving average over say 5 or 10 innings as sometimes players have purple patches. Tough calculation but realistic at that time.

2. Just take the average score for batsmen in that test - it is a true reflection of current performance?

I have never bothered about numbers..But i found the last 2 blogs extremely interesting..I have come to know some bowlers whom i have not heard of..and i have followed those names and analysed their career..and i have come up with some fascinating players..
This blog is even more good..as u took time to sort out differences and ur interaction with readers is just great!
But i would like u to answer this?
As u are a numbers man..it would be interesting to see ur reply..
Do u think that numbers tells the story abt a batsman or a bowler..or is there a limitation with that?
Please do answer if u find it worth..

The new tables, taking into account as fixed previous batting averages tend to favour England bowlers, and I think there is a reason why.
Those bowlers (I have checked this) played a great number of matches against very strong Australian and West Indies batsmen. All these batsmen had very good averages (far better then their England counterparts).
What this means is that a top-order wicket taken by an England bowler will automatically be worth more then a similar wicket taken by an australian bowler, even if such a wicket is not of more importance to match result.
Hence the English bowler will be rated higher, even though most times their efforts were less effective then the Australian or Windies bowlers.
I have not checked the NZ stats, but I'm sure the results there would be similar (no batsman with an average over 40).

I like Peter Parker's suggestion about coniditions coming into play. This might iron out some stats that are skewed due to uncovered pitches of yesteryear, where bowlers had a better chance of getting wickets.
But then again, if you take the match where England got 903-7 (in 1938) you also need to consider the 201 and 123 (both all out) that Aus got in the match. Was this a batting paradise, or was it a horrible wicket? Tricky...
I feel sorry for you always being bombarded with "AKRAM IS DA BEST" etc, pitiful really.
I think you need an infinite number of stats and analyses to get the complete picture, and i'd just like to thank you for your contribution!

Ananth .. Thanks for adding rule number two.
I must concur that your blog is a tremendeous service to cricket world. It has opened the traditional definition of brilliance in contemprory cricket and may very well just tip of an iceberg.
I always found the old method of calculating averages bogus. Your new method may not be perfect and some people may find it hard to digest, but I reckon it is way better than current system .. and we all should push for the implementation !!

PS: Flintoff is the best bowler in the history, next comes Akram !!!!!!!!!!!!!!!!!!!!!!!!!

PS:

one more thing if i may... could you compile a list of "The Greatest Match Winners" ? where a significent contribution from a player lead to test and ODI matches being won?

I think the best thing to do is to go back to your original calculations (where BOJE was on top) and then divide the bowlers strike rate by the original BQi. The bowlers with the lower numbers would be best. What this does is it accounts for lower order wickets and gives a better result.

I was wondering if at some point you could do an analysis on a batsmans success score, this being the score that once reached results in a victory for his team. eg Graeme smiths is 87 in onedayers as his highest score in a lost cause is 86. Sorry if i have already posted this, computer froze.

Interesting analysis, as always. Just a suggestion regarding the cut-off point for being considered for the tables - how about making it 100 wickets taken at an average of more than, say, four per match? That would allow the pre-WWII bowlers who played far fewer Tests to be included, while not considering part-time bowlers who scrape past 100 wickets at barely one per match (eg George Lohmann - 112 wickets in 18 Tests - versus Carl Hooper - 114 in 102).

Appreciate you're trying to improve on the basic average, which can distort a career.

But hasn't a far more sophisticated analysis been done by the former PWC ratings, now known as the LG ICC ratings. This considers the relative values of each batsman dismissed - including their current form - and also the relative condition of the match (e.g. low scoring vs run feast games).

That deals with snapshots in time, but an average career rating would give a better indication than your computation.

Not sure if anyone else has suggested this one. Given that opening bowlers have the advantage of being fresh and have a new ball a good measure of quality would be wickets taken after about 30 overs have been bowled. The effect of a second new ball is not so great since the bowlers will be tired.

Ananth,
Appreciate your effort. Looks like a lot of thinking has gone into this latest list. And table 5 looks closest to what people might have thought when you are talking about taking quality wickets.

