October 22, 2010

Measuring batting averages effectively

Madhusudhan Ramakrishnan
Brian Lara: the highest effective average in the 2000s  © Getty Images
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The quality of a batsman is usually measured against the bowling and conditions in which he performed. Very few matches in the 2000s have provided the opportunity to witness high quality knocks. The bowling standard has drastically fallen away in the second half of the decade and the pitches have been lifeless. In contrast, the 1990s still had fantastic fast bowlers in each team and run scoring was not the easiest. Zimbabwe's problems and Bangladesh's entry have meant there are ample opportunities for most batsmen to boost their averages.

The average has always been an excellent measure of consistency and quality, but has a flip side because it does not quite consider the difference between a half century made on a minefield (read Sunil Gavaskar's 96) and a century made on a featherbed (most matches at the SSC). A batting average of 50 which was earlier considered elite has now become commonplace this decade due to poor bowling attacks and placid tracks. The 2000s remains the decade with the highest batting average after the 1940s, which was a decade with very few matches. In this piece, I try to come up with a method to measure the true average of batsmen by considering the bowling strength of the opposition and the conditions encountered in the match.

The parameters used for the analysis are quite basic. 1. The bowling average for each opponent (in matches involving the player) is taken into consideration for home and away games. 2. The match average for all the matches is used to measure the difficulty level encountered. In matches involving Zimbabwe and Bangladesh, I do not consider the batting average of the minnows as the figure can skew the numbers badly. In these cases, the measure is purely the batting average of the other team.

The base value to measure the quality of an innings is calculated as the geometric mean (square root of the product) of the batting average (30.61) and bowling average (32.31) since Jan 1 1940. The quality index value obtained is 31.44. For each batsman, the similar values are calculated and measured with respect to the base value to obtain the accurate or effective average. For example if the batting and bowling average are 30 and 32 respectively , then the geometric mean is 30.98 and the quality factor is obtained by dividing the base value by the mean which yields 1.0147.

The table below lists the top run-getters in the 2000s (minimum qualification of 6000 runs). The table provides the details of runs aggregated home and away against each opponent (neutral venues also considered for Pakistan). Read the values as runs (innings played).

Ricky Ponting has had a wonderful decade as can be seen from his position at the top of the tree. After his horror run in India in 2000-01, he was unstoppable for the next six years, but has shown signs of decline over the last two years. Jacques Kallis and Rahul Dravid have been the rocks of the middle order for their respective teams. Dravid though has been slightly on the wane over the last three years which has seen his average drop from almost 59 to around 54. Mahela Jayawardene and Kumar Sangakkara have contributed immensely to Sri Lanka's rise as a competitive Test team, especially at home. Sachin Tendulkar's recent resurgence has stunned everybody and the early years of the 2000s when his injuries led to some poor performances have now been forgotten completely.

VVS Laxman and Virender Sehwag have eased much of the burden on Tendulkar in this decade with some exceptional performances. Shivanrine Chanderpaul and Brian Lara were the best batsmen for the West Indies in an otherwise forgettable decade. Lara retired on a high scoring 21 centuries in the 2000s. Mohammad Yousuf had a brilliant first half of the decade including a record breaking 2006 when he went past Viv Richards' aggregate runs in a calendar year.

** The tables are in two parts for sake of clarity ***Ricky Ponting and Matthew Hayden played one Test against ICC W XI scoring 54 and 188 runs in two innings respectively. The calculations for these are done separately and included.

