Alpha average

Cricket has had a curious relationship with numbers. The sport compiles the achievements of its players in rich and detailed statistics. It celebrates a batting average in the 50s and a bowling average in the 20s as some kind of an irrefutable stamp of greatness. At other times, cricket and its patrons can be notorious in completely ignoring it in favour of subjective narratives too. Looking at the numbers alone, to argue for Gavaskar over Viswanath is a no brainer. But I strongly advise anyone to stay away from it with Indian cricket fans of that generation.

To be fair, it's not necessarily contradictory. In fact, for a sport which has undergone tremendous amount of change over the years, some of its statistical measures have survived rather well. One such measure is the batting average of 50: it is one of cricket's great constants. Of course, it's not always unimpeachable. There are the 50ers who aren't quite hall of famers, and there are hall of famers without achieving the 50 benchmark. But its value as a currency of greatness has largely stood the test of time almost throughout Test cricket's life term. Even with noticeable exceptions, that's quite an incredible feat.

While acknowledging the idea of putting the 50 benchmark on a pedestal, cricket fans tend to get into the nuances. How does the 50 spread out? Is it too skewed in favour of performances at home? How is the record against the top ranked teams of that era? Didn't he play in an era of mediocre bowlers and flat pitches? and so on. Some of the questions are entirely subjective, others may not be. For instance, let me take up the point about playing in an era of mediocre bowlers and flat pitches. Is there a way to make it more objective for comparisons? I make an attempt.

A batsman can only play in an era that he belongs to. If a particular era is more favourable to score runs than others, it should have been the case for all players of that era and vice versa. So, instead of looking at the absolute averages, we can perhaps look at the incremental average of a batsman over the rest of his contemporaries. Now, how do we define contemporaries? Gooch was Tendulkar's contemporary and so is Murali Vijay.

I am going to take the first day and last day of test cricket of a batsman and calculate the aggregate average of all batsmen in that time period. For instance, for Kallis, the time period is from December 14, 1995 to December 30, 2013. The average of a batsman (runs scored by all batsmen/number of dismissals) in the period is 31.42, and the career average of Kallis was 55.37. On an average he scored 23.94 runs more per innings than the aggregate average. Let's call this incremental average the alpha average. Now, batsmen can be compared across eras on the basis of the alpha average.

I get it, the incremental percentage of the runs scored over the aggregate average is a marginally more sound indicator, but I like the idea of an absolute number of alpha average because of my bias for the portability of a standalone metric but have given both below.

For the purpose of this exercise, I have taken all batsmen who average 50 and more and have played a minimum of 20 tests. Cut off date is Sep 18, 2014.

Player	Span	Mat	Ave	Average rank
DG Bradman (Aus)	1928-1948	52	99.94	1
RG Pollock (SA)	1963-1970	23	60.97	2
GA Headley (WI)	1930-1954	22	60.83	3
H Sutcliffe (Eng)	1924-1935	54	60.73	4
E Paynter (Eng)	1931-1939	20	59.23	5
KC Sangakkara (SL)	2000-2014	128	58.76	6
KF Barrington (Eng)	1955-1968	82	58.67	7
ED Weekes (WI)	1948-1958	48	58.61	8
WR Hammond (Eng)	1927-1947	85	58.45	9
GS Sobers (WI)	1954-1974	93	57.78	10
JB Hobbs (Eng)	1908-1930	61	56.94	11
CL Walcott (WI)	1948-1960	44	56.68	12
L Hutton (Eng)	1937-1955	79	56.67	13
JH Kallis (ICC/SA)	1995-2013	166	55.37	14
GS Chappell (Aus)	1970-1984	87	53.86	15
AD Nourse (SA)	1935-1951	34	53.81	16
SR Tendulkar (India)	1989-2013	200	53.78	17
S Chanderpaul (WI)	1994-2014	158	53.1	18
BC Lara (ICC/WI)	1990-2006	131	52.88	19
AD Mathews (SL)	2009-2014	44	52.65	20
Javed Miandad (Pak)	1976-1993	124	52.57	21
R Dravid (ICC/India)	1996-2012	164	52.31	22
Mohammad Yousuf (Pak)	1998-2010	90	52.29	23
RT Ponting (Aus)	1995-2012	168	51.85	24
J Ryder (Aus)	1920-1929	20	51.62	25
A Flower (Zim)	1992-2002	63	51.54	26
MEK Hussey (Aus)	2005-2013	79	51.52	27
MJ Clarke (Aus)	2004-2014	105	51.5	28
Younis Khan (Pak)	2000-2014	91	51.41	29
HM Amla (SA)	2004-2014	79	51.32	30
SM Gavaskar (India)	1971-1987	125	51.12	31
SR Waugh (Aus)	1985-2004	168	51.06	32
AB de Villiers (SA)	2004-2014	95	51.02	33
JE Root (Eng)	2012-2014	22	50.94	34
ML Hayden (Aus)	1994-2009	103	50.73	35
AR Border (Aus)	1978-1994	156	50.56	36
IVA Richards (WI)	1974-1991	121	50.23	37
DCS Compton (Eng)	1937-1957	78	50.06	38

