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.

Mini-session Analysis 2nd Test, Australia vs Sri Lanka, MCG, Melbourne, Australia 2012/13

Here is the final mini-session analysis for the second test between Australia and Sri Lanka at MCG, Melbourne, Australia

A mini-session is (normally) half a session, either between the start of the session and the drinks break or the drinks break and the end of the session. Occasionally a long session will have 3 mini-sessions where it will be broken up with 2 drinks breaks.

Mini-Session	Score	Winner
1-1a	Sri Lanka 36/2 off 12	Australia
1-1b	Sri Lanka 43/1 off 13	Sri Lanka
1-2a	Sri Lanka 55/2 off 13	draw
1-2b	Sri Lanka 22/5 off 5.4	Australia
1-3a	Australia 90/0 off 16	Australia
1-3b	Australia 60/3 off 23	Sri Lanka
2-1a	Australia 47/0 off 15	Australia
2-1b	Australia 41/0 off 15	Australia
2-2a	Australia 60/0 off 16	Australia
2-2b	Australia 34/3 off 11	Sri Lanka
2-3a	Australia 51/1 off 16.3	Australia
2-3b	Australia 57/1 off 16.3	Australia
3-1a	Australia 20/2 off 5.4	Sri Lanka
3-1b	Sri Lanka 43/4 off 13	Australia
3-2a	Sri Lanka 59/2 off 10.3	Australia
3-2b	Sri Lanka 1/1 off 0.5	n/a

Final update, click here
Australia win the mini-session count 10 - 4

First drinks, Day 1: Australia lead the mini-session count 1-0

Great start for Australia, after Sri Lanka chose to bat. Bird looks like a handy bowler. There is a little in this pitch, but I think it should settle down this afternoon, it doesn't look like the sort of pitch that will misbehave for too long.

Lunch, Day 1: The mini-session count is tied up, 1-1

Take a bow Kumar Sangakkara! He battled through reasonably difficult conditions and saw off some good bowling to bring up his 10000 career runs in the same number of innings as Tendulkar and Lara. He chose a good way to bring it up too, with a scorching square drive along the slow outfield to what is probably the longest square boundary in world cricket.

Middle drinks, Day 1: The mini-session count is tied up, 1-1

While Sri Lanka scored quickly enough that the formula almost gave them the hour, the two wickets were very big wickets. Australia are probably actually in the lead in this match. Sri Lanka need a very big partnership here, and probably one other if they are going to stay in this match.

Tea, Day 1: Australia lead the mini-session count 2-1

Absolutely awful stuff from Sri Lanka. There was some good bowling and (particularly) good captaincy, but it was just brainless by Sri Lanka. Within 3 balls of every break Sri Lanka lost a wicket. And a lot of the wickets in the match have been to particularly poor shots. Sri Lanka have tried to attack, but I think they have been just too aggressive.

Final drinks, Day 1: Australia lead the mini-session count 3-1

Sri Lanka are in a world of trouble. Eranga looks very poor against left-handers, Welegedera has had trouble with his length, Prasad has been erratic, and Warner and Cowan have been imperious.

I was asked earlier today who I felt the best batsmen I had seen were, and I mentioned Matthew Hayden. I don't think even Hayden had scored an attacking 50 while opening as good as this innings from Warner. The big feature has not been his power, but his placement. He has only faced 17 dot balls so far in his innings. Phenomenal batting.

Stumps, Day 1: Australia lead the mini-session count 3-2

Sri Lanka struck back well there. It started when Angelo Matthews removed Warner, and then Rangana Herath came on and started to build the pressure.

It could have been a lot better too. First Dilshan dropped Michael Clarke on 5 and then, 3 overs later, Sangakkara put down a relatively tough chance off Watson. If those two had been taken the match would have potentially been all square, but Sri Lanka couldn't take the opportunities, and are behind in the match as a result.

Australia are still well in control, but Sri Lanka are back in it.

First drinks, Day 2: Australia lead the mini-session count 4-2

A good mornings cricket. Both batsmen were looking to attack, but the bowlers were bowling well enough to keep them honest. Eranga in particular put both batsmen under pressure. He hit Clarke on the head, and generally had him looking quite uncomfortable. Australia will be very pleased to have come out of this hour without losing a wicket and having scored at about 3 an over.

Lunch, Day 2: Australia lead the mini-session count 5-2

Both batsmen brought up their fifties in that hour, but both were given lives in the same over by Herath. First Clarke should have been stumped, but Sangakkara couldn't gather cleanly. Then Watson edged a ball that hit Mahela in the chest, but was moving too quickly for him to grab. Sri Lanka are generally a good fielding side, and they will be very disappointed to have missed 4 chances so far in this innings.

Middle drinks, Day 2: Australia lead the mini-session count 6-2

Michael Clarke is relentless. Despite the bowlers generally bowling very well in this hour, he has advanced the score, and brought up his hundred. Watson is almost fading into the background of this fantastic Clarke knock.

Clarke's innings hasn't been chanceless, however. Herath has really caused him some problems. In this hour he edged one between keeper and slip. Sri Lanka have now given him 3 lives. He's not often one to pass up such generosity.

Tea, Day 2: Australia lead the mini-session count 6-3

Sri Lanka finally hung onto a catch. And it was contagious. After they got one they picked up two more. But it couldn't last: Hussey was missed by Sangakkara off the luckless Herath in the last over before tea. It was a good hour for Sri Lanka, but it's a long way back from here.

Final drinks, Day 2: Australia lead the mini-session count 7-3

Another good hour for Australia, but with a significant highlight for Sri Lanka, a brilliant catch by Rangana Herath to dismiss Hussey. Australia batted quite cautiously, but managed to score relatively quickly regardless. The Sri Lankan bowlers are starting to look tired.

Stumps, Day 2: Australia lead the mini-session count 8-3

Mitchell Johnson is working his way towards being back for the ashes. He has been sublime in this innings, looking almost completely untroubled throughout. It was Australia's day today. Sri Lanka are going to need to bat very very well in order to get back into this game. They really need to bowl Australia out quickly, then score something like 500 to have any chance.

The pitch is not nearly as easy as the score would indicate. There have been a couple keep low, balls have moved off the seam (even with the old ball) and some have stood up and bounced sharply. This has really been a fantastic effort from Australia, and they deserve to be in the lead.

First drinks, Day 3: Australia lead the mini-session count 8-4

Sri Lanka have managed to clean up the tail for the addition of only 20 runs. Another right hander dismissed by Eranga, although this one was not in the usual manner of caught behind the wicket. Now they have the small matter of knocking off the 304 run lead then posting a target.

Lunch, Day 3: Australia lead the mini-session count 9-4

If there was any doubt who was winning this hour has cleared it up. First Karunaratne was run out after turