It Figures

As before, an example should help to clarify the approach and, because it's always helpful to use as much data as you can get your hands on, let's start with Muttiah Muralitharan. Murali's Longitudinal Career Graph (LCG) is shown in Figure 1. It shows, in the shaded area, his 20-innings moving average (i.e. his bowling average for every consecutive 20 innings in which he bowled). The moving average is shown relative to the average with which he finished his career: whenever the black area is above the axis, he averaged more over the previous 20 innings than he did over his whole career and, whenever the black area is below the axis, his average for the last 20 innings was worse than he achieved in the long run. The innings-by-innings progress of his career average (what StatsGuru calls the cumulative average) is shown by the red line.

Looking at the red line, we can see that, from the beginning of 1996 until the end of 2008, Murali's career average showed a pretty steady improvement (it fell from 33.89 to a low-point of 21.26). But, if we were to concentrate on that career average alone, we'd probably be tempted to infer that Murali was getting better and better during this period. However, the LCG helps us to understand that wasn't exactly the case: what actually happened was that he got quite a lot better fairly suddenly, then got a bit better again, and then maintained the level of achievement for a number of years while his long-run average slowly caught up (in lengthy careers, long-run averages will only ever catch up slowly, and they'll never catch up completely). At his best during this period, Murali achieved a 20-innings streak of 89 wickets at 15.13.

It should be clear that, the greater the black area on a bowler's LCG, the streakier his performance over his career. In the same way, a single streakiness statistic can be calculated that is directly related to the area of black on each bowler's LCG. [Technically, the measure is the root mean squared deviation of the moving average relative to the long-run career average, which is then scaled by the overall average, to provide CV(RMSD).] Table 1 gives a list of the most and least streaky bowlers in Test history, sorted according to this measure.

Table 1: Streakiest bowlers in Test cricket, according to variation [CV(RMSD)] in 20-innings moving average

	Name	M	I	W	Ave	20-Inns Min	20-Inns Max	20-Inns Rng	CV(RMSD)	p
1.	W Rhodes	57	90	127	26.97	15.58	74.60	59.02	0.498	0.021
2.	TM Alderman	41	73	170	27.15	19.25	58.45	39.20	0.435	0.001
3.	Intikhab Alam	47	78	125	35.95	23.42	81.83	58.41	0.429	0.010
4.	N Boje	43	72	100	42.65	26.00	95.38	69.38	0.398	0.073
5.	AV Bedser	51	92	236	24.90	13.84	43.58	29.73	0.384	0.004
6.	DL Underwood	85	151	297	25.84	14.26	58.12	43.86	0.375	0.017
7.	Mushtaq Ahmed	52	89	185	32.97	22.33	65.60	43.27	0.372	0.006
8.	GAR Lock	49	88	174	25.58	9.40	37.90	28.50	0.368	0.048
9.	GS Sobers	93	159	235	34.04	24.28	75.58	51.30	0.363	0.011
10.	TE Bailey	61	95	132	29.21	15.84	66.14	50.30	0.346	0.206
	...
13.	IT Botham	101	168	383	28.40	15.56	54.21	38.64	0.305	0.031
14.	A Flintoff	77	135	219	33.35	22.31	60.05	37.74	0.296	0.014
	...
16.	SF Barnes	27	50	189	16.43	11.85	24.29	12.45	0.289	0.004
17.	SM Pollock	108	202	421	23.12	14.85	48.50	33.65	0.288	0.011
	...
21.	Imran Khan	86	142	362	22.81	13.15	34.87	21.72	0.277	0.023
	...
30.	JH Kallis	144	238	269	31.99	18.27	59.93	41.66	0.260	0.536
	...
48.	RJ Hadlee	86	150	431	22.30	15.48	37.34	21.86	0.228	0.068
	...
52.	M Muralitharan	130	228	795	22.67	15.13	36.42	21.29	0.219	0.040
53.	Waqar Younis	86	154	373	23.56	15.95	35.97	20.02	0.217	0.111
	...
57.	Z Khan	79	144	273	31.78	22.46	54.80	32.34	0.213	0.183
	...
67.	SK Warne	144	271	702	25.53	17.96	43.17	25.21	0.195	0.215
	...
70.	Kapil Dev	131	227	434	29.65	17.54	42.29	24.75	0.194	0.458
	...
75.	DW Steyn	46	85	238	23.22	15.14	31.55	16.41	0.186	0.187
	...
92.	AA Donald	72	129	330	22.25	17.38	31.65	14.27	0.160	0.361
	...
96.	GD McGrath	123	241	560	21.69	15.20	33.26	18.06	0.156	0.770
	...
106.	GP Swann	36	66	153	28.82	21.40	37.62	16.22	0.146	0.425
107.	MD Marshall	81	151	376	20.95	15.44	32.39	16.96	0.146	0.680
	...
115.	FS Trueman	67	127	307	21.58	16.56	28.33	11.78	0.127	0.787
	...
124.	CEL Ambrose	98	179	405	20.99	15.67	26.81	11.14	0.122	0.945
125.	DK Lillee	70	132	355	23.92	20.00	33.97	13.97	0.121	0.751
	...
127.	MG Johnson	42	80	181	29.71	23.22	37.56	14.33	0.120	0.745
	...
131.	J Srinath	65	121	236	30.49	22.75	40.00	17.25	0.114	0.925
	...
140.	SL Malinga	30	59	101	33.16	28.90	39.80	10.90	0.101	0.817
141.	DE Malcolm	40	72	128	37.09	31.23	45.03	13.81	0.100	0.961
142.	S Ramadhin	43	76	158	28.98	24.61	38.67	14.06	0.095	0.962
143.	DA Allen	39	65	122	30.98	26.30	36.84	10.54	0.094	0.854
144.	GR Dilley	40	65	138	29.76	25.58	36.12	10.54	0.087	0.892
145.	PR Adams	45	76	134	32.87	27.08	38.55	11.48	0.084	0.977
146.	RC Motz	32	55	100	31.48	27.42	37.57	10.15	0.084	0.913
147.	NAT Adcock	26	46	104	21.11	17.86	24.23	6.36	0.083	0.838
148.	AN Connolly	29	55	102	29.23	23.40	33.08	9.68	0.077	0.931
149.	WJ O'Reilly	27	48	144	22.60	19.87	25.88	6.00	0.070	0.889
qual. = 100 wkts, 40 inns, 1.5 inns bowled per match; stats correct at 14-Aug-2011; full list with links to each bowler's LCG available here

Wilfred Rhodes's position at the top of the list reflects the very different ways in which his skills were deployed during his career: in his first Test, he batted at no. 10 and opened the bowling; a decade later, he was routinely opening the batting and his bowling had become occasional. Little wonder, then, that his bowling average fluctuated enormously: he achieved a 20-innings average of 15.58 in 1900–05 whereas, in 1909–13, the same measure sank to 74.60 (note how many did-not-bowleds there are in the latter sample, underlining Rhodes's change of role).

It's little surprise to see Andrew Flintoff high on the list of streaky bowlers. His LCG (Figure 2) gives a clear depiction of the well recognised tripartite nature of his career record. In the worst 20-innings period of his distinctly unimpressive first 50 or so innings, Flintoff managed just 21 wickets at an average of 60.05. Just a couple of years later, he achieved his best 20-inns streak, averaging 22.30 (although note that he only amassed 42 wickets – without a single five-fer – in that period).

Shift that whole profile down by the best part of ten runs, and you have something eerily similar: Imran Khan's career as a Test bowler (Figure 3). Again, you have the (relative) famine followed by the (relative) feast, with an unhappy coda where the body could no longer do justice to the ability. In Imran's case, the highlight was an amazing 79 wickets at 13.15 from these 20 consecutive innings in 1982–83. His worst 20 innings were the last 20 in which he bowled but, as worst runs go, 31 wickets at 34.87 is very far from an embarrassment.

With Flintoff and Imran as our clue, we might notice that there are a fair few allrounders at the top of the streakiness league. Sobers (another whose bowling was pretty ordinary through his first 50 innings), Botham (whose "streakiness" was actually a fairly linear deterioration), Shaun Pollock (pretty constantly great for most of his career, but suffered an extended horrible streak at the end of it), and Jacques Kallis (up and down throughout) are all amongst the 30 most identifiably streaky, as are Trevor Bailey, Ravi Shastri, and Monty Noble. Conversely, it seems like those at the bottom of the list have a tendency to be pretty poor with the willow. In fact, there is a noisy but identifiable statistical correlation between a bowler's streakiness (CV[RMSD]) and his batting average (r²=0.102; p<0.001). The most likely explanation for this finding, it seems to me, is that bowlers who bat are more likely to endure prolonged streaks of poor form with the ball without getting dropped (it's fair to assume that Flintoff would have been given up as a lost cause long before his 50th innings if he had no capacity to contribute with the bat). As a result, bowlers with extended poor streaks – be that true underperformance or just a run of bad statistical luck – are under-represented in this dataset. If everybody was allowed to play 100 test matches regardless of how well they were doing, then I wouldn't expect allrounders' bowling figures to be any different.

When judged according to these methods, the least streaky bowler in Test history is Bill O'Reilly. His LCG (Figure 4) illustrates the serenely excellent progress of his career. In his worst 20 innings, he took 54 at 25.87; in his best 20 innings, he took 54 wickets at 19.87.

According to the maths, the least streaky bowler with at least 100 innings under his belt is Javagal Srinath but, for me, it's Dennis Lillee's numbers that really stand out, with a career record almost as smooth as his bowling action. As his LCG (Fig 5) shows, it was only really his last few Test matches that spoiled what was otherwise an incredibly consistent career. Aside from his last six innings, his 20-innings moving average never left the twenties.

