Second only to Bradman?

Steven Smith has just celebrated his test come back by scoring a century in each innings at Edgbaston in Birmingham. Not content with just scoring a "come-from behind fighting century" when the bowlers were on top, he also added a "rub the salt in" century when the batsmen were on top.

It was such a match defining performance that the questions have been asked again, is he the best since Bradman?

I won't attempt to do a complete statistical breakdown right here now, but I will focus on a couple of statistics that suggest either "yes" or "not quite."

One thing that I've started to be more and more interested in is the performance of a batsman at their peak. It is hard to deny that a batsman's skill level changes throughout their careers. Some start off as amazing players, but then fade, others start slowly, then blossom into better players. Most start off slowly, have a strong middle period of their career then fade again at the end.

The graph below illustrates three players that had quite different career trajectories, but were all very good players.

Dennis Compton started off with an amazing run of scores, only Don Bradman averaged more in his first 30 test matches. His career never really reached those heights again, however, and he had a period where he really struggled, before modifying his game and ending his career on a (less dramatic) high.

Martin Crowe was picked as a teenager, and sent on a difficult tour, before he was really ready. He struggled and was in and out of the side at first. It took him a while to really own his position. After a while, he developed into one of the best batsmen in the world. Later on he struggled with injuries and his career petered out to a shadow of what he had previously been.

Marvin Atapattu scored only one run in his first 6 innings. That start was not an easy one to recover from. Throughout his career he tended to have a mixture of exceptionally large scores and regular ducks, which meant that it looked like he had patchy form. But for the majority of his career he tended to average above 40 in any given 30 match sequence after his horrific early period.

The story is clear, however, that an overall career average does not necessarily tell us about how good a player actually was. Looking at a player's peak is actually a better idea than looking at their overall career. That's especially true when comparing former players with current ones, or comparing players who retired at their peak with ones who continued on because even though they were no longer at their best, they were still better than the alternatives.

To compare players at their peak requires finding a way to define their peak. It's difficult to know how many matches to choose as a player's peak. It will certainly differ from player to player. Some will maintain their peak form for a number of years, while others may get injured, banned for ball tampering or retire just as they are starting to hit it. Added to that, the number of tests played has greatly increased for most nations, so while an old player like Jack Cowie never missed a test for 12 years and yet never made it to 30, someone playing for England now could potentially reach 30 tests after only playing test cricket for 20 months.

There's also the issue of sampling variability in small samples. If we look at 30 tests as defining a player's peak, that makes a maximum sample size of 60 innings (more likely to be closer to 55). 50 tests would make a maximum sample size of 100 innings (more likely to be close to 90).

If we simulate innings based on a player with a batting average of 45, we can find the range of likely 30 match and 50 match averages if the results are distributed randomly. For this, I've used geometric distribution to create random scores, and then found the average of them. This has been shown to be a reasonably useful way of simulating cricket scores, so it will give some indication of the expected variance in the averages.

The red and green lines here are the 95% bands for the simulated data. With the 30 match averages, the player who should have averaged 45 tended to average somewhere between 33 and 58. With 50 matches, the player tended to average between 36 and 54.

This needs to be remembered whenever comparing averages. A peak can be a player's skill improving, or it can be just random variation. Someone who averages 52 is not necessarily a better player than another one who averaged 49. It is just not possible to be confident statistically that there's a difference between these two player's ability. That's just based on sampling variability, and not accounting for non-sampling factors such as the opposition that they faced or the conditions that they played in.

Given that, is there any point in comparing at all? Well, it's not going to definitively say who was the best, but it can tell us who played the best.

For this analysis I am only including matches for players where they actually batted. As a result Don Bradman only has 50 tests, as there are two where he got injured fielding/bowling and did not end up batting. I am also not including the WSC Supertests or any matches played for the ICC World XI.

The top 21 instances of the best 30 matches by either average or total runs are the 21 combinations of 30 in a row out of Bradman's 50 matches.

He is so far ahead of the rest of the players in history that in his worst ever 30 matches he still scored 14% more runs than the best 30 matches by any other player.

Here are the tables of the top 10.

 

The top name is consistent, but the other names in table are much less consistent. 18 players appear at least once, with Bradman, Ponting, Sangakkara and Smith being in all 4 tables, while Sobers, Kallis and Yousuf all in the list 3 times.

This does not tell us definitively who is second. There is enough sampling variation alone that there's not enough evidence to say that Waugh was better in his best 30 innings than Hayden was, just that he performed better. But that's really all we can hope for.

Steven Smith may not be the best since Bradman, but he may well be also.

Comparing between eras part 2. The survey results

In the previous post I looked at some New Zealand batsmen throughout the years and compared them, by trying to take into account some of the factors that might have batting either easier or harder for them.

