July 16, 2012

Developing a bowling value index

Ric Finlay
Muttiah Muralitharan bowled one third of the team balls and maintained an excellent strike rate  © AFP
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While looking back statistically over the career of the recently-retired Brett Lee, I mused over ways of assessing the value of bowlers to their team. Lee, of course, was a fast bowler best used in short spells, and was not one who one would use to plug up an end and bowl all day. He thus had quite a good strike rate (10th in the list of 35 Test bowlers with 250 wickets or more), but for limited times of the playing day only. He only bowled 21.25% of the balls bowled while his team was fielding, ranking him only 25th in the same list of 35 bowlers. Obviously, his value to his team would have been enhanced if could have bowled more while preserving his strike rate - but there is a risk, of course, that the strike rate diminishes if a bowler is asked to bowl more.

I am thus inching towards a statistical measure of the value of a bowler, V, that is a function of Strike Rate (balls per wicket), i.e., V = k(SR)

where k is a constant representing the amount of bowling a bowler does.

The simplest way to calculate this is to divide the proportion of overs that each bowler bowls for his team by the strike rate. Thus for Lee, V = 21.25/53.33 = 0.398

The table below displays the value of V for each of the 35 bowlers with 250 Test wickets or more:

* % tbb represents percentage of teams balls bowled by the bowler

Value of a bowler (V) - bowlers with 250-plus wickets
Player Wickets SR % tbb V
Muttiah Muralitharan 800 55.05 33.31 0.605
Dale Steyn 272 40.94 21.73 0.531
Richard Hadlee 431 50.85 24.86 0.489
Shane Warne 708 57.49 28.00 0.487
Waqar Younis 373 43.50 21.09 0.485
Dennis Lillee 355 52.02 25.19 0.484
Malcolm Marshall 376 46.77 22.62 0.484
Glenn McGrath 563 51.95 24.36 0.469
Joel Garner 259 50.87 23.41 0.460
Allan Donald 330 47.03 21.50 0.457
Anil Kumble 619 66.00 28.77 0.436
Wasim Akram 414 54.65 23.58 0.431
Danish Kaneria 261 67.80 29.06 0.429
Fred Trueman 307 49.44 21.11 0.427
Curtly Ambrose 405 54.58 23.17 0.425
Imran Khan 362 53.75 21.88 0.407
Courtney Walsh 519 57.84 23.18 0.401
Brett Lee 310 53.33 21.25 0.398
Harbhajan Singh 406 68.11 27.09 0.398
Craig McDermott 291 57.00 22.34 0.392
Shaun Pollock 421 57.85 22.47 0.388
James Anderson 267 57.29 22.02 0.384
Makhaya Ntini 390 53.42 20.50 0.384
Jason Gillespie 259 54.96 20.63 0.375
Ian Botham 383 56.96 21.29 0.374
Bob Willis 325 53.41 18.66 0.349
Bishen Singh Bedi 266 80.32 27.75 0.345
Zaheer Khan 288 58.05 19.09 0.329
Brian Statham 252 63.71 20.77 0.326
Daniel Vettori 359 78.98 25.59 0.324
Derek Underwood 297 73.61 23.85 0.324
Chaminda Vaas 355 66.02 20.71 0.314
Kapil Dev 434 63.92 20.05 0.314
Lance Gibbs 309 87.75 26.85 0.306
Jacques Kallis 276 68.67 12.64 0.184

Murali was clearly, under this measure, the most valuable bowling commodity to his team in Tests - not only does he possess a strike rate more in tune with that of strike fast bowlers (compare it with Kumble, Bedi and Vettori, for example), but he bowled an extraordinarily high percentage of Sri Lanka's overs in Tests in which he took part, bowling one over in three.

It would appear, too, that Dale Steyn is forging a career that will put his name up in lights alongside the great bowlers of yesteryear. No one can question Hadlee's high index, given his value to an otherwise unexceptional New Zealand team, while the high positions held by Warne and McGrath formed the basis of Australia's period of domination in the first decade of this century. Similarly, Waqar and Wasim formed a potent Pakistani partnership as did Marshall and Garner for West Indies. The recently-retired Lee is where you might expect him, about half-way down this list, just outside the indices of the really great bowlers. The index of Kallis is significantly below those of others in this table, just emphasising that there are limits to what even great all-rounders like the South African can do. An index of around 0.4 seems to separate the really great bowlers from those who were perceptibly less so.