Top run-getters in the 2000s (minimum qualification 6000 runs)
Batsman Aus(h) Aus(a/n) Eng(h) Eng(a/n) Ind(h) Ind(a/n) NZ(h) NZ(a/n) Pak(h) Pak(a/n)
Ricky Ponting - - 993(16) 1082(25) 1115(16) 530(18) 496(11) 362(8) 781(12) 440(8)
Jacques Kallis* 700(17) 708(17) 1118(19) 292(13) 327(8) 760(15) 826(13) 354(6) 408(5) 521(8)
Rahul Dravid* 737(24) 972(24) 574(14) 915(15) - - 313(4) 766(14) 524(11) 550(9)
Mahela Jayawardene 185(6) 274(4) 1070(14) 502(12) 863(14) 628(10) 434(7) 194(7) 430(15) 630(15)
Sachin Tendulkar 1173(22) 925(17) 546(13) 629(12) - - 71(4) 444(9) 394(8) 268(7)
Matthew Hayden - - 909(17) 552(18) 861(13) 1027(22) 461(11) 197(7) 128(6) 246(4)
Kumar Sangakkara 112(6) 391(6) 671(14) 336(12) 892(14) 365(10) 317(7) 334(7) 619(10) 695(9)
Graeme Smith* 260(11) 493(14) 696(17) 1083(17) 227(6) 431(12) 220(8) 290(6) 347(9) 358(8)
Virender Sehwag* 763(20) 833(14) 290(12) 237(6) - - 177(4) 180(9) 544(6) 732(8)
VVS Laxman 1082(22) 1034(17) 180(9) 404(11) - - 279(4) 322(9) 375(10) 262(9)
Shivnarine Chanderpaul 699(12) 260(12) 400(12) 1061(20) 863(15) 260(5) 103(3) 276(8) 464(9) 306(9)
Mohammad Yousuf - 367(12) 684(9) 815(15) 741(10) 366(11) 29(1) 718(14) - -
Brian Lara* 533(4) 707(18) 500(7) 503(17) 413(15) - 149(3) 90(5) 331(4) 448(5)
Chris Gayle 186(6) 449(10) 474(13) 721(21) 481(16) 160(5) 280(3) 540(8) 115(5) 324(9)

Top run-getters in the 2000s (minimum qualification 6000 runs)
Batsman SA(h) SA(a/n) SL(h) SL(a/n) WI(h) WI(a/n) Bang(h) Bang(a/n) Zim(h) Zim(a/n)
Ricky Ponting 915(17) 867(17) 207(5) 198(6) 707(19) 846(11) 69(2) 191(3) 259(3) -
Jacques Kallis - - 257(7) 318(10 929(11) 942(22) 254(4) 63(3) 112(2) 388(3)
Rahul Dravid 453(12) 504(16) 542(7) 662(21) 148(5) 1260(22) - 560(10) 504(6) 475(7)
Mahela Jayawardene 1158(12) 314(10) - - 335(8) 294(7) 556(7) 304(7) 167(4) 137(2)
Sachin Tendulkar 414(11) 392(10) 386(9) 485(11) 306(5) 331(8) - 820(9) 616(6) 199(4)
Matthew Hayden 862(18) 540(11) 381(7) 283(6) 681(14) 379(8) 61(2) 107(3) 501(3) -
Kumar Sangakkara 790(12) 392(10) - - 452(8) 238(7) 592(7) 284(7) 255(4) 281(2)
Graeme Smith - - 88(3) 179(4) 717(12) 876(13) 408(4) 335(5) 162(2) -
Virender Sehwag 924(11) 238(9) 547(7) 692(11) 286(5) 357(7) - 176(6) 74(1) 102(3)
VVS Laxman 333(9) 330(9) 370(9) 494(11) 271(4) 731(15) - 117(4) 31(2) 249(6)
Shivnarine Chanderpaul 820(15) 533(11) 130(4) 154(4) - - 108(2) 39(3) 73(3) 186(6)
Mohamamad Yousuf 96(3) 255(8) 285(12) 338(11) 665(5) 549(9) 227(4) 276(2) - 222(3)
Brian Lara 793(15) 531(8) 299(3) 688(6) - - 173(2) - - 222(4)
Chris Gayle 814(20) 545(10) 164(7) 54(6) - - 221(3) 126(3) 46(3) 307(7)