I did this by looking at the runs that each player scored at a particular ground, and then looking at how easy/difficult that ground was to score at during that player's career. After that I allocated each ground a modifier value, and multiplied the runs scored at each ground by that ground's modifier. As a result (for example) the 188 runs that Martin Crowe scored at the Bourda in Georgetown were worth 164.5, because (during Crowe's era) it was a batting friendly pitch. However, his 120 runs that he scored at Karachi were worth 135.1 because that ground favoured bowlers.

I wanted to try the technique across a wider range of batsmen, so I put a simple request on twitter, for people to send me their top 5 batsmen. The tweets started pouring in.

I need some crowd-sourcing help. I want a lot of top of head lists of the 5 best batsmen ever. Please reply with your 5 and then RT. Thanks!

— Michael Wagener (@Mykuhl) January 7, 2015

I received a few humerous replies such as 5 votes for Rohit Sharma, 5 votes for Graham Thorpe and my personal favourite:

@Mykuhl @TheCricketGeek Adam West Michael Keaton Del Boy Val Kilmer George Clooney

— Adrian Toomey (@adriantoomey) January 7, 2015

But eventually I had 159 serious lists of 5.

From the top 20 (plus ties) I then worked out their Normalised Averages. I left out two players, Barry Richards and WG Grace, as neither of their test careers were really the reason that people put them in the list. For both, test matches made up less than 5% of their first class career. I'll deal with them (and Charles Bannerman) in a future post.

Here's the list:

Rank	Name	Votes	Average	Norm Average
1	Don Bradman	119	99.94	101.03
2	Sachin Tendulkar	112	53.79	54.10
3	Brian Lara	108	52.89	54.41
4	Viv Richards	84	50.24	54.96
5	Ricky Ponting	55	51.85	52.50
6	Kumar Sangakkara	52	58.45	58.27
7	Gary Sobers	31	57.78	57.71
8	Rahul Dravid	28	52.31	52.73
9	Jacques Kallis	27	55.37	59.55
10	Jack Hobbs	24	56.95	63.01
11	Barry Richards	12	72.57	*
11	Wally Hammond	12	58.46	58.44
13	AB de Villiers	11	52.10	52.99
13	Steve Waugh	11	51.06	53.56
15	WG Grace	10	32.29	*
16	Graeme Pollock	9	60.97	59.91
16	Sunil Gavaskar	9	51.12	54.76
18	Herbert Sutcliffe	4	60.73	62.00
18	Dennis Compton	4	50.06	53.44
18	Martin Crowe	4	45.37	47.91
18	Adam Gilchrist	4	47.61	49.24
18	Allan Border	4	49.54	54.30

There are a couple of interesting things here. Less than 3/4 of people picked Bradman. Often they said that it was because they had never watched him bat, and that's understandable, but I would have thought his extraordinary average alone was sufficient to put him in the mix. You don't need to know much about batting averages to know that Bradman's numbers are almost unbelievable.

The tendency to only vote for batsmen that people had seen meant that players who had played since 2000 had to score at a lower average than players who had played before that. Here's a graph comparing the number of votes that a batsmen got with their normalised average:

There was also a tendency for people to nominate players who had done well against their sides. Most votes out of England included Brian Lara who hit both of hit triple centuries against England, while votes from India often included Ricky Ponting who averaged mid fifties against the Indians.

Here's the list ordered by their Normalised Average. I've added in two other older players who only got one vote each, Ken Barrington and Everton Weekes but who both had exceptional records.

Name	Average	Norm Average
Don Bradman	99.94	101.03
Ken Barrington	58.67	64.00
Jack Hobbs	56.95	63.01
Herbert Sutcliffe	60.73	62.00
Graeme Pollock	60.97	59.91
Jacques Kallis	55.37	59.55
Everton Weekes	59.46	59.39
Wally Hammond	58.46	58.44
Kumar Sangakkara	58.45	58.27
Gary Sobers	57.78	57.71
Viv Richards	50.24	54.96
Sunil Gavaskar	51.12	54.76
Brian Lara	52.89	54.41
Allan Border	49.54	54.30
Sachin Tendulkar	53.79	54.10
Steve Waugh	51.06	53.56
Dennis Compton	50.06	53.44
AB de Villiers	52.10	52.99
Rahul Dravid	52.31	52.73
Ricky Ponting	51.85	52.50
Adam Gilchrist	47.61	49.24
Martin Crowe	45.37	47.91

A couple of interesting things here are the way that players are rewarded for scoring on the harder pitches. Sutcliffe and Hobbs played together through a large part of their careers. But Hobbs was the one that scored the most runs when the conditions were the hardest for batting. As a result Hobbs' average increased by 6.06 while Sutcliffe's only increased by 1.27.