The following table gives the same results for those Test bowlers with between 100 and 249 Test wickets (min V = 0.4):

Value of a bowler (V) - bowlers with 100 to 249 wickets
Player Wickets SR % tbb V
George Lohmann 112 34.20 27.00 0.789
Sydney Barnes 189 41.66 30.81 0.740
Charlie Turner 101 51.28 33.72 0.658
Charlie Blythe 100 45.46 27.25 0.599
Saeed Ajmal 122 61.32 31.98 0.522
Bobby Peel 101 51.64 26.14 0.506
Mohammad Asif 106 48.77 23.28 0.477
Colin Croft 125 49.32 23.23 0.471
Clarrie Grimmett 216 67.19 30.84 0.459
Hugh Trumble 141 57.44 25.65 0.447
Saqlain Musthaq 208 67.64 30.09 0.445
Stuart MacGill 208 54.02 23.98 0.444
Fazal Mahmood 139 70.75 30.66 0.433
Bill O'Reilly 144 69.61 30.07 0.432
Graeme Swann 188 57.73 24.47 0.424
Darren Gough 229 51.62 21.63 0.419
Michael Holding 249 50.92 21.30 0.418
Terry Alderman 170 59.89 24.79 0.414
Shoaib Akhtar 178 45.75 18.66 0.408
Andy Roberts 202 55.12 22.40 0.406
Alec Bedser 236 67.45 27.40 0.406
Andy Caddick 234 57.94 23.27 0.402
Ian Bishop 161 42.25 20.92 0.400

Lohmann and Turner bowled in conditions that are rarely replicated today, small innings totals allowing them to bowl a greater proportion of overs, and with a more potent strike rate. Barnes is confirmed as the genius he truly was, while the index for Saeed Ajmal is interesting, and may in time, if continued, allow him to be classified as an all-time great.

The bottom five in this list are also of interest:

Bottom five in the list (100-249 wickets)
Player Wickets SR % tbb V
Trevor Bailey 132 73.58 14.72 0.200
Garry Sobers 235 91.91 17.84 0.194
Ravi Shastri 151 104.31 18.60 0.178
Ray Illingworth 122 97.82 16.82 0.172
Carl Hooper 114 120.95 13.22 0.109

At the risk of destroying the reputation of an icon, the placing of Sobers at this end of the table really does suggest that history may be overrating his contribution as a bowler. The jury is still out on whether he or Kallis has been Test cricket's greatest allrounder - but that is a topic for another day.

The complete list of the statistical measure V for all bowlers can be downloaded here

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Posted by John on (July 25, 2012, 11:55 GMT)

Another really interesting article, thank you. Chatting about it to my dad yesterday, also a big cricket fan, he wondered about the impact of bowler at the other end. In his words; "but does it show what impact a very accurate bowler at one end has on the wickets taken at the other." We were not immediately sure how that might easily be measured (value of bowler X as a whole v value in a particular partnership in some form pehaps) but thought it worth a comment!

Posted by Noah on (July 18, 2012, 17:06 GMT)

One factor that your equation does not take into consideration is the quality of the team that any particular bowler plays for, and therefore their bowling percentage. For example had Kallis played for Sri Lanka, a side without the fast bowling quality of Ntini, Stein or Morkel, he would have bowled far more that 11% of the total. The same is true for non all rounders as well, Jason Gillespie for example would have bowled more if he was born in New Zealand and didn't compete with Warne, Lee and Mcgrath. It is amplified by 5 man attacks with players like Steven Harmison not making the list as a result of sharing the workload by virtue of being part of a team that had 5 bowlers due to the presence of an all rounder.

Otherwise very interesting

Ric: I think you are just confirming what I formulated: Kallis in a hypothetical Sri Lankan team would have had a higher value of V, and hence would have been more valuable to them than being the fourth or fifth bowler in a South African outfit.

Posted by Waspsting on (July 18, 2012, 12:35 GMT)

I rank Sobers the 2nd greatest batsman ever.