The fact that Ponting played in a top class team meant that victories were assured more often than not and also meant he faced weaker attacks for much of the 2000s. He struggled in the subcontinent, but was very successful at home and in South Africa. The Pakistani attacks were far less potent away in the 2000s after the retirement of Wasim Akram and Waqar Younis. All this pointed to Ponting facing comparatively weaker attacks in fairly easy conditions which is quite clearly a blot on an otherwise superb decade. Kallis has faced fairly consistent attacks throughout. His run glut against the minnows does pull his average down. Rahul Dravid's best performances usually came when the chips were down and he has been very prolific in almost all away conditions. A considerable proportion of his runs though, have been made against the weakened West Indies and the minnows. Jayawardene and Sangakkara have scored tons of tuns against Bangladesh home and away boosting their averages. They have hardly played and succeeded in Australia and South Africa though Sangakkara's 192 at Hobart was one of the best innings of the decade. Sri Lanka's awesome home record and ordinary away record is very evident from the less impressive showing of these two batsmen in away matches. Matthew Hayden resurrected his career on the 2000-01 tour of India and proceeded to amass 30 centuries at a rate only next to Bradman. He, like Ponting, played in a top team and faced ordinary attacks throughout. His away performance was definitely under par when compared to his home batting.

Tendulkar's prolific recent run has seen him score at a Bradmanesque average and he recently registered his sixth double century. His records in the 2000s against Australia has been excellent but the lack of quality in the attack in recent years does pull down his performance a little. He has also aggregated plenty against the minnows home and away in the past decade. Sehwag and Laxman also average more than 50 in the 2000s. Sehwag has two triple hundreds and four double tons. The Chennai and Lahore efforts though came on very flat tracks and the innings against Sri Lanka in Mumbai was against a highly weakened attack. Laxman usually has reserved his best against the top teams and hardly ever makes massive scores against the lesser opponents which have ensured that his contributions are always valued highly.

Brian Lara played in a team accustomed to losing in the 2000s. Right from the remarkable 2001 tour of Sri Lanka where he scored 688 runs in 3 Tests only to lose 3-0, he has made runs home and away against all opponents. His average against Australia is 47 in matches involving McGrath. His otherwise ordinary showing against England is boosted by the unbeaten 400 in Antigua. His consistency was exceptional in the last 3-4 years as he scored hundreds against Pakistan and South Africa home and away. Chanderpaul's case is similar as he has been part of a very weak outfit for much of this decade and has done brilliantly in losing causes.

Quality measure (bowling average of opposition and runs/wicket in match)- base value: 31.44
Batsman Aus(h) Aus(a/n) Eng(h) Eng(a/n) Ind(h) Ind(a/n) NZ(h) NZ(a/n) Pak(h) Pak(a/n)
Ricky Ponting - - 0.7602 0.8975 0.7362 0.9803 0.7495 0.6821 0.8298 1.2303
Jacques Kallis 1.0493 0.9353 0.9367 0.9295 0.9824 0.8805 0.9599 0.7748 0.9757 0.8589
Rahul Dravid* 0.9357 0.8458 0.9295 0.8048 - - 0.5993 0.9980 0.7167 0.6545
Mahela Jayawardene 1.0799 1.0310 0.9034 0.9935 0.7756 0.8823 0.7634 1.1236 1.0553 0.8867
Sachin Tendulkar 0.9183 0.8893 0.8808 0.8072 - - 0.7478 0.8450 0.8148 0.6840
Matthew Hayden - - 0.7555 0.9176 0.7055 0.9833 0.7476 0.7841 0.7949 1.1382
Kumar Sangakkara 1.0799 1.0465 0.9034 0.99135 0.7756 0.8823 0.7645 1.1236 1.0657 0.7290
Graeme Smith* 1.0679 0.9171 0.9308 0.8195 1.1856 0.8141 0.9921 0.7748 0.9756 0.8589
Virender Sehwag* 0.9356 0.8076 0.9390 0.7216 - - 0.5994 0.9980 0.7741 0.6545
VVS Laxman 0.9584 0.8530 0.8513 0.7994 - - 0.5994 0.9980 0.7899 0.6545
Shivnarine Chanderpaul 0.9517 1.1543 0.9722 1.0476 0.9237 1.0987 0.9347 1.0011 1.0465 1.0459
Mohammad Yousuf - 1.1473 0.8558 0.9556 0.6944 0.7859 0.7107 0.9887 - -
Brian Lara* 1.0891 1.2303 1.0850 1.2345 0.9250 1.0804 1.1582 1.0622 0.9080
Chris Gayle 0.8670 0.9263 0.8804 1.0749 0.9250 1.1637 1.0804 1.0527 1.1037 0.9351