Jacques Kallis likewise scored a lot of runs at Newlands, which has been a graveyard for batsmen, and he has been rewarded for that. Kumar Sangakkara however, has scored a lot of his at the SSC, which is a place that batsmen have prospered, and so that saw his normalised average end up lower than his actual average.

I still have a number of players that I'd like to look at such as Victor Trumper, Bruce Mitchell, Zaheer Abbas and Andy Flower. But there's plenty of time for that in the next installment.

1000 test runs in a year.

Michael Clarke had a fantastic year in 2012. He scored 1596 runs at an average over 100. It brought up the question, how often do players score 1000 runs in a calendar year, and who has done it the most?

So I put together some data for all you trivia buffs out there

First the batsmen who have done it the most:

We can see that most of the players are from the modern era. The only players who are in this list who didn't play post 2000 are Taylor (retired '99), Border (retired '94) and Gavaskar (retired '87).

Interestingly Hayden managed the feat in 5 consecutive years, from 2001 to 2005, which is particularly impressive consistency. Mark Taylor is also quite impressive, because he only played test cricket in 11 years, so to score 1000 runs 3 times is outstanding.

The top few names are as we would expect for this sort of statistic. Tendulkar at the top, then Lara, Kallis, Hayden and Ponting. For me they are/were 5 of the 6 best batsmen of this era (along with Sangakkara).

The next list to look at is what countries have done the best.

Some countries play a lot more test matches than others. Of the 128 times that a player has scored 1000 runs in a year, only 11 times did that player play less than 10 test matches, and never less than 8. England have played 10 or more tests in a year 40 times, while Bangladesh have never played 10 tests in a year, so we would expect more English batsmen to have achieved the feat more often than Bangladeshi batsmen.

We would also expect batsmen from countries with easier conditions to do it more often than players who play half their matches on bowler friendly pitches. Since 1990, there have been more than 1.95 hundreds per match in India, Australia, England and Pakistan, but less than 1.7 in New Zealand, South Africa and Zimbabwe. As a result it's fair to expect there to be less South Africans, New Zealanders and Zimbabweans in the list than players from the India, Pakistan, Australia or England.

The surprise is that there are so many South Africans on the list. It is a clear example of their outstanding batting strength in recent years. Andy Flower managed it against the odds, having to play half of his cricket in Zimbabwe, and his team only playing 9 matches in 2000 when he achieved it. He was also keeping wickets that year, making him the only keeper to achieve the feat. He also lies second on the list for most runs in a year as keeper, with 899 in 2001, when he also only payed 9 matches.

The final thing to look at is how many times 1000 runs has been scored in any particular decade.

The trend towards bigger bats, shorter boundaries (except in the West Indies and New Zealand where cricket is being played more on single purpose stadia rather than rectangular ones) and more tests should lead to more players scoring 1000 runs in a year, and it has.

When Clem Hill scored 1060 runs in 1902 it was remarkable. Then Compton and Bradman joined the club in 1947 and 1948 respectively, with amazing years. However I don't think that Jonathan Trott scoring 1005 runs in 15 tests at 38.65 this year is quite as impressive an achievement.

It is another record who's significance has diminished somewhat in the age of the batsman, but that does not diminish from Michael Clarke's achievement. By any standard he has had a fantastic year.

Adding value with the ball

A while ago Nicholas Rohde wrote a series of articles that got some people upset. He used an economic model to look at which batsmen had made the greatest contribution.

His basic method was to compare the runs they had scored to the runs that an average batsman would have scored finding the added value that they provided their team.

I read through his article and was impressed with his approach despite feeling there are some issues in the way that he interpreted his results. He did not take in account the extra frequency of matches in the modern era when suggesting that a current selector should pick a young Tendulkar over a young Bradman. Bradman should be judged on his opportunities, not on someone elses (Bradman played in 87% of Australia's matches during his career, only just behind Tendulkar's 92%). However the background theory is actually quite intuitive and also provides some very interesting results.

I took his idea and applied it to test bowling. My method was probably not identical to his, but what I did was break down each year to find out how many runs bowlers had conceded and how many wickets had been taken in that year. For each bowler I then found the total runs and wickets in the years that they played, to give a value for what the average bowler would have done. There are some issues with this method for figuring out added value, but I feel that it gives a better guide than any other practical method I can think of.

Here is an example of how it works:

Shabir Ahmed played 10 tests between 2003 and 2005 for Pakistan. He took 51 wickets for 1175 runs. In 2003 there were 1305 wickets taken for 47145 runs. 2004 had 1555 wickets for 54916 runs and 2005 had 1508 wickets for 50377 runs. The total runs per wicket for those three years was roughly 34.9. So we multiply his wickets (51) by 34.9 to get 1780. We then subtract the runs he conceded (1175) to get his value of 605. Effectively he saved his team 605 runs more than an average player would have.

So once we add up the figures, who comes out on top?

First we'll look at the aggregates, and there are a few familiar names there.

Player	Matches	Wickets	Average	Added Value
M Muralitharan (ICC/SL)	133	800	22.72	8410
GD McGrath (Aus)	124	563	21.64	6260
SK Warne (Aus)	145	708	25.41	5174
CEL Ambrose (WI)	98	405	20.99	4261
Sir RJ Hadlee (NZ)	86	431	22.29	4115
SM Pollock (SA)	108	421	23.11	4105
MD Marshall (WI)	81	376	20.94	4096
CA Walsh (WI)	132	519	24.44	3891
Wasim Akram (Pak)	104	414	23.62	3472
Imran Khan (Pak)	88	362	22.81	3328
Waqar Younis (Pak)	87	373	23.56	3273
AA Donald (SA)	72	330	22.25	3110
DW Steyn (SA)	51	263	23.07	3088
FS Trueman (Eng)	67	307	21.57	2745
DK Lillee (Aus)	70	355	23.92	2715
J Garner (WI)	58	259	20.97	2654
RGD Willis (Eng)	90	325	25.20	2071
MA Holding (WI)	60	249	23.68	1939
A Kumble (India)	132	619	29.65	1919
M Ntini (SA)	101	390	28.82	1849
JN Gillespie (Aus)	71	259	26.13	1750
SF Barnes (Eng)	27	189	16.43	1749
AK Davidson (Aus)	44	186	20.53	1731
JC Laker (Eng)	46	193	21.24	1636
CV Grimmett (Aus)	37	216	24.21	1625

We notice that the likes of Barnes and Davidson are a lot higher than they would be in a pure wickets table.

Muralitharan is miles ahead of McGrath in 2nd place. Regardless of what Bishan Singh Bedi thinks his record is formidable. Once his action was cleared he still had to put the ball in the right place, and do the right thing with it, and he did that, time after time after time.

Glenn Mcgrath jumps over Anil Kumble and Shane Warne into second spot. Both he and Shaun Pollock changed the way that bowlers thought about opening the bowling, with his metronomic accuracy and aggressive approach being incredibly valuable to his team. His economy being the difference between him and Warne on the table.

Now when we are looking for the best bowler consistency is important, but really we want to know who could be expected to do the best in the next game, so how well they do per innings is more important.

Here is the table of added value per innings. (I've limited it to bowlers who bowled more than 10 innings and took more than 25 wickets)

Player	Wickets	Average	Added Value	AV per innings
J Cowie (NZ)	45	21.53	641	49.31
MJ Procter (SA)	41	15.02	615	43.90
H Ironmonger (Aus)	74	17.97	1036	38.35
RAL Massie (Aus)	31	20.87	407	37.02
M Muralitharan (ICC/SL)	800	22.72	8410	36.56
SF Barnes (Eng)	189	16.43	1749	34.99
SE Bond (NZ)	87	22.09	1087	33.97
RJ Harris (Aus)	35	21.37	459	32.76
DW Steyn (SA)	263	23.07	3088	32.51
Shabbir Ahmed (Pak)	51	23.03	605	31.83
AE Hall (SA)	40	22.15	436	31.16
K Higgs (Eng)	71	20.74	833	30.83
BN Schultz (SA)	37	20.24	423	30.23
ERH Toshack (Aus)	47	21.04	652	28.33
GA Lohmann (Eng)	112	10.75	997	27.70
Sir RJ Hadlee (NZ)	431	22.29	4115	27.44
MD Marshall (WI)	376	20.94	4096	27.13
WJ O'Reilly (Aus)	144	22.59	1288	26.83

The name at the top is one that most readers won't know. The 1938 Wisden said this about Jack Cowie, "Had he been an Australian, he might have been termed a wonder of the age." During the 12 years that he played, New Zealand only played 9 test matches and he famously only got to bowl once to Bradman, getting him out for 11. Hutton described him as the best bowler he had faced. An example of how much better Cowie was than his contemporaries is that the rest of New Zealand bowlers averaged over 54 in the same 9 tests.

The second name is more familiar: Mike Procter was the match referee at the 2006 match where Pakistan refused to come out and field, and also was the one who banned Harbajhan Singh in Sydney 2008. He only played a small number of tests due to being from South Africa, but in his 401 match first class career he managed to keep his bowling average under 20 (as well as averaging over 36 with the bat)

The third name on the list, Dainty Ironmonger didn't make his debut until he was 45, but was very effective with his left-arm slow medium, and very ineffective with the bat (having a similar average to Chris Martin).

Murali is the first of the recent players on the list, which is a credit to him, as he kept that up for a very long time. Steyn is also remarkably high, ahead of the likes of Hadlee, Marshall and Lillee.