Mitchell Johnson's low position in the streakiness table may be a surprise to some; after all, he doesn't have much of a reputation for steady results. However, it turns out that, over periods of 20 innings, any real or perceived fluctuations in his performance tend to even themselves out, and the range over which his moving average oscillates (23.22 to 37.56) is, in comparative terms, not so great. On average, across this dataset, a bowler's performance in his best and worst 20-innings streaks are 72% and 150% of his career average, respectively. If Johnson were entirely typical, in this respect, his best and worst streaks would be 21.40 and 44.62, which confirms that his performance has been a bit less variable than average. You don't get a very different picture when you use shorter windows, either (I also looked at 10-innings averages and 5-innings averages; see Technical Appendix for a brief description and links to the results). I conclude that Johnson has a bit of an unfair reputation for wildly varying performances, though one thing these stats can't confirm or deny is that he goes through phases of conspicuously looking terrible and brilliant.

Immediately following what may be the most famous 1-wicket match-haul in Test history (at Old Trafford in 1956), Tony Lock achieved something almost as exceptional as his partner's feat: during his next twenty innings, he became the only bowler amongst those analysed here to average less than 10.00 over a period of that length, taking 54 wickets in the process. He even managed to get dropped during this streak although, to be fair to the selectors, the man they preferred – Johnny Wardle – was in the middle of a sub-20 streak of his own. With Laker's 20-innings moving average dropping to 11.86 in the same period, it's fair to assume England's spin-bowling resources of that time are unlikely ever to find a statistical equal.

There are only ten bowlers in the history of Test cricket who never averaged over 30.00 in any 20 consecutive innings. Most of them belong to an era of pervasively lower averages, but there are two modern-day exceptions – Curtly Ambrose, whose highest 20-innings moving average was just 26.81, and Mohammad Asif, who never did worse than the 28.19 he averaged in his last 20 Test innings (it's probably appropriate to speak about Mohammad Asif in the past tense, now, right?).

As with batsmen, there is no association between streakiness (or the lack of it) and success, either in terms of average (r ²=0.007; p=0.298) or win-rate (r ²<0.001; p=0.993). Some bowlers achieved great figures with up-and-down performance; others were closer to their long-run average throughout; there's no evidence that one profile or another leads to more wins or better stats at the end of your career.

What does it all mean?

As ever, though, this story only really gets interesting when we question the patterns underlying the data. Statisticians like to make a distinction between descriptive statistics (those that simply present observed data) and inferential statistics (those that seek to make sense of it). In this case, what we need to do is account for the play of random variation in bowlers' careers. It is inevitable that chance alone will lead to variation in each player's figures, and we need to distinguish this from real swings of performance.

I investigated this in exactly the same way as with batsmen – shuffling each bowler's career into a purely random order 10,000 times, and seeing how often a career as streaky as the real one emerged (the technical term for this technique is bootstrapping). This way, we get to quantify how likely it is that their careers would have happened in a world where form didn't exist (this is the figure marked p in the table – technically, it is a one-tailed empirical p-value).

The results provide a very similar picture to that which I found when analysing form amongst batsmen. The key finding is that there are surprisingly few bowlers whose careers give a convincing picture of variation in form over and above that which would be expected by chance.

One example is Terry Alderman. There are only two possible explanations for his career showing as much variation as it did: (i) for one reason or another, his essential wicket-taking ability varied over the course of his career (i.e. he really did have runs of good and bad performance), or (ii) a statistical event with probability 0.0007 (1-in-1,429) has occurred. In this circumstance, we can probably conclude with some confidence that there's some non-random variation afoot and, indeed, looking at Alderman's LCG (Figure 6), it's hard to imagine that horrible 1984 and that dazzling 1989–1990 could have happened to the same bowler.

However, bowlers whose careers show such an identifiably streaky pattern are the exception rather than the rule. The relatively small number of very low p-values suggests that random variation around a career-long mean is very often a pretty plausible explanation of the peaks and troughs we tend to think of as form. Turning back to Mitchell Johnson, we can see that shuffling his career into a random order produces at least as much up-and-down as we've seen in his actual career about three-quarters of the time. Similarly, the prevailing wisdom is that a career like Steve Harmison's has been massively influenced by swings of form. However, when I took form out of the equation by putting his career in a random order, something that was – on the whole – every bit as streaky emerged nearly a quarter of the time (although less than a twentieth of the virtual careers featured a single streak as hot as Harmison's 50 wickets at 18.64 in 2003–2004). In any other field, a statistician faced with such numbers would be very unlikely to conclude that there was anything other than random variation at play.