Quality measure (bowling average of opposition and runs/wicket in match)- base value: 31.44
Batsman SA(h) SA(a/n) SL(h) SL(a/n) WI(h) WI(a/n) Bang(h) Bang(a/n) Zim(h) Zim(a/n)
Ricky Ponting 0.8006 0.9059 0.5873 0.9594 0.8462 0.7027 0.3539 0.5627 0.4184 -
Jacques Kallis - - 0.9848 1.1188 0.6881 0.8749 0.4910 0.5941 0.3962 0.3210
Rahul Dravid 1.0164 1.1325 0.6701 0.9353 0.8365 0.9240 - 0.6127 0.4725 0.8009
Mahela Jayawardene 0.8508 1.4016 - - 0.8985 0.9608 0.4264 0.7099 0.5016 0.3336
Sachin Tendulkar 0.9096 1.1583 0.7320 0.7995 0.9168 0.9678 - 0.6139 0.4663 1.1030
Matthew Hayden 0.8052 0.8969 0.7573 0.9623 0.8646 0.6560 0.3533 0.5627 0.4184 -
Kumar Sangakkara 0.8508 1.4016 - - 0.8985 0.9608 0.4273 0.7099 0.5016 0.3336
Graeme Smith - - 1.0559 1.0277 0.6880 0.6903 0.4772 0.6267 0.3970
Virender Sehwag 0.8245 1.1322 0.6957 0.8791 0.8366 0.8608 - 0.6407 0.9945 0.6754
VVS Laxman 0.9350 1.0955 0.7290 0.8358 0.8366 0.9271 - 0.6930 0.3630 0.8692
Shivnarine Chanderpaul 0.9740 1.0715 0.9560 1.6700 - - 0.4079 0.7548 1.3315 0.8383
Mohammad Yousuf 0.8219 1.2829 1.0985 1.0370 0.7561 1.0519 0.5406 0.5872 - 0.8901
Brian Lara 1.0368 0.8171 0.8839 1.0385 - - 0.4079 - - 1.1129
Chris Gayle 1.0411 0.9132 0.9259 1.0385 - - 0.4079 0.7548 1.3315 0.8383

** The quality value for Ponting and Hayden in the ICC World XI match is 1.2964.

The table below lists the effective averages of the top batsmen in the 2000s. Brian Lara is on top in terms of quality of innings played and Ricky Ponting and Matthew Hayden are at the bottom. This is not a method that questions the quality of a player, but merely an alternative to measure the average effectively.

Effective averages of top batsmen in 2000s
Batsman Actual runs Actual average Effective runs Effective average Quality deviation
Brian Lara 6380 54.06 6572.1 55.69 1.0301
Shivnarine Chanderpaul 6735 53.03 6805.0 53.58 1.0103
Rahul Dravid 8904 53.63 8733.0 52.6 0.9807
Mohammad Yousuf 6633 56.21 5950.5 51.29 0.9124
Jacques Kallis 9277 59.08 8022.3 51.09 0.8647
Kumar Sangakkara 8016 56.85 6800.9 48.23 0.9112
Mahela Jayawardene 8475 55.39 7324.3 47.87 0.8642
Sachin Tendulkar 8399 57.13 6933.4 47.16 0.8295
Ricky Ponting 10158 57.38 8207.3 46.36 0.8079
VVS Laxman 6864 52.00 5920.4 44.85 0.8625
Virender Sehwag 7152 53.37 5838.1 43.56 0.8161
Matthew Hayden 8364 52.93 6803.6 43.06 0.7537
Graeme Smith 7170 50.49 5818.2 40.97 0.8114
Chris Gayle 6007 40.31 5758.6 38.64 0.9585