.

Player	Average	Average rank	Aggregate Average	Alpha average	Alpha Avg Rank	Avg rank - alpha avg rank
DG Bradman (Aus)	99.94	1	31.85	68.09	1	0
RG Pollock (SA)	60.97	2	30.73	30.24	2	0
H Sutcliffe (Eng)	60.73	4	30.87	29.86	3	1
GA Headley (WI)	60.83	3	31.05	29.78	4	-1
ED Weekes (WI)	58.61	8	29.19	29.42	5	3
KF Barrington (Eng)	58.67	7	29.87	28.80	6	1
E Paynter (Eng)	59.23	5	30.57	28.66	7	-2
CL Walcott (WI)	56.68	12	28.7	27.98	8	4
GS Sobers (WI)	57.78	10	29.97	27.81	9	1
WR Hammond (Eng)	58.45	9	31.21	27.24	10	-1
JB Hobbs (Eng)	56.94	11	29.82	27.12	11	0
KC Sangakkara (SL)	58.76	6	32.33	26.43	12	-6
L Hutton (Eng)	56.67	13	30.58	26.09	13	0
JH Kallis (ICC/SA)	55.37	14	31.43	23.94	14	0
GS Chappell (Aus)	53.86	15	30.42	23.44	15	0
SR Tendulkar (India)	53.78	17	31.17	22.61	16	1
Javed Miandad (Pak)	52.57	21	30.09	22.48	17	4
BC Lara (ICC/WI)	52.88	19	30.57	22.31	18	1
A Flower (Zim)	51.54	26	29.67	21.87	19	7
S Chanderpaul (WI)	53.1	18	31.35	21.75	20	-2
AD Nourse (SA)	53.81	16	32.49	21.32	21	-5
SR Waugh (Aus)	51.06	32	30.16	20.90	22	10
R Dravid (ICC/India)	52.31	22	31.42	20.89	23	-1
SM Gavaskar (India)	51.12	31	30.43	20.69	24	7
Mohammad Yousuf (Pak)	52.29	23	31.62	20.67	25	-2
RT Ponting (Aus)	51.85	24	31.49	20.36	26	-2
AR Border (Aus)	50.56	36	30.22	20.34	27	9
DCS Compton (Eng)	50.06	38	29.77	20.29	28	10
AD Mathews (SL)	52.65	20	32.36	20.29	29	-9
IVA Richards (WI)	50.23	37	30.2	20.03	30	7
ML Hayden (Aus)	50.73	35	30.82	19.91	31	4
J Ryder (Aus)	51.62	25	31.73	19.89	32	-7
Younis Khan (Pak)	51.41	29	32.11	19.30	33	-4
JE Root (Eng)	50.94	34	31.68	19.26	34	0
MJ Clarke (Aus)	51.5	28	32.43	19.07	35	-7
HM Amla (SA)	51.32	30	32.51	18.81	36	-6
MEK Hussey (Aus)	51.52	27	32.86	18.66	37	-10
AB de Villiers (SA)	51.02	33	32.54	18.48	38	-5

Out of the 38 players, 8 players jump down by 5 ranking slots or more when the  parameter is changed from average to alpha average: Hussey(-10), Mathews(-9), Ryder(-7), Clarke(-7), Sangakkara(-6), Amla(-6), Nourse (-5) and De Villiers (-5). Except Nourse and Ryder, the other 6 players belong to the last decade and half. This lends credibility to the notion that run scoring has become easier in recent times partly because of dearth of quality bowlers, flatter tracks and perhaps even better bats.