I think that the analysis you make is a very intelligent one. The problem is that cricket is ateam oriented game and any wicket taken is not just one bowler's wicket.Zaheer creates pressure while Pathan reaps benefits. (Happens to me all the time!). Or imagine Wasim Akram and Waqar Younis playing for Australia, with their high fielding standards. Pakistan plays with Kamran Akmal! Talk about low standards. Look at the pitches the sub-continent bowlers mostly bowl. Flat pitches with nothing in 'em. Kapil's 29 avg. is so much better than some Australian's 25, or 24 just for hte quality of pitches.

What I am trying to get at is that even tohugh the results of your calcualtions are telling; they are just not adequate enough to rank any bowler as having a better quality than others. The study of numbers without taking pitches, fielding standards, quality of the grounds (some are grassless) and the fact of 'hunting in pairs'. The list will always be biased against sub-continent players.

Ananth, I love the work that you've put into all this!

Data mining through large databases myself at work, I fully appreciate how difficult it is to design a test that best captures the attributes that you're looking for, but it's great that you can apply it to something you love. (I on the other hand, am a simple wage slave...)

Possible improvements:

Looking at wicket value being 50% current average and 50% contribution to innings average (rather than (1 - dismissal score/average)). Although this would now mean that you would need to calculate yet another statistic, it wouldn't require that much additional processing time if you're getting 'current average', and would both remove some of the 'plays against Australia/WI a lot' bias and increase the 'key wicket' bias. If Sehwag is on 80-100, he usually goes on to get a big score, it shouldn't be that his (1-score/average) weighting should be zero!

Using strike rate somehow - (BQI - Average)*60/SR would then be able to adjust for which bowlers were taking those wickets faster.

At the moment, there isn't a distinction bewteen taking lower order wickets only and taking wickets against lesser teams. The comment about Murali, Akram and Younis taking plenty of lower order wickets assumes that all teams that they played against are equal, whereas there is plenty of controversy around Murali's ability to take wickets against teams like Bangladesh, whereas not against teams like Australia.

Not sure how one would adjust for that, but I suspect think that the % of team score adjustment would help in some way to identify that - if Lee has an average of 20, but only 5% of his team's runs, compared to Abdur Razzak, with an average of 21 but probably closer to 10-15% of his team's runs, Razzak should be a much higher weighted wicket.

While not explicit, if you rise in rank after this, it is a sign of taking wickets against minnows.

Hi Ananth: Interesting analysis! Also it is interesting to see how different bowlers excel in different aspects. I request you to present the following analysis if possible: Just like how we say good batsmen are those who thrive in all conditions and contribute when the team is in trouble, can we have a similar ratings for bowlers? For example a spinner with a good bowling average in say Perth which normally assists fast bowlers or say in a placid pitch like Nagpur has traditionally been, then that deserves more weightage. Similarly, if we look at those bowlers who are partnership breakers then we can add points to them. I guess in such an analysis, the all time greats would be right up there (which is what made them all time greats in the first place I suppose).

I liked Habib Jalib's post, and i agree with him. There are so many factors that need to be considered in actually 'ranking' the bowlers. I loved his comment about Akmal ;).
I would just like to add a couple of things:
1. What about taking economy rate into consideration. Now that we have a list of BQI and other parameters, lets see who has taken these top quality wickets while giving away lesser no. of runs?.
2. Similarly for strike rate, lets see who has taken these quality wickets in lesser no. of balls?
3. Is it possible to do an analysis of the most unfortunate bowlers? :).. like most missed chances, dropped catches etc off each bowler. It may be done as a separate analysis.

I liked these analysis very much, and this is a wonderful work. I appreciate it, and please keep doing it :).

One thing missing from this analysis is the type of wicket the match is played in. I think it is fair to say that most batsmen score more in subcontinental conditions than in say, Australia / England.
In that case, bowlers in the subcontinent will have poorer (BQI - bowl ave) if the BQI is calculated over the entire career of the batsman.
To tackle this discrepancy, while calculating BQI for a bowler, the average of the batsman only in that particular part of the world should be considered (not his career average). This can even out the playing conditions and make the list more fair.

I have a couple of points:
1. If a bowler does not have good support or if he DOES have good support (someone who actually ends up taking the wicket) I'm not sure that the analysis would pick up on it. As one of the previous posters has pointed out perhaps the bowling figures in the context of a game needs to be identified as well (as per Habib Jalib's post). For if one bowler is 'plugging up' an end forcing the batsmen to take risks against their partner bowler to 'break the shackles' should not some of the credit go to the pressure bowler? Is there a way to give credit to a bowler if their partner takes a wicket from the other end during their spell?
2. In order to get around the "tailender" conundrum could it be effective to take the 'best 100 wickets' (rather than a percentage which could end up including more tailenders).