A similar approach yields an average of 85.23 for Bradman (three weak teams played considered minnows) and 51.45 for Gavaskar. The approach can be further modified to calculate period wise averages to understand the batting quality better. Gavaskar for example averages almost 83 with 10 centuries against the West Indies prior to 1980 when the bowling attack was not at its best, but only 41 after 1980 with just three hundreds in dull draws, in between falling seven times to Malcolm Marshall before crossing 20.

A more detailed approach analysing period wise performance and in matches involving particular bowlers will be taken up later.

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Madhusudhan Ramakrishnan is a sub-editor (stats) at ESPNcricinfo

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Posted by Waspsting on (November 6, 2010, 18:35 GMT)

@Gerry the Merry

Regarding Gavaskar's figures against West Indies - its one of the most mis-represented stats in cricket. Some say - "he scored 13 centuries against those great teams - shows his class" others say - "when they had their best bowling attacks, he didn't do to well - overrated".

Heres the truth about it. Most of his 13 100s weren't against the "fearsome foursome" attacks (only 3 were i think - and those were on flattish tracks). HOWEVER, scoring all those hundreds even against weaker attacks was A WONDERFUL feat. why didn't everyone do it, if it was so easy? It did show his class, just not as much as if he'd done it all against the pace attacks (which i doubt anyone could have) Second, averaging 41 against West Indies pace attacks is also a credible performance, especially for an opener. How many others managed it? 41 isn't 50 - but obviously, a career total of 50 will be divided into bigger scores against weaker attacks and smaller against strong attacks. 41 is solid

Posted by KalluMaMa on (November 3, 2010, 8:52 GMT)

Nice analysis. I think you should check the effective averages of these batsmen when the series was alive(i.e no dead rubbers included). The results would be interesting to say the least! :)

Posted by Alex on (November 3, 2010, 6:58 GMT)

@Gerry, this is an excellent comment. However, SMG was in super form entering the '82 series in WI and '83 series in India but simply got dismantled by the WI. The average of 41 in 11 tests (& 20 innings) is courtesy 4 outstanding scores: 147*, 124, 90, and 236*. SMG managed just 148 in the other 16 innings at ave=9.25!

SMG's slump over '80-'85 is more due to the quality of attacks during this period: (i) Hadlee & Lillee down under in '80-'81, (ii) Willis & Botham in Eng '82. His lowest point was vs a sub-par Eng in '84. After that, he did well primarily because the attacks faced by him since then (except Pak '86) were not that great. SMG's legacy is the matchless technique, penchant for big scores (vs anyone ... once he got in), and the professionalism he instilled in Indian cricket. However, his selection in the second XI of Cricinfo is flattering at best!

Posted by Gerry the merry on (October 31, 2010, 4:17 GMT)

On Gavaskar's failure against WI, it is made to seem as if he failed against WI with a 41 average when their attack was at its most potent. However, one must place the average in the context of his career. In his first 50 matches, ending in 1979 at the Oval, he averaged 57, with 20 centuries. In the next 75 matches, he averaged 43, with 14 centuries. This contrast is hardly brought about because of WI since his average against them in this period is not significantly below his overall stats for this period, and WI were hardly the life threatening force they have been in the period 1977 to 1981 when India did not play them at all. The plain fact is that Gavaskar went through a prolonged 5 year slump from 1980 to 1985, and was roused out of this slump in 1-2 series against Pak in Pak and WI in India. After 1985 he gave captaincy up and his stats started improving. Generally, since his career is associated with WI, any failure is also attributed in a shallow manner to WI. Hardly so.