However, one interesting finding is that Muttiah Muralitharan – although his streakiness stat (CV[RMSD]) is nothing out of the ordinary – has a pretty low p-value (much lower than those around him on the list). One reason for this is that, because his career is longer than most, it provides more data and, hence, more opportunity to distinguish signal from noise (a statistician would say that, when we look at Murali's career, we get a more powerful analysis, meaning it is less susceptible to Type II error). This raises the possibility that, if we had more data on other bowlers, we'd be able to detect streakiness in their careers more easily (in the same way that it's a lot easier to tell whether you've got an unevenly weighted coin by tossing it 200 times than it is when you toss it only 20).

Conclusions

One thing it's important to emphasise is that, although I've used the word form throughout this analysis, that's really just a shorthand term for variation-of-performance-for-whatever-reason. The methods described here can identify up-and-down results, and can account for the play of chance in contributing to apparent hot and cold streaks. What they can't do is explain the causes of any non-random variation in performance. It may be that a bowler really was worse at taking wickets in a given period, but it's equally likely that he was bowling in unfavourable circumstances beyond his control. Above, we saw that Terry Alderman's Test career appears to have more than a hint of up-and-down about it. However, that monstrous hump in his LCG just happens to coincide with a period during which he spent a disproportionate amount of time bowling at a pretty formidable West Indies side. Maybe he would have done just as badly against other opponents at this time, or maybe he would have achieved a level of performance that was more consistent with the rest of his career; nothing in the numbers alone helps us to guess.

One way or another, though, the findings described in this blog – in conjunction with my earlier analysis of test batting form – lead me to question whether, as cricket fans, we read rather too much into apparent peaks and troughs of performance. I'm quite sure few bowlers would dispute the assertion that their figures are susceptible to dumb luck; they'd certainly acknowledge that, in any individual innings, their best balls may beat the bat while they pick up wickets with deliveries that they wouldn't otherwise have wanted to remember. So it's maybe not so great a leap to conclude that the fact that bowlers end up with figures that can be quite variable across sequences of matches does not necessarily imply that there was fundamental variation in their wicket-taking capacity over those periods. In this way, it's not so surprising to see that, in a substantial majority of cases, you get just as much peak and just as much trough if you rearrange test bowlers' careers in any old order. One thing's for certain: every bowler who gets dropped after a bad trot feels certain he was on the verge of a performance that would have redressed the balance. Maybe more of them are right than we would've guessed.

---

Technical appendix

1. As before, I should start by acknowledging that the approach set out in this blog is heavily influenced by an excellent baseball stats book, Curve Ball by Jim Albert and Jay Bennett.

2. As I did for batsmen, I undertook a series of sensitivity analyses, varying the size of the window over which the moving average is calculated. I looked at longer and shorter windows; here are the results for 5 innings, 10 innings, and 30 innings. Once again, none of these analyses is very different from the 20-innings version. Funnily enough, the six bowlers with the most successful 10-inns streaks are all Englishmen – Lock, Barnes, Laker, Wardle, Statham, and Bedser – five of them achieving the feat in the 1950s! Most of them are also amongst the best 30-inns streaks, where they're joined by the likes of Imran, Hadlee, and Muralitharan. I also saw what difference it makes to use a different type of moving average – the exponentially weighted moving average – in which innings are never completely discarded; they just receive ever-decreasing weight as they recede into the past. The weighting coefficient I used was 0.066967, which dictates that the weight applied halves every ten innings. The results table is here. By and large, there is very little difference between these results and those calculated according to the simple moving average. I notice that a couple of bowlers whose career had a distinct upward or downward trend rise up the list (Richard Hadlee is a good example of someone who got better and better). On the whole, though, I can't tell much difference between them.

3. In the comments of my column about batting streakiness (which used an identical statistical approach to this analysis), there was some interesting discussion about p-values and multiple testing. This is an important issue in statistical analyses which look at the same thing repeatedly – in this case, the streakiness of 149 different bowlers. For example, when we say Terry Alderman appears to be a significantly streaky bowler because he has a very low p-value of 0.0007, we mean that there are only two possible explanations for his career showing as much variation as it did: (i) for one reason or another, his essential wicket-taking capacity varied over the course of his career (i.e. he really did have runs of good and bad performance), or (ii) a statistical event with probability 0.0007 (1-in-1,429) has occurred. At first glance, 1-in-1,429 seems very long odds, so it's tempting to conclude that we have a robust finding of streakiness. After all, you'd be amazed if you rolled four dice and got four sixes, and that's a slightly more likely event. However, we need to remember that there are 149 separate bowlers being analysed, here; if we repeated our dice-rolling experiment that many times, would we be very surprised to see 6-6-6-6 come up at least once along the way? So we need to be careful before assuming that something unlikely couldn't have happened when it had many opportunities to do so. There are several methods for adjusting p-values for multiple comparisons, but I chose not to extend and complicate my analysis by applying them (not least because I'm not much of a fan of obsessive p-value-spotting, in any case).