Have a simple suggestion? Instead of career averages, why don't you use averages against that country? Some averages are inflated by their performances against weak bowling attacks.

Ignore those philistines who don't appreciate the stats of cricket! Two great articles that I will be mulling over again and again!!!!!!

Factoring in the batsman's score at the point of dismissal seems to me to be the wrong thing to do. One interpretation is that bowling Bradman out for a duck means that he must've been out of form and that bowling him for 300 means it must have been a truly amazing ball to stop the master in flight. The other interpretation says that bowling Bradman for a duck is an incredible feat, while bowling him for 300 indicates that it took an awful long time to get a decent ball in. The truth is, obviously, somewhere in the middle but you can't hope to quantify that just from knowing the batsman's score.

Regarding Gough, Caddick and Hoggard all being in the top ten. Much as I like these guys they do seem to be an anomaly. Could it be caused by the fact they played on swinging English wickets more than the others. This would lead to high average sub continent cricketers being turned over more often. How would it distort the figures if you used the batting average figures for the country concerned? Alternatively I have lived through a golden age of English bowling without even realising it.

Even though all of these comments and your post, Ananth, are very interesting, I cant but feel that if a person have to look at every aspect of a bowler's career, including conditions he bowled in, the amount of overs bowled prior to dismissing a batsmen, the quantity of Cola he had with dinner the previous night, the temperature they were playing in (dehydration)...etc...all useless info.

The fact remains, as a club cricketer that bowls and bats in the top order, I know there is serious competition between team mates all the time! I dont believe that Nel sits in the dressing room after a match and have a gripe about Steyn's bagful of sticks he pouched. Who cares who bowled at who...the fact remains...:

Over a period of 5 to ten years all averages flattens out, all bowlers had opportunities to pick up wickets against top, middle and lower order batsmen. If you trail a team mate by 100 wickets you have yourself to blame!

Nice topic, but irrelevant. Its the roll of the dice!!

Excellent analysis and some very interesting comments.

There are a number of anomalies that come to light. For instance, the difference between top order and lower order batsman, playing top ranked teams and lesser teams and home and away performance. I think one of the most interesting careers to look at is Murali's and the comparison with Warne's. Murali's figures fluctuate dramatically between home and away and also top and lower ranked teams. I am not usre how you factor this into your table but no doubt others might add further comments.

You comment on bowling partnerships but what difference do you think the strength of the whole bowling line up makes. Again, I look at Murali and Warne. Effectively Murali only had Vaas but Warne was part of a very strong bowling attack. The same could be said of the WI attack in the 1970's and 1980's and arguably the likes of Roberts, Garner and Croft suffer.

Overall great work and a very interesting read.

Thank you.

Terrific analysis. Just that, because of "rounding", the data in Table 5 is incorrectly ordered. For example, Marshall should head up the table and not Ambrose. And Lance Gibbs should follow Kumble

Have you done any similar analysis on batting? Perhaps I missed it. I have always held that the "Not Out" factor must be eliminated in order to arrive at the "Real" average. Otherwise, people like Hussey (or Bevan in ODIs) have overstated averages.

Regarding Wasim Akram, what you are ignoring is the fact that he hd to bowl a lot in the subcontinent. Even, say, if the average per wicket in the subcontinent is lesser than in Aus, it is still much, much easier for spinners to take wickets. Compare India's trio of Sree Shanth's, RP Singh's, and Pathan's bowling when they went to Aus and there form now at home. I think you'd agree it has substantially deteriorated. Pak's pitches like Multan where Sehwag got 300 are not the most refreshig site for bowlers. Whereas in India, most wickets are taken by spin bowlers. At least in the long-term, bowlers like Mcgrath and Ambrose-- very good bowlers in their right-- would find difficult to bowl out batsman in pitches like Multan with such Monotony. Of course, when Pak visisted India recently, again, spin took most the wickets. Conversely, the reason why Warne's average is quite high (compared to other greats) is again that Aus pitches are more conducive to pace bowling.

There are tons of information to be known about this. You made some great points that answered my questions.