On other hand, 6 players jump up the ranking by 5 ranking slots or more when you change the parameter: Hayden, Flower, Gavaskar, Richards, Border, Waugh and Compton. Curiously, all these players average over 50, none average more than 51.54.

Ranking based on alpha percentage:

Player	Average	Average rank	Aggregate Average	Alpha average	Alpha percentage	Alpha % Rank	Avg rank - alpha % rank
DG Bradman (Aus)	99.94	1	31.85	68.09	214%	1	0
ED Weekes (WI)	58.61	8	29.19	29.42	101%	2	6
RG Pollock (SA)	60.97	2	30.73	30.24	98%	3	-1
CL Walcott (WI)	56.68	12	28.7	27.98	97%	4	8
H Sutcliffe (Eng)	60.73	4	30.87	29.86	97%	5	-1
KF Barrington (Eng)	58.67	7	29.87	28.80	96%	6	1
GA Headley (WI)	60.83	3	31.05	29.78	96%	7	-4
E Paynter (Eng)	59.23	5	30.57	28.66	94%	8	-3
GS Sobers (WI)	57.78	10	29.97	27.81	93%	9	1
JB Hobbs (Eng)	56.94	11	29.82	27.12	91%	10	1
WR Hammond (Eng)	58.45	9	31.21	27.24	87%	11	-2
L Hutton (Eng)	56.67	13	30.58	26.09	85%	12	1
KC Sangakkara (SL)	58.76	6	32.33	26.43	82%	13	-7
GS Chappell (Aus)	53.86	15	30.42	23.44	77%	14	1
JH Kallis (ICC/SA)	55.37	14	31.43	23.94	76%	15	-1
Javed Miandad (Pak)	52.57	21	30.09	22.48	75%	16	5
A Flower (Zim)	51.54	26	29.67	21.87	74%	17	9
BC Lara (ICC/WI)	52.88	19	30.57	22.31	73%	18	1
SR Tendulkar (India)	53.78	17	31.17	22.61	73%	19	-2
S Chanderpaul (WI)	53.1	18	31.35	21.75	69%	20	-2
SR Waugh (Aus)	51.06	32	30.16	20.90	69%	21	11
DCS Compton (Eng)	50.06	38	29.77	20.29	68%	22	16
SM Gavaskar (India)	51.12	31	30.43	20.69	68%	23	8
AR Border (Aus)	50.56	36	30.22	20.34	67%	24	12
R Dravid (ICC/India)	52.31	22	31.42	20.89	66%	25	-3
IVA Richards (WI)	50.23	37	30.2	20.03	66%	26	11
AD Nourse (SA)	53.81	16	32.49	21.32	66%	27	-11
Mohammad Yousuf (Pak)	52.29	23	31.62	20.67	65%	28	-5
RT Ponting (Aus)	51.85	24	31.49	20.36	65%	29	-5
ML Hayden (Aus)	50.73	35	30.82	19.91	65%	30	5
AD Mathews (SL)	52.65	20	32.36	20.29	63%	31	-11
J Ryder (Aus)	51.62	25	31.73	19.89	63%	32	-7
JE Root (Eng)	50.94	34	31.68	19.26	61%	33	1
Younis Khan (Pak)	51.41	29	32.11	19.30	60%	34	-5
MJ Clarke (Aus)	51.5	28	32.43	19.07	59%	35	-7
HM Amla (SA)	51.32	30	32.51	18.81	58%	36	-6
AB de Villiers (SA)	51.02	33	32.54	18.48	57%	37	-4
MEK Hussey (Aus)	51.52	27	32.86	18.66	57%	38	-11

