1 January 2010

Ploughing your own furrow or making hay?

Following discussion of the oft-repeated stat about Ian Bell never scoring 100 if no-one else has, Spaceman! of the TMSB Exiles wanted to know

... who has the best average when no-one else in the innings has scored a 50/100?

This is a really neat little question, with what I think are some quite revealing answers.

Table 1 shows the career records of batsmen in innings in which no-one (other than the batsman himself) made it to 50. For comparison, the remainder of each player's career (i.e. innings where at least one team-mate scored a half-century) is shown alongside, and the relative difference between batting averages in the two scenarios is given in the final column.

Table 1: Test batting records divided into innings in which no other batsmen made 50 and those in which at least one did

<--- no other batsman made 50 ---> <----- other batsmen made 50 -----> Name I NOs R Ave HS 50 100 I NOs R Ave HS 50 100 Diff% 1. BL D'Oliveira 14 5 614 68.22 114* 3 2 56 3 1,870 35.28 158 12 3 193.4% 2. SJ McCabe 13 4 594 66.00 189* 1 2 49 1 2,154 44.88 232 12 4 147.1% 3. DL Amiss 17 7 657 65.70 262* 2 1 71 3 2,955 43.46 203 9 10 151.2% 4. KS Ranjitsinhji 10 3 437 62.43 154* 2 1 16 1 552 36.80 175 4 1 169.6% 5. KF Barrington 29 7 1,314 59.73 132* 6 3 102 8 5,492 58.43 256 29 17 102.2% 6. DL Haynes 53 20 1,968 59.64 143 8 5 149 5 5,519 38.33 184 31 13 155.6% 7. JB Hobbs 21 6 893 59.53 126* 9 1 81 1 4,517 56.46 211 19 14 105.4% 8. AI Kallicharran 17 5 708 59.00 126 4 2 92 5 3,691 42.43 187 17 10 139.1% 9. Saleem Malik 24 8 927 57.94 99 8 0 130 14 4,841 41.73 237 21 15 138.8% 10. H Sutcliffe 17 5 676 56.33 135 2 2 67 4 3,879 61.57 194 21 14 91.5% 11. NCL O'Neill 15 6 505 56.11 134 2 1 54 2 2,274 43.73 181 13 5 128.3% 12. DM Jones 20 5 838 55.87 184* 3 2 69 6 2,793 44.33 216 11 9 126.0% 13. L Hutton 46 13 1,817 55.06 202* 10 3 92 2 5,154 57.27 364 23 16 96.1% 14. RA Smith 25 6 1,031 54.26 148* 6 3 87 9 3,205 41.09 175 22 6 132.1% 15. RC Fredericks 24 5 1,029 54.16 138 5 3 85 2 3,305 39.82 169 21 5 136.0% 16. GC Smith 24 4 1,053 52.65 154* 6 2 113 5 5,386 49.87 277 20 16 105.6% 17. KC Wessels 13 2 578 52.55 118 4 1 58 1 2,210 38.77 179 11 5 135.5% 18. TT Samaraweera 16 2 723 51.64 125 5 2 74 11 3,215 51.03 231 16 9 101.2% 19. HP Tillakaratne 27 8 981 51.63 119 4 3 104 17 3,564 40.97 204* 16 8 126.0% 20. BC Broad 10 2 409 51.13 139 0 2 34 0 1,252 36.82 162 6 4 138.8% 21. IVA Richards 31 4 1,378 51.04 130 11 3 151 8 7,162 50.08 291 34 21 101.9% ... 