4. So, if we have to be a bit hesitant about identifying individual bowlers as especially streaky, can we tell whether there's any streakiness going on? One way to get a handle on that question (thanks to Russ and Dave, whose comments on my last column led me in this direction) is to calculate a global p-value – that is, an estimate of the weight of evidence that there's at least some streakiness somewhere amongst all the bowlers analysed. This can be done by counting the number of individual p-values below a certain level, and estimating the probability that that many bowlers (or more) would have streaky-looking records if there were nothing but random variation at play. In this instance, we can say that, with a global dataset of 149 bowlers, we would expect roughly 7 of them to have a p-value of 0.05 or less, just by chance, if there were no such thing as streakiness amongst bowlers (149 × 0.05 = 7.45). In fact, there are 21 such players in the dataset. Comparing this observed frequency to a Poisson distribution, we can calculate that the probability of getting 21 streaky players when you expect 7.45 is 0.00004. In other words, the amount of streakiness observed across all bowlers is extremely unlikely to have occurred by chance alone (in technical terms, we are likely to reject the global null hypothesis that there's no such thing as a streaky bowler).

Most successful teams in Test history were built on a solid foundation at the top of the innings. England's great pre-war pairing of Jack Hobbs and Herbert Sutcliffe remains the finest in terms of batting average and consistency (min 3000 runs aggregate). They shared 15 century stands in just 37 Tests and averaged over 80 both home and away. In wins, they were exceptional, with nine century stands at an average over 95. Furthermore, their performance across the four match innings has also been remarkably consistent, with their lowest average of 55.66 coming in the fourth innings. The Australian pairing of Bill Lawry and Bob Simpson was a highly successful combination in the 1960s aggregating over 3500 runs at an average of nearly 61.

India struggled without a good opening pair after the retirement of Sunil Gavaskar and Chetan Chauhan in the 1980s. The pair was very consistent both home and away, and did much better in the team second innings as compared to the first innings. Despite sharing ten century partnerships with Gavaskar, Chauhan himself never made a single hundred in Tests. The recent pairing of Virender Sehwag and Gautam Gambhir has been successful, but is yet to score substantially in away conditions. The pair has, however, been a huge factor in India's Test success in the last three years. Australia's dominance of world cricket from the mid 1990s until recently has largely been due to the presence of world-class opening pairs. After the end of the successful Michael Slater-Mark Taylor partnership in the 1990s, Hayden and Justin Langer continued to dominate bowling attacks. They shared 14 century stands including a record six 200-plus partnerships. However, they had very little to do in the third and fourth innings of matches given the strength of their bowling attack, and shared only two century stands in the team second innings.

The West Indian hegemony in the late 1970s and 1980s was largely due to an outstanding bowling attack, but their powerful batting line-up also had a lot to do with the unprecedented dominance. Greenidge and Haynes, who shared a record 16 century stands for the opening wicket were brilliant at home, but slightly less successful in away games. They averaged under 35 in Australia and England which can be attributed to a combination of the high quality opening bowling and sporting pitches in those years. Surprisingly, in sharp contrast to many other pairs, they did much better as the match progressed, and shared 15 of their 16 century partnerships in the second, third and fourth innings.

Record of top opening pairs (minimum 3000 partnership runs)- (Runs, average, 100/50)

Pair (Team)	Innings	Overall	Home	Away	Wins	1st innings	2nd innings	3rd innings	4th innings
Jack Hobbs, Herbert Sutcliffe (England)	38	3249, 87.81, 15/10	2047, 93.04, 9/8	1202, 80.13, 6/2	1720, 95.55, 9/4	806, 89.55, 3/5	1512, 108.00, 7/3	597, 74.62, 3/1	334, 55.66, 2/1
Bill Lawry, Bob Simpson (Australia)	62	3596, 60.94, 9/18	1604, 59.40, 4/8	1992, 62.25, 5/10	1045, 69.66, 3/5	1283, 71.27, 2/6	873, 58.20, 3/2	1099, 64.64, 4/7	341, 37.88, 0/3
Gautam Gambhir, Virender Sehwag (India)	63	3551, 59.18, 10/19	2243, 62.30, 7/11	1308, 54.50, 3/8	1841, 68.18. 6/9	908, 56.75, 2/6	1417, 70.85, 5/6	790, 46.47, 2/4	436, 62.28, 1/3
Chetan Chauhan, Sunil Gavaskar (India)	59	3010, 53.75, 10/10	1402, 53.92, 5/5	1608, 53.60, 5/5	788, 56.28, 3/2	929, 48.89, 4/3	548, 34.25, 0/4	1031, 73.64, 5/1	502, 71.71, 1/2
Matthew Hayden, Justin Langer (Australia)	113	5655, 51.88, 14/24	3308, 56.06, 9/12	2347, 46.94, 5/12	3567, 46.32, 7/18	2554, 75.11, 8/8	1360, 46.89, 4/4	982, 39.28, 1/6	759, 36.14, 1/6
Michael Slater, Mark Taylor (Australia)	78	3887, 51.14, 10/16	2193, 57.71, 7/9	1694, 44.57, 3/7	2250, 62.50, 6/11	1437, 55.26, 4/6	928, 51.55, 2/5	902, 47.47, 3/4	620, 47.69, 1/1
Gordon Greenidge, Desmond Haynes (WI)	148	6482, 47.31, 16/26	3534, 65.44, 10/14	2948, 35.51, 6/12	3500, 49.29, 9/15	1156, 30.42, 1/6	2693, 54.95, 7/10	1242, 42.82, 4/3	1391, 66.23, 4/7