Didn't mean to give the impression i was comparing Sobers the bowler to Sehwag the bowler. kind of like pointing out if a bowling all-rounder had the same batting average as Ajit Agarkar - a legit point made, slightly 'cutely' (i.e. ironic, not particularly accurate but still legit)

I think of him more as "One of the greatest batsman ever, and he could be a useful bowler" rather than the usual "undisputed greatest all rounder ever"

@Jeff - telling stats about Gibbs and Sobers. Kind of supports a thought i had about a spinner being unnecessary if you have 4 great pacemen on the previous article on this blog

Posted by Gerry_the_Merry on (July 18, 2012, 11:50 GMT)

My top picks (only last 40 years, since 75% of test cricket has been played in last 40 years) 1. Ambrose 2. Marshall 3. Lillee 4. Holding 5. McGrath 6. Hadlee 7. Imran 8. Wasim 9. Roberts 10. Gillespie/Waqar/Steyn/Donald 10.

Posted by Harsh Thakor on (July 18, 2012, 8:53 GMT)

My list in order in terms of performance of paceman(over 250 wkts) are 1,Hadlee 2.Imran 3.Lillee 4.Marshall 5.Mcgrath 6.Ambrose 7.Waqar 8.Wasim Akram 9.Dale Steyn 10.Fred Trueman

Ambrose was arguably,the best match -winner amongst paceman particularly in the 4th innings as he showed against England in 1994 at Trinidad and South Africa at Barbados in 1992.Mcgrath.and Marshall were the best match-winners in terms of percentage of games won.

Posted by Harsh Thakor on (July 18, 2012, 8:45 GMT)

Imran Khan,is to me too low in your ranking,who had the 2nd best match-winning average and best performance by any paceman in his hey day in average and strike rate.Above all Imran was an all-time great match-winner who was a better performer than Wasim Akram if you asses his role in shaping wins in test matches and series versus the best opposition,be it England,Australia or West Indies.Marshall and Mcgrath bowled for top quality attacks and teams while Wasim Akram was hardly supported by the batting side.In his peak years Wasim performed better than Mcgrath .Overall to me Lillee and Marshall were the greatest and vie for the top spot,with their great competitivenes.What goes against Hadlee was his inability to be outstanding on slow tracks like Wasim Akram or Imran Khan.Waqar Younus was not as effective as Wasim against the best opponents like Australia,S.Africa or England and capitalized against weaker teams

Posted by Harsh Thakor on (July 18, 2012, 8:34 GMT)

A very good effort Ric.I praise your ranking of Sir Richard Hadlee ,who to me on pure statistics is the best pace bowler ever.He has the best match performance analyis by any pace bowler ,more 5 and 10 wicket hauls,the best average in matches won,and has the best relative performance by any pace bowler in his peak,capturing 330 wickets in 60 tests from 1978-1988.Above all he bore the brunt of a weak attack.In the statistical light Imran Khan would come 2nd,considering that in his peak years from 1980-88 he had the best strike rate and average of any pace bowler of the modern era and was the best performer against the mighty West Indies.Howevever he also missed years from 1983-1985.3rd,I place Lillee.Sadly ,Lillee's scalps in Packer cricket and against rest of the world are excluded,otherwise he would have had 458 wkts.in 89 tests.To me, Marshall and Mcgrath are almost equal at 4th and 5th place but I give Marshall the edge.They were assisted by great bowlers and teams.

Posted by anand on (July 18, 2012, 8:01 GMT)

i think your formula is heavily skewed to the percentage of team balls bowled, since that dramatically increases or decreases the net value.

Posted by Ananth on (July 18, 2012, 3:59 GMT)

Ric: Perfectly acceptable, Ananth, and probably more encompassing in that it explicitly includes runs conceded. As I explained to another commentator earlier, I have implicitly assumed runs conceded in the bowling proportion in an attempt to minimise for simplicity's sake the number of variables involved. Ric: What I have suggested does not add any complexity at all. In fact the Bowling Average is often the only measure available and is used in many an analysis. I have only suggested that the Bowling Averages be used instead of Strike Rates. If anything, it makes the calculations simpler. Let me add that I have no problem with using the Strike Rate. The key measure is the % of Team bowling load which remains intact. This important career aspect is part of all my Ratings work.

Posted by Sohail on (July 18, 2012, 3:35 GMT)

Interesting work, Ric. But I believe an important measure of bowler's worth is the bowling average. That should also play some part in your formula; maybe another division by the bowling average.

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