27. BC Lara 63 2 2,976 48.79 226 15 8 167 4 8,936 54.82 400* 33 26 89.0% 28. G Boycott 51 13 1,828 48.11 121* 12 3 142 10 6,286 47.62 246* 30 19 101.0% ... 31. JH Kallis 40 9 1,466 47.29 162 7 3 183 23 8,930 55.81 189* 45 29 84.7% ... 36. KP Pietersen 19 1 812 45.11 142 3 3 81 3 3,987 51.12 226 13 13 88.3% 37. DCS Compton 36 7 1,308 45.10 158 7 3 95 8 4,499 51.71 278 21 14 87.2% ... 46. DG Bradman 13 2 485 44.09 131 1 3 67 8 6,511 110.36 334 12 26 40.0% ... 54. WR Hammond 31 5 1,095 42.12 113 4 1 109 11 6,154 62.80 336* 20 21 67.1% ... 66. V Sehwag 26 3 939 40.83 195 4 2 95 1 5,226 55.60 319 14 15 73.4% ... 73. GA Headley 17 1 631 39.44 107 3 2 23 3 1,559 77.95 270* 2 8 50.6% 74. AJ Strauss 28 5 905 39.35 128 4 2 98 0 4,462 45.53 177 14 16 86.4% ... 77. SR Tendulkar 52 5 1,837 39.09 122 9 5 213 23 11,133 58.59 248* 45 38 66.7% ... 79. SR Waugh 50 11 1,520 38.97 122* 7 3 210 35 9,407 53.75 200 43 29 72.5% ... 84. RS Dravid 49 13 1,387 38.53 118 8 1 186 14 9,846 57.24 270 50 27 67.3% ... 106. AC Gilchrist 16 2 516 36.86 144 2 1 119 18 4,959 49.10 204* 23 16 75.1% ... 109. RT Ponting 31 4 991 36.70 156 5 2 201 22 10,434 58.29 257 44 36 63.0% ... 115. AR Border 60 12 1,734 36.13 163 8 4 205 32 9,440 54.57 205 55 23 66.2% ... 122. GS Sobers 27 2 893 35.72 168 3 2 133 19 7,139 62.62 365* 27 24 57.0% ... 139. Yousuf Youhana 30 0 1,027 34.23 115 5 3 116 12 6,220 59.81 223 26 21 57.2% ... 195. IR Bell 15 2 385 29.62 83 3 0 76 7 2,906 42.12 199 18 9 70.3% ... 252. VT Trumper 29 2 704 26.07 159 2 1 60 6 2,459 45.54 214* 11 7 57.3% ... 298. PD Collingwood 13 2 251 22.82 74 1 0 83 8 3,481 46.41 206 17 9 49.2% ... 387. KR Miller 20 3 288 16.94 61 1 0 67 4 2,670 42.38 147 12 7 40.0% ... 483. RA Woolmer 10 2 73 9.13 19* 0 0 24 0 986 41.08 149 2 3 22.2% ... 487. LEG Ames 11 1 90 9.00 17* 0 0 61 11 2,344 46.88 149 7 8 19.2% ... 538. BS Chandrasekhar 14 7 20 2.86 6 0 0 66 32 147 4.32 22 0 0 66.1% 539. HK Olonga 10 1 19 2.11 5 0 0 35 10 165 6.60 24 0 0 32.0% 540. TM Alderman 13 6 10 1.43 4 0 0 40 16 193 8.04 26* 0 0 17.8% 541. CS Martin 17 6 6 0.55 4* 0 0 59 34 77 3.08 12* 0 0 17.7% qual. 10 innings in which no 50 was scored by other players; full list available here