As the bowling quality declined in the early 2000s, the Australian batting feasted on the weak new-ball attacks around the world. Not even South Africa were able to pose much of a threat when they travelled to Australia. Langer and Ponting averaged nearly 80 for the second wicket, and an incredible 116.72 in away matches. Hayden and Ponting, the most prolific batting pair in wins, were far more dominant in home games (average 83.32) when compared to away matches (average 59.40). They were brilliant in the fourth innings, with four century stands at an average of 81.08. On comparing the stats of the two Australian pairs with those of Haynes-Richie Richardson and David Boon-Taylor, it becomes very clear that the fast bowling faced in the 1980s and 1990s was of a much higher standard than that in the early 2000s.

Record of batting pairs for the second wicket (min 2500 runs)- (Runs, average, 100/50)

Pair (team)	Innings	Overall	Home	Away	Wins	1st innings	2nd innings	3rd innings	4th innings
Justin Langer, Ricky Ponting (Australia)	40	2790, 79.71, 12/12	1506, 62.75, 7/7	1284, 116.72, 5/5	2098, 95.36, 10/7	1236, 77.25, 6/5	729, 60.75, 2/4	430, 107.50, 2/1	395, 131.66, 2/2
Matthew Hayden, Ricky Ponting (Australia)	71	4734, 71.71, 16/22	2833, 83.32, 10/12	1901, 59.40, 6/10	3917, 83.34, 14/16	1117, 62.05, 3/5	1268, 70.44, 2/10	1376, 76.44, 7/3	973, 81.08, 4/4
Desmond Haynes, Richie Richardson (WI)	63	3187, 53.11, 10/12	1987, 64.09, 7/6	1200, 41.37, 3/6	1935, 71.66, 8/6	870, 48.33, 2/4	1448, 62.95, 4/5	464, 38.66, 2/2	405, 57.85, 2/1
David Boon, Mark Taylor (Australia)	63	2712, 45.20, 7/13	1356, 43.74, 3/6	1356, 46.75, 4/7	1721, 50.61, 5/9	843, 38.31, 1/7	659, 38.76, 2/1	787, 60.53, 2/4	423, 52.87, 2/0

While the Dravid-Tendulkar partnership is the most prolific for the third wicket, it is the Pakistan pairing of Mohammad Yousuf and Younis Khan that takes the honours for the highest average. In 20 innings, they aggregated 2020 runs at an average over 106 with six century stands. However, only 248 of those runs were scored in wins, which is highly indicative of the inconsistency of the rest of Pakistan's batting line-up and the placid nature of the pitches in the subcontinent. Hashim Amla and Jacques Kallis have been instrumental in South Africa's recent rise in the Test rankings, and have an excellent conversion rate from fifties to hundreds.

Mahela Jayawardene and Kumar Sangakkara, who have formed the core of the Sri Lankan middle order in the last few years average over 85 in home Tests but only 50 in away matches. Their numbers are exaggerated by their performances against Bangladesh and Zimbabwe, against whom they average over 81 in ten innings. In contrast, they have played Australia in just three innings and average close to 27. In a West Indian team that lost far more matches than it won, Brian Lara and Ramnaresh Sarwan were superb. They averaged over 60 and boasted an excellent conversion rate with ten century stands and four fifty partnerships. Tendulkar and Dravid share the most century stands for any batting pair, and have been a symbol of consistency for more than a decade. Their only blip, however, is an below-par performance in the fourth innings, where they average under 39.

Record of batting pairs for the third wicket (min 2000 runs)- (Runs, average, 100/50)