Posted by Satyajit on (October 30, 2010, 5:50 GMT)

Sorry to say but the analysis looks flawed. The team strength for the period gets too much importance. Ponting who was supposed to have one of the best decades is not not only below Lara but 7 points behind Chanderpaul! VVS and Sehwag who do so well in the decade languish pretty low as their contribution was more consistent towards second half when India was considered stronger.Hayden and Smith cut a very sorry figure as well. This analysis says that if you perform well as unit to see your country doing well then your numbers will be pulled down :-) I don't know where would Viv Richards stand in the eightees as he played for the best team. Can we get Viv's number for eightees and same figures for Sachin and Lara in ninetees going by your analysis?

Posted by Alex on (October 28, 2010, 16:57 GMT)

@Boll: I simply responded to Mark James in the manner he wrote that comment. India has won >40% tests vs Eng/SA/Aus over 2008-10, and SRT/VVS/Sehwag/Gambhir have struck gold over this period. These guys are *really* batting as well as their numbers indicate.

It is true that Aussies' backyard record is way better than India's backyard record over this decade (in fact, over most decades). They were quite clearly the better team and actually should have gone at least 1-1 even in the last series vs Ind (Ojha was clearly out --- lbw b Johnson --- in the 2nd innings). Much to his credit, Ponting handled the press this time around as a great leader should.

Posted by Boll on (October 27, 2010, 12:28 GMT)

@Alex, it was hardly a case of SAf, Eng and Aus having their butts kicked in India throughout the decade. By my reckoning India played 26 home tests against these 3 teams in the 2000s for 10 wins, 7 losses and 9 draws - a good but hardly dominant home performance.

Against Eng/SAf/Ind in the 2000s at home, Australia in comparison played 28 tests for 19 wins, 5 losses and 4 draws.

For all the talk about India being the hardest place to win in, here are the overall home figures for the 2000s.

Australia played 59 tests, won 45, lost 5, drew 9 India played 47 tests, won 21, lost 8, drew 18

Australia played 21 series, won 18, lost 1, drew 2 India played 17 series, won 11, lost 2, drew 4

Posted by Waspsting on (October 26, 2010, 0:29 GMT)

I'd be curious to see how Viv Richards figures come out under this formula - given the strenght of his teams.

Couple of points - I wouldn't call the West Indies side Bradman faced as "minnows", at least not as bowlers. Hammond had a poor record against them - they had decent pace bowlers. South Africa and India, he simply massacared by contrast.

Article makes very interesting reading, though I don't entirely follow what you've done with the stats. Some of it, I confess, doesn't "feel" quite right - as though players are punished if they have good batting partners and come from a good bowling side. Not all runs are worth the same, as you mention to start with, but (for example), I think Ponting's 5 centuries in 6 tests against South Africa a PHENOMENAL feat, better than Dravid's run on the subcontinent pitches (which were flat at the time).

And how to measure performances in difficult conditions if multiple players perform? - e.g Hobbs and Sutcliff on wet wicket?

food for thought

Posted by Waspsting on (October 26, 2010, 0:15 GMT)

Very interesting. Just some intuitive thoughts on the matter.

Every batsman is bound to play about half his matches in home country, which biases averages. A Kiwi like Martin Crowe playing on all those green wickets will have a hard time averaging 50, while Mohammed Yousuf, playing on all those flat tracks, will have a much easier time. Can't blame the batsmen. naturally, they base their skills on the conditions they encounter most often. Sehwag can be a killer on subcontinent, but while no pushover in England, Australia, South Africa etc. - he's not consistent enough to be great. It seems to me that Ponting and Hayden are being "punished" in these stats for playing in strong teams. I wouldn't call Australian conditions "easy", its just "different". Lara and Chanderpaul are being "boosted" for the opposite reason (keep in mind, West Indies pitches have been very flat in 2000s, its just that their batsmen have been poor). (continued)

Posted by Karthik on (October 25, 2010, 11:55 GMT)

Interesting to see adjusted averages of the great batsmen. I would see the averages of all who have 50+ average over their career (full or to-date) to see where each of them stand. For the sake of purists, I would like to see a considerable difference in adjusted averages for people like Sachin/ Lara and Samaraweera, et al!

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