The batsmen at the top of this list are those who scored most heavily when their team-mates went missing. Consequently, it is interesting to see a good proportion of individuals who are known for backs-to-the-wall grit amongst them, including McCabe, Barrington, Dean Jones, and Graeme Smith. By and large, the highest ranked players fall into one of two categories: those who consistently averaged well, regardless of what was going on around them (Barrington, Hobbs, Sutcliffe, Hutton), and those who appear to have raised their performance when their team-mates were doing less well. Our leader, Basil D'Oliveira, is the most conspicuous example of the latter: his average in innings in which the other ten failed to reach fifty is very nearly twice what he achieved when team-mates passed that landmark.

Perhaps the most notable feature of this analysis, though, is that it doesn't have a certain, familiar name at the top; indeed, it arguably does not reflect especially well on Bradman at all. When you spend as much time staring at cricket statistics as I do, you end up looking at Donald Bradman's record very closely indeed. This is the first time I have seen anything approaching objective evidence to corroborate the fairly pervasive anecdotal view that Bradman may have fallen short of his usual superhuman standards when circumstances were most hostile for batsmen. If we interpret the absence of 50-plus scores as a proxy for the presence of such conditions, perhaps it is significant that there are 45 test batsmen who have outperformed Bradman in those innings.

Mind you, if we're raising an eyebrow at the Don, we probably have to wag a finger at the Nugget. Keith Miller's record in innings in which none of his team-mates passed 50 is conspicuously dreadful. Only one of his 12 50s and none of his seven centuries came in such knocks, with the result that his stats have the appearance of a batsman who was most at home making hay while the sun shone (maybe he was just so damned sociable that he couldn't bear to make runs on his own).

It is also a bit surprising to note the terrible records of a couple of Ashes-winning Kent stalwarts. Neither Les Ames nor Bob Woolmer once passed 50 unless at least one of their team-mates had also registered a half-century; in fact, neither of them ever scored as much as 20 in such innings.

In contrast to the kinks in the middle of the table, it's reassuring to see things return to form at the bottom end. Poor old Chris Martin is as far adrift as ever: when no-one around – let's face it, above – him has made it to 50, he can only be expected to score a run every other innings.

Table 2 shows exactly the same kind of analysis but, this time, the threshold is the magical three figures.

Table 2: Test batting records divided into innings in which no other batsmen made 100 and those in which at least one did

<--- no other batsman made 100 ---> <----- other batsmen made 100 ----> Name I NOs R Ave HS 50 100 I NOs R Ave HS 50 100 Diff% 1. J Ryder 15 4 843 76.64 201* 5 2 17 1 551 34.44 112 4 1 222.5% 2. DG Bradman 44 5 2,860 73.33 334 7 11 36 5 4,136 133.42 304 6 18 55.0% 3. VG Kambli 13 1 843 70.25 227 0 4 8 0 241 30.13 82 3 0 233.2% 4. CAG Russell 13 2 708 64.36 140 0 5 5 0 202 40.40 96 2 0 159.3% 5. KS Duleepsinhji 10 2 484 60.50 173 2 1 9 0 511 56.78 117 3 2 106.6% 6. CP Mead 16 2 838 59.86 182* 2 3 10 0 347 34.70 102 1 1 172.5% 7. A Melville 10 2 475 59.38 117 1 3 9 0 419 46.56 189 2 1 127.5% 8. WR Hammond 90 13 4,569 59.34 336* 18 11 50 3 2,680 57.02 227 6 11 104.1% 9. JB Hobbs 68 7 3,518 57.67 187 21 9 34 0 1,892 55.65 211 7 6 103.6% 10. SJ McCabe 34 5 1,661 57.28 232 7 4 28 0 1,087 38.82 149 6 2 147.5% 11. RG Pollock 26 3 1,310 56.96 209 7 5 15 1 946 67.57 274 4 2 84.3% 12. JDB Robertson 15 2 729 56.08 133 6 2 6 0 152 25.33 44 0 0 221.4% 13. H Sutcliffe 51 8 2,400 55.81 161 13 7 33 1 2,155 67.34 194 10 9 82.9% 14. IVA Richards 112 10 5,661 55.50 291 25 17 70 2 2,879 42.34 178 20 7 131.1% 15. GA Headley 34 3 1,714 55.29 270* 4 7 6 1 476 95.20 169* 1 3 58.1% 16. KC Sangakkara 89 8 4,474 55.23 232 15 13 58 2 3,075 54.91 287 17 8 100.6% 17. KC Bland 27 4 1,263 54.91 144* 6 3 12 1 406 36.91 78 3 0 148.8% 18. CL Walcott 46 5 2,216 54.05 220 10 8 28 2 1,582 60.85 152 4 7 88.8% 19. EAB Rowan 38 5 1,760 53.33 236 11 3 12 0 205 17.08 67 1 0 312.2% 20. SR Watson 12 1 584 53.09 120* 4 1 9 0 236 26.22 53 2 0 202.5% 21. DR Jardine 17 3 740 52.86 127 7 1 16 3 556 42.77 98 3 0 123.6% 22. KF Barrington 87 10 4,035 52.40 151* 20 11 44 5 2,771 71.05 256 15 9 73.8% 23. L Hutton 93 14 4,102 51.92 205 21 10 45 1 2,869 65.20 364 12 9 79.6% 24. G Boycott 136 22 5,907 51.82 191 28 18 57 1 2,207 39.41 246* 14 4 131.5% 25. Yousuf Youhana 87 7 4,126 51.58 202 20 13 59 5 3,121 57.80 223 11 11 89.2% 26. RT Ponting 121 19 5,260 51.57 242 20 17 111 7 6,165 59.28 257 29 21 87.0% ... 40. GS Sobers 95 12 4,036 48.63 198 17 11 65 9 3,996 71.36 365* 13 15 68.1% ... 43. BC Lara 177 5 8,349 48.54 375 32 25 53 1 3,563 68.52 400* 16 9 70.8% ... 46. KP Pietersen 61 2 2,830 47.97 158 10 10 39 2 1,969 53.22 226 6 6 90.1% ... 52. JH Kallis 144 21 5,788 47.06 189* 33 13 79 11 4,608 67.76 186 19 19 69.4% ... 59. RS Dravid 148 22 5,873 46.61 270 31 9 87 5 5,360 65.37 233 27 19 71.3% ... 68. DT Lindsay 20 0 912 45.60 182 3 3 11 1 218 21.80 65 2 0 209.2% ... 71. ED Weekes 48 1 2,126 45.23 162 11 6 33 4 2,329 80.31 207 8 9 56.3% ... 84. GC Smith 80 9 3,152 44.39 154* 22 4 57 0 3,287 57.67 277 4 14 77.0% ... 91. V Sehwag 75 4 3,121 43.96 201* 10 8 46 0 3,044 66.17 319 8 9 66.4% 92. SR Tendulkar 166 17 6,544 43.92 248* 29 19 99 11 6,426 73.02 241* 25 24 60.1% 93. G Gambhir 27 3 1,051 43.79 167 5 2 21 0 1,502 71.52 206 5 6 61.2% 94. AJ Strauss 73 5 2,977 43.78 161 9 11 53 0 2,390 45.09 177 9 7 97.1% ... 146. VT Trumper 72 7 2,564 39.45 214* 9 7 17 1 599 37.44 135* 4 1 105.4% 147. PD Collingwood 53 7 1,813 39.41 135 11 3 43 3 1,919 47.98 206 7 6 82.2% ... 188. RA Woolmer 25 2 852 37.04 149 1 3 9 0 207 23.00 82 1 0 161.1% ... 211. AC Gilchrist 51 6 1,605 35.67 144 10 2 84 14 3,870 55.29 204* 15 15 64.5% ... 267. DW Randall 59 5 1,809 33.50 174 8 6 20 0 661 33.05 164 4 1 101.4% ... 336. IR Bell 49 3 1,400 30.43 97 14 0 42 6 1,891 52.53 199 7 9 57.9% ... 456. KR Miller 51 5 1,199 26.07 145* 3 2 36 2 1,759 51.74 147 10 5 50.4% ... 481. LEG Ames 40 5 892 25.49 126 4 1 32 7 1,542 61.68 149 3 7 41.3% ... 1140. JV Saunders 15 5 19 1.90 9 0 0 8 1 20 2.86 11* 0 0 66.5% 1141. M Mbangwa 20 7 24 1.85 8 0 0 5 1 10 2.50 5 0 0 73.8% 1142. CS Martin 58 31 46 1.70 7 0 0 18 9 37 4.11 12* 0 0 41.4% 1143. Mohammad Akram 11 3 11 1.38 5 0 0 4 3 13 13.00 10* 0 0 10.6% qual. 10 innings in which no 100 was scored by other players; full list available here

Although he is pipped to top spot by his first test skipper, Bradman's reputation might be restored somewhat by this analysis. It speaks volumes for his astonishing weight of runscoring that his unsupported average is the second-best in test history and is still only just over half as good as his performance when other batsmen got to three figures! On the opposite side of the coin, it is in keeping with Douglas Jardine's reputation as a batsman that his one test hundred and seven of his ten test fifties came in innings in which none of his team-mates had reached 100.