While the change in ranks gives a sense of who has been relatively better off or worse off in playing in the era that they did, just sorting the alpha average from high to low presents an interesting picture too. Down the bottom, we see the players of the last 15 years crowd out others - Sangakkara is the stand out exception. But at the same time, players whose careers stretched from the 1990s till the 2000s and even the 2010s, like Tendulkar, Kallis, Dravid, Lara, Ponting, and Chanderpaul are still somewhere in the middle. This could mean two things: 1) Run scoring in the 90s was difficult and these guys were a class above the rest or 2) They made up for their relative drought of the 90s by feasting in the 2000s and boosting their overall alpha average. Let's see:

	Individual Average			Aggregate Average			Alpha Average			Matches
	1990s	2000s	2010s	1990s	2000s	2010s	1990s	2000s	2010s	1990s	2000s	2010s
Tendulkar	56.70	54.35	50.01	29.63	32.02	32.03	27.07	22.33	17.98	73	89	38
Kallis	41.08	58.70	53.68	29.13	32.02	32.04	11.95	26.68	21.64	32	101	33
Dravid	49.96	54.85	46.18	28.99	32.02	32.51	20.97	22.83	13.67	34	103	27
Lara	51.60	54.06	N.A	29.41	31.66	N.A	22.19	22.40	N.A	65	66	0
Ponting	44.51	58.38	37.30	29.19	32.02	32.57	15.32	26.36	4.73	33	107	28
Chanderpaul	40.61	52.31	71.78	29.23	32.02	32.22	11.38	20.29	39.56	37	86	35

 Note: 1990s includes from the date of debut (In Tendulkar's case from Nov 15, 1989) to 31 Dec 1999, 2000s includes the whole decade or from 01 Jan 2000 to last day of test played. 2010s includes from 01 Jan 2010 to day of last test played.

Tendulkar's alpha average was way higher in the 1990s than in the 2000s. It's both a testimony to the fact that he was a notch above the rest in the 90s when run scoring was harder, and also a reflection of his somewhat relatively more mortal self in the 2000s that he doesn't quite tower above the rest.

In the case of Kallis, Ponting and Chanderpaul, the lower alpha averages is more an indication of their early phase of batting career and trying to establish themselves rather than their struggle in a harder decade for batting. But they were clearly helped by the fact that their batting peak reached in a relatively easier time for batting. Chanderpaul seems to be peaking where most careers will be on the wane.

For a player establishing himself in the 1990s, Dravid was considerably better than Kallis, Ponting and Chanderpaul. But he didn't capitalize in the next decade as much as Kallis and Ponting did, though his alpha average in the 2000s is very healthy too.

The decade of play doesn't make a difference to Lara as he was equally consistent in both, though he didn't particularly tower over the rest in either decades.

While it is fair to compare the incremental average over the aggregate average, it still leaves room for ambiguity because of the inclusion of tail enders and keepers in the mix. There are the often repeated assertions in cricket that the ability of tail enders with the bat has improved considerably in modern times, and wicket keeper batsmen aren’t the same since Gilchrist happened. It’ll be a worthwhile exercise to test these notions separately, but for the sake of this theme, let’s just remove them from the equation and compare the just the top order aggregate averages and work the batsman’s alpha average based on that.