Pair (team)	Innings	Overall	Home	Away	Wins	1st innings	2nd innings	3rd innings	4th innings
Mohammad Yousuf, Younis Khan (Pakistan)	20	2020, 106.31, 6/6	1046, 130.75, 4/2	974, 88.54, 2/4	248, 62.00, 1/1	634, 126.80, 2/2	704, 140.80, 2/2	533, 106.60, 2/1	149, 37.25, 0/1
Hashim Amla, Jacques Kallis (SA)	38	2558, 69.13, 8/5	1391, 73.21, 4/4	1167, 64.84, 4/1	1623, 85.42, 5/2	767, 85.22, 3/1	887, 59.13, 3/2	725, 145.00, 2/1	179, 22.37, 0/1
Mahela Jayawardene, Kumar Sangakkara (SL)	66	4485, 69.00, 12/18	2918, 85.82, 8/8	1567, 50.54, 4/10	2721, 100.77, 8/7	1116, 46.50, 2/6	2086, 104.30, 5/7	1179, 69.35, 5/4	104, 26.00, 0/1
Alastair Cook, Kevin Pietersen (England)	36	2106, 60.17, 8/10	1004, 50.20, 3/6	1102, 73.46, 5/4	998, 66.53, 4/5	843, 38.31, 1/7	632, 63.20, 2/5	831, 118.71, 5/2	28, 28.00, 0/0
Brian Lara, Ramnaresh Sarwan (WI)	38	2286, 60.15, 10/4	1092, 54.60, 5/2	1194, 66.33, 5/2	517, 86.16, 3/0	713, 64.81, 3/1	632, 63.20, 2/5	297, 29.70, 1/0	489, 81.50, 2/2
Rahul Dravid, Sachin Tendulkar (India)	109	5258, 50.55, 17/18	2478, 45.88, 7/7	2780, 55.60, 10/11	2436, 62.46, 9/10	1930, 50.78, 6/8	1481, 47.77, 6/2	1342, 61.00, 5/4	505, 38.84, 0/4

Jayawardene and Thilan Samaraweera, who average over 74 for the fourth wicket, have featured in just nine partnerships outside the subcontinent. Eight of their nine century stands have come in the subcontinent. Inzamam-ul-Haq and Yousuf have featured in 50 partnerships, and have an average of nearly 91 in wins. Mark Waugh and Steve Waugh, who put on 231 in Jamaica in 1995 to help Australia win their first series in the West Indies in 22 years, average just over 50 overall, but slightly over 66 in victories.

Steve Waugh, who has forged successful stands with Allan Border and Ponting for the fifth wicket, dominates the middle-order partnership stats. VVS Laxman and Rahul Dravid, who put on 376 runs against Australia in the unforgettable Kolkata Test in 2001, have an average of 67 with five century stands. Adam Gilchrist and Damien Martyn, who average over 75 for the sixth wicket, have been ordinary in home Tests. However, they average nearly 91 in away matches while scoring nearly 72% of their runs in wins. Ian Healy and Steve Waugh have aggregated the most runs for the sixth wicket, and have also featured in the most century stands (6).

Top batting pairs for 4th, 5th and 6th wickets

Pair (team)	Wicket	Innings	Overall	Home	Away	Wins
Mahela Jayawardene, Thilan Samaraweera (SL)	4	33	2317, 74.74, 9/5	1208, 75.50, 5/3	1109, 73.93, 4/2	1003, 83.58, 5/2
Sourav Ganguly, Sachin Tendulkar (India)	4	44	2695, 64.16, 7/11	1220, 81.33, 3/4	1475, 54.62, 4/7	950, 86.36, 3/4
Inzamam-ul-Haq, Mohammad Yousuf (Pakistan)	4	50	2677, 58.19, 9/11	1390, 60.43, 4/6	1287, 55.95, 5/5	1180, 90.76, 4/6
Mark Waugh, Steve Waugh (Australia)	4	53	2515, 50.30, 7/12	1203, 52.30, 3/6	1312, 48.59, 4/6	1855, 66.25, 6/7
Ricky Ponting, Steve Waugh (Australia)	5	23	1649, 74.95, 6/5	919, 83.54, 4/2	730, 66.36, 2/3	866, 66.61, 3/3
Rahul Dravid, VVS Laxman (India)	5	23	1410, 67.14, 5/3	608, 67.55, 2/0	802, 66.83, 3/3	948, 105.33, 3/2
Allan Border, Steve Waugh (Australia)	5	23	1384, 65.90, 3/5	686, 57.16, 2/2	698, 77.55, 1/3	1084, 83.38, 3/3
Adam Gilchrist, Damien Martyn (Australia)	6	20	1351, 75.05, 4/3	171, 34.20, 0/1	1180, 90.76, 4/2	969, 74.53, 3/3
Tony Greig, Alan Knott (England)	6	30	1277, 42.56, 4/6	590, 49.16, 1/5	687, 38.16, 3/1	90, 15.00, 0/1
Ian Healy, Steve Waugh (Australia)	6	53	2170, 42.54, 6/6	1020, 46.36, 3/3	1150, 39.65, 3/3	1228, 51.16, 4/3

The table below features the best batting pairs in wins. Australia's dominance in recent years means that the presence of four Australian pairs in the top seven is not entirely surprising. The Hayden-Ponting combination has scored 3948 runs in wins (82.9%) and is followed by Hayden-Langer (62.6% in wins). Greenidge and Haynes scored 3500 runs in wins which is nearly 15% of the team runs in those matches. In terms of percentage of team runs in wins, rhe Hayden-Langer pairing comes next, with 11.94%.

Best pairs in wins (min 2500 runs in wins)

Pair (team)	Overall runs	Runs in Wins	% runs in wins	% team runs in wins
Matthew Hayden, Ricky Ponting (Aus)	4765	3948	82.9	10.38
Matthew Hayden, Justin Langer (Aus)	6081	3808	62.6	11.94
Gordon Greenidge, Desmond Haynes (WI)	6482	3500	54.0	14.48
Rahul Dravid, Sachin Tendulkar (India)	6352	3067	48.3	10.94
Mahela Jayawardene, Kumar Sangakkara (SL)	4988	2808	56.3	11.62
Justin Langer, Ricky Ponting (Aus)	2671	2671	77.4	7.71
Mark Waugh, Steve Waugh (Aus)	2540	2540	73.9	7.40

Visiting opening pairs have generally struggled in Australia and England when compared to the home batsmen. Home openers average nearly 41 in Australia and England whereas overseas pairs average close to 33. However, visiting opening pairs have done better than home batsmen in India, New Zealand and Sri Lanka. For the second wicket, overseas pairs have not been able to match the home pairs in all countries except South Africa and New Zealand. South Africa, however, have been a very competitive side at home after their readmission to international cricket in 1991. Their average for wickets 1-6 is comfortably higher than those of visiting teams in the period from 1991-2011.

Among visiting batting pairs who have played a minimum of ten innings and scored atleast 500 runs in a particular country, the Waugh brothers have been the best. They average nearly 88 in England between 1993 and 2001 with four century stands. Hobbs and Sutcliffe are by far the best visiting pair in Australia, with 1292 runs at an average of 81. Greenidge and Haynes have scored over 900 runs in Australia but at a modest average of 34. Mike Atheron and Alec Stewart were impressive in the West Indies, aggregating 873 runs at 43.65. Geoff Boycott and Graham Gooch were the best overseas pair in India, with 520 runs at an average of 65. During the 1980s, at the peak of West Indian dominance, their top four pairs averaged 61, 57, 50 and 47 in Tests in West Indies while overseas pairs averaged 37, 35, 30 and 29.

Performances by wicket in each country (excluding Bangladesh and Zim matches) - Home avg, away avg

Wicket	Australia	England	India	New Zealand	Pakistan	South Africa	Sri Lanka	West Indies
1	40.42, 33.94	41.77, 32.98	41.43, 41.61	32.22, 36.60	42.03, 35.12	36.95, 37.03	34.80, 39.10	43.62, 41.20
2	45.58, 36.89	43.05, 38.53	42.23, 39.41	34.21, 36.44	40.04, 35.95	33.38, 35.02	40.65, 36.03	44.78, 39.83
3	43.60, 38.63	43.32, 39.15	47.66, 42.34	34.17, 45.76	52.74, 42.10	40.96, 38.20	53.32, 42.16	46.35, 42.88
4	47.74, 36.85	43.13, 36.82	42.85, 38.09	35.05, 43.33	42.79, 38.14	38.76, 38.15	48.23, 39.92	51.47, 41.33
5	41.56, 33.10	35.51, 34.24	39.77, 38.31	30.49, 44.86	39.86, 39.09	31.44, 31.34	47.96, 34.20	41.85, 35.82
6	36.69, 28.79	34.33, 31.00	37.74, 34.93	29.38, 37.39	42.23, 31.30	29.72, 30.44	35.63, 39.04	35.78, 33.58

Despite the win over Australia in their first match and the early troubles they caused to India, Zimbabwe were comfortable to beat in the 1983 and 1987 tournaments. They were far more competitive from the 1992 edition onwards. Bangladesh and Kenya have caused ripples, but are not a consistent force in global tournaments. When a minimum of 750 runs against top teams is considered, only Viv Richards makes the cut. His outstanding World Cup career can be appreciated even more because he averages over 66 against top teams during his period. Tendulkar, on the other hand, averages just over 45 against top teams, which is far lower than his overall average of nearly 58. Three of his four hundreds have come against Kenya and Namibia. While Tendulkar has made nearly a third of his World Cup runs against the weaker teams, Sourav Ganguly has scored over 50% of his runs against the minnows. Except in the cases of Ricky Ponting and Lara, the averages of most batsmen have been considerably boosted due to their 'brilliant' batting against the minnows.

The first table lists the number of batsmen in each team possessing an average greater than 40. I have considered a minimum qualification of 3000 runs. England have played the most Tests and also have the most batsmen averaging over 40 followed closely by Australia. West Indies have fallen been ordinary over the last decade, but had dominated world cricket earlier for almost three decades. The fact that they have 19 batsmen averaging over 40 clearly indicates the quality of batting they possessed in those years. India's batting has been at its best since the mid 1990s with five batsmen in the period averaging greater than 40. South Africa also have an impressive number of batsmen averaging over 40 since their return to international cricket. Andy Flower has an excellent Test record and is the only batsman from Zimbabwe to make the list.