I love that Jack Hobbs is right near the top of the list (as he was in the 50s table), with a better record when he was going it alone than when his team-mates were joining in the fun. This finding is perfectly reflective of a quotation from Hobbs to which TMSB Exiles contributor rob.cricketpunk drew our attention in a related discussion. Speaking to John Arlott about batting for Surrey, Hobbs said,

If Sandy [Andy Sandham] was going well, we had plenty of batting to come and I would give one of my old bowler mates a chance; but if Sandy and Tom [Shepherd] and Andy [Ducat] got out, then I had to earn my money from Surrey and get some runs.

It also doesn't surprise me to find Viv Richards in the upper reaches, with quite a pronounced discrepancy between his unsupported and supported knocks. The fact that 17 of his 24 tons were achieved as sole centurion is characteristic of a man who loved to raise his game to meet an occasion.

So what about the man who sparked the whole debate off? Is it fair to get on Ian Bell's back for his apparently lopsided record? The defence has to plead guilty to the charge as it is commonly formulated: nobody in the history of test cricket has scored as many as Bell's nine centuries without ever being a lone centurion (Bill Woodfull is second with seven). Still, it's worth highlighting the extent to which, in terms of relative levels of performance between the two scenarios, Bell is far from the worst offender generally. He scores getting on for 60% as many runs in innings where no-one has reached three figures as he does when there is at least one centurion other than him, which puts him in the same ballpark as Weekes, Headley, Laxman, and Tendulkar, and a little way ahead of Miandad, Worrell, Dexter, and Miller. Although Bell has yet to be the only man to reach three-figures in a test innings, he has 14 half-centuries in innings in which no one passed 100 which, from 49 attempts, isn't terrible.

Moreover, when you look back at the innings in which no-one else passed 50 (which you have to think of as the most challenging circumstances of all – those in which Bell is supposed to be at his most inadequate), his record looks pretty okay. For example, we've all seen Bell's supposed mental frailty compared unfavourably to Paul Collingwood's supposed capacity for dogged resistance. Actually, Collingwood's record, in this area, is quite a lot worse. Of Collingwood's 27 test innings of 50 or more, there was one solitary occasion on which no-one else on the team registered at least a half-century (though, it has to be said, that was quite an important one), and his average of 22.82 in such innings is a fair bit worse than Bell's 29.62.

Ultimately, though, I remain to be convinced that any of this matters very much. It seems to me that successful teams need batsmen who can capitalise on good starts every bit as much as they need those whose heroics might rescue a parlous situation. The accepted wisdom is that the players who perform best when circumstances are least favourable are the most valuable; these are the kind of players we tend to call "matchwinners". But you'd never win any matches if you had to rely solely on batsmen who only turn it on when the spotlight is dialled up to sufficient wattage (I'm on record, elsewhere, advancing a similar argument in – slight – criticism of Viv Richards who, certainly over the later two-thirds of his career, was still capable of astonishing performances, but only tended to pull them out of the bag on a whim). After all, someone needs to score runs when they are most obviously there to be scored. So maybe we should stop repeating that stat about Ian Bell and start circulating a new one: England have never lost a test match in which he scored a century.



I feel obliged to offer a little postscript, here. Statistically speaking, I've done something deeply questionable, in these analyses. Assuming that apparent discrepancies between different subsets of batsmen's careers are meaningful on face value alone is pretty dumb. Actually, there is enough variation in all batsmen's records that, if you cut their record up into two random halves, you'd expect a good number of them to end up with two very different looking sets of performance. (David Barry gave a neat demonstration of this on his blog a little while ago.) This means that, even if all batsmen were equally good regardless of how well their team-mates got on in each of their innings, random variation alone would result in some of their records looking very different when you cut them up in the way I have, above. Distinguishing meaningful signal from random noise is at the heart of proper statistical analysis (it's what commonly gets labelled as identifying "statistical significance"), and it's really bad practice to stick up lists of numbers without doing anything of the sort. However, I'm not alone, in this respect: I'm not aware of anyone, ever, in the history of cricket stats taking this basic step. As it happens, I have (what I think are) some really good methods for beginning to make robust comparisons within and between batsmen's careers, but I'm unlikely to introduce them to this blog for a while, yet (partially because it'll take forever to write them up; partially because I'm kinda hoping to get them published in an academic journal, first). I just wanted to register the fact that all the above has a very good chance of being – like the vast majority of things presented as cricket statistics – absolute rubbish.

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