Player	Average	Average rank	Top 6	Alpha Top 6 Avg	Alpha Avg (Top 6) Rank	Alpha avg rank - Alpha top 6 avg rank	Alpha Avg Rank
DG Bradman (Aus)	99.94	1	39.99	59.95	1	0	1
RG Pollock (SA)	60.97	2	38.07	22.90	2	0	2
H Sutcliffe (Eng)	60.73	4	38.20	22.53	3	0	3
ED Weekes (WI)	58.61	8	36.17	22.44	4	1	5
GA Headley (WI)	60.83	3	38.94	21.89	5	-1	4
KF Barrington (Eng)	58.67	7	36.98	21.69	6	0	6
CL Walcott (WI)	56.68	12	35.63	21.05	7	1	8
E Paynter (Eng)	59.23	5	38.27	20.96	8	-1	7
GS Sobers (WI)	57.78	10	36.88	20.90	9	0	9
JB Hobbs (Eng)	56.94	11	36.49	20.45	10	1	11
WR Hammond (Eng)	58.45	9	38.92	19.53	11	-1	10
KC Sangakkara (SL)	58.76	6	39.82	18.94	12	0	12
L Hutton (Eng)	56.67	13	38.13	18.54	13	0	13
GS Chappell (Aus)	53.86	15	37.23	16.63	14	1	15
JH Kallis (ICC/SA)	55.37	14	38.80	16.57	15	-1	14
Javed Miandad (Pak)	52.57	21	36.86	15.71	16	1	17
SR Tendulkar (India)	53.78	17	38.50	15.28	17	-1	16
BC Lara (ICC/WI)	52.88	19	37.92	14.96	18	0	18
A Flower (Zim)	51.54	26	36.80	14.74	19	0	19
S Chanderpaul (WI)	53.1	18	38.63	14.47	20	0	20
SM Gavaskar (India)	51.12	31	37.13	13.99	21	3	24
SR Waugh (Aus)	51.06	32	37.30	13.76	22	0	22
R Dravid (ICC/India)	52.31	22	38.84	13.47	23	0	23
AR Border (Aus)	50.56	36	37.09	13.47	24	3	27
IVA Richards (WI)	50.23	37	36.94	13.29	25	5	30
DCS Compton (Eng)	50.06	38	36.80	13.26	26	2	28
J Ryder (Aus)	51.62	25	38.43	13.19	27	5	32
Mohammad Yousuf (Pak)	52.29	23	39.14	13.15	28	-3	25
AD Mathews (SL)	52.65	20	39.50	13.15	29	0	29
RT Ponting (Aus)	51.85	24	38.86	12.99	30	-4	26
AD Nourse (SA)	53.81	16	41.11	12.70	31	-10	21
ML Hayden (Aus)	50.73	35	38.11	12.62	32	-1	31
JE Root (Eng)	50.94	34	38.68	12.26	33	1	34
Younis Khan (Pak)	51.41	29	39.53	11.88	34	-1	33
MJ Clarke (Aus)	51.5	28	39.69	11.81	35	0	35
HM Amla (SA)	51.32	30	39.80	11.52	36	0	36
MEK Hussey (Aus)	51.52	27	40.23	11.29	37	0	37
AB de Villiers (SA)	51.02	33	39.83	11.19	38	0	38

  

As convincing as the argument to separate the keepers and tail enders was, the result isn’t particularly telling. Richards and Ryder move up 5 ranks, possibly indicating the relatively better batting abilities of tail enders and/or the keepers of their time. They did much better when compared against their contemporary top 6 than when compared against their contemporary aggregate of all 11. Rest are all marginal differences in ranks except Nourse, who quite amazingly moves down by 10 ranks. The top 6 of his time averaged a whopping 41.11! Does the fact that his career coincided with that of Bradman's have anything to do with this handsome top order average?

The aggregate record during Bradman's time:

	Players	Span	Mat	Inns	NO	Runs	HS	Ave	100
overall	409	1928-1948	128	4376	584	120798	364	31.85	254

Bradman's record:

	Mat	Inns	NO	Runs	HS	Ave	100
Tests	52	80	10	6996	334	99.94	29

Removing Bradman alone from the 409 players over those two decades:

	Players	Span	Mat	Inns	NO	Runs	HS	Ave	100
Aggregate	408	1928-1948	128	4296	574	113802	364	30.58	225

The top 6 record of his time:

Players	Span	Mat	Inns	NO	Runs	HS	Ave	100
259	1928-1948	128	2612	196	96631	364	39.99	238

Removing Bradman from the list:

	Players	Span	Mat	Inns	NO	Runs	HS	Ave	100
	258	1928-1948	128	2532	186	89635	364	38.21	209

Bradman as an individual makes a difference of 1.27 runs per batsman for the 408 players of his era and an even more impressive 1.78 runs per top 6 batsman. A big part of the reason is, well, he's Bradman. But a part of it is also because he played in 41% of the total matches played in his time. Contrast that with someone like George Headley who only played 11% of the matches of his time. 

To get some perspective on that, I compared the Bradman's influence on his era with another batsman from a different era whose average was in the healthy 50s and who featured in 60% of the matches of his time: Jack Hobbs. He improved the average of the batsmen of his era by 0.83 runs for all and by 1.04 for the top 6 of his time.

Modern batsmen play a lot less proportion of the overall matches in addition to the fact that the number of matches have shot up by 4 to 5 times from the earlier eras and are at a disadvantage to make such significant impact individually. Sangakkara, who averages the most among modern batsmen and has played 20% of the matches in his time, improves the average of his era by 0.27 for all and by 0.31 for the top 6 of his time.

End of digression. Back to the main thread.

Getting back to the point made earlier in computing the alpha average by considering only the top 6 batsmen, there are two widely floated around theories in modern cricket: Wicketkeepers bat way better since Gilchrist and tail enders aren't mugs with the bat in modern day cricket.

Let's consider wicket keepers first.

This is the total aggregate of wicket keeper batsmen record in Test cricket: 

	Players	Span	Mat	Inns	NO	Runs	HS	Ave	100
Aggregate	258	1877-2014	2139	6706	902	155553	232*	26.8	191

Wicket keeper batting record decade wise:

	Players	Mat	Inns	NO	Runs	HS	Ave	100
2000s	47	464	1490	179	41705	232*	31.81	65
2010s	62	195	641	71	19597	224	34.38	35
1970s	24	198	624	83	14764	152	27.29	11
1990s	37	347	1086	135	25950	173	27.28	30
1930s	26	89	272	45	5829	149	25.67	9
1940s	15	45	130	18	2648	152	23.64	3
1980s	39	266	773	109	15696	210*	23.63	14
1960s	35	186	588	73	12150	192	23.59	12
1950s	38	164	505	68	9005	209	20.6	10
1890s	13	32	106	23	1637	134*	19.72	1
1920s	16	51	157	36	2373	84	19.61	0
1900s	9	41	133	26	1825	115	17.05	1
1880s	11	29	97	16	1293	82	15.96	0
1910s	9	29	93	20	954	72	13.06	0
1870s	3	3	11	0	127	38	11.54	0

Note: The decisive shift in a trend could have happened at any time, but I have just chosen to compare them on the parameters of decades solely on discretion rather than any compelling rationale. Also the comfort that even if something decisive happened midway, it would still show up in these filters.

Prima facie, the idea of wicket keeper batsmen seems to have been a serious thing since the 1930s. And from there till almost 1990s, there has been spikes and troughs in different time periods. The average jumped up by 3.70 runs from the 1960s to the 1970s. But somehow the significance was lesser because of the lack of follow up in the next decade. That is where the jump of 4.53 runs from the 1990s to the 2000s achieves greater significance. More than the normal volatility, this seemed like a big leap for the discipline.

That Gilchrist made his debut towards the end of 1999 makes it appealing to think of him as the single biggest factor  but it's a bit too simplistic. Even excluding him from the records, the average in 2000s is a very impressive 30.26.

List of wicket keepers with at least 1000 runs and average above 30 in the 2000s:

	Mat	Inns	Runs	HS	Ave	100
A Flower (Zim)	20	34	1972	232*	73.03	6
AC Gilchrist (Aus)	91	129	5130	204*	46.63	16
MJ Prior (Eng)	25	40	1390	131*	42.12	2
BJ Haddin (Aus)	23	38	1404	169	41.29	2
KC Sangakkara (SL)	48	81	3117	230	40.48	7
MS Dhoni (India)	40	62	2176	148	40.29	3
AJ Stewart (Eng)	40	66	2056	124*	36.07	3
Kamran Akmal (Pak)	47	80	2525	158*	34.12	6
BB McCullum (NZ)	48	79	2394	143	31.92	3
HAPW Jayawardene (SL)	30	40	1044	154*	30.7	2
MV Boucher (ICC/SA)	104	152	4024	122*	30.02	2

Somewhere between the end of 1990s and into the 2000s cricket either seems to have moved towards placing greater emphasis on batting credentials of keepers or just fortunate to be flooded with a rich vein of talent clustered around the same time. That is the key difference in the 2000s. Gilchrist is no doubt a phenomenon, but so was Les Ames in his time. That Gilchrist played in an era of great keeper batsmen is what made his era so special.

List of keeper batsmen with more than 1000 runs in 2010s

	Mat	Inns	Runs	HS	Ave	100
AB de Villiers (SA)	19	31	1726	169	59.51	6
BJ Watling (NZ)	17	27	1041	124	45.26	3
Mushfiqur Rahim (Ban)	24	44	1673	200	40.8	3
MJ Prior (Eng)	54	83	2709	126	39.26	5
MS Dhoni (India)	48	78	2632	224	37.07	3
BJ Haddin (Aus)	34	58	1629	136	31.32	2
HAPW Jayawardene (SL)	26	39	1031	120	30.32	2

All of them average more than 30 with De Villiers setting a whole new benchmark for wicket keeper batsmen.

Stats or anecdotes, there is no disputing the notion that wicket keeper batsmen have had a huge leap in terms of ability and achievement with the bat since the 2000s.

On to the lower order: 

This is the record of batsmen from no.8 to no.11 in the history of cricket:

	Players	Mat	Inns	Runs	HS	Ave	100
Aggregate	1928	2136	24067	277051	257*	15.25	96

Quite obviously, there'll be exceptions here of top order batsmen batting lower down the order for various reasons. But spread over such a large population, it's insignificant. 

Decade	Matches	Average of Nos. 8 to 11
1920s	51	17.72
2010s	195	16.54
1980s	266	16.05
1960s	186	15.78
1890s	32	15.75
1940s	45	15.57
2000s	464	15.51
1870s	3	15.3
1900s	41	15.12
1970s	198	14.79
1990s	347	14.34
1930s	89	14.22
1950s	164	14.05
1910s	29	14.01
1880s	29	12.57

The total range of averages across all decades is 5.15 runs between 1880s and 1920s. The best decade for run making, 2000s, has a tail ender average of 15.51 which puts it in the 7th place, way behind the 1980s - the glory era of fast bowling.

There is no real improving or worsening pattern over time here.

List of batsmen (8 to 11) who have scored at least 1000 runs and average >= 20:

	Span	Mat	Runs	HS	Ave	100
MV Boucher (ICC/SA)	1997-2012	53	1577	122*	35.04	2
SM Pollock (SA)	1995-2008	75	2330	111	32.81	2
N Kapil Dev (India)	1978-1993	61	1967	116	32.78	2
DL Vettori (ICC/NZ)	1997-2012	100	3502	140	30.71	5
IDS Smith (NZ)	1981-1992	55	1667	173	27.78	2
SMH Kirmani (India)	1976-1986	63	1598	102	27.55	1
KS More (India)	1986-1993	47	1180	73	26.81	0
N Boje (SA)	2000-2006	40	1125	82	26.78	0
WPUJC Vaas (SL)	1994-2009	105	2785	100*	25.55	1
WAS Oldfield (Aus)	1920-1937	40	1003	65*	25.07	0
Sir RJ Hadlee (NZ)	1973-1990	56	1641	103	24.49	1
SCJ Broad (Eng)	2007-2014	73	2120	169	24.09	1
MG Johnson (Aus)	2007-2014	57	1559	123*	23.26	1
DJG Sammy (WI)	2007-2013	33	1185	106	22.78	1
TG Evans (Eng)	1946-1959	41	1062	104	22.59	1
Wasim Akram (Pak)	1985-2002	87	2160	257*	22.26	2
GP Swann (Eng)	2008-2013	60	1370	85	22.09	0
HH Streak (Zim)	1993-2005	48	1187	127*	21.98	1
JE Emburey (Eng)	1978-1995	53	1212	75	21.26	0
AF Giles (Eng)	1998-2006	54	1421	59	20.89	0
B Lee (Aus)	1999-2008	75	1415	64	20.8	0
RR Lindwall (Aus)	1946-1960	51	1103	118	20.42	2

Most of the solid record belongs to all rounders who were batting out of position and wicket keepers. Even here, the numbers are heavily skewed in favour of 1980s and beyond. But that hardly seems to impact the aggregate numbers of the recent decades.

Anecdotally, the theory that tail enders have become better batsmen in recent times is so sound. Cricket fans can recollect a sizeable number of matches where tail enders have played out spells and spells of incisive bowling to bat out for a draw. The ugly blindfold like slog is history. Cricket is a lot more professional with an ever expanding support staff assisting cricketers to hone their secondary skill. Bats are better and so are protection equipments. It all adds up to make perfect sense.

But at a macro level, stats just don't add up to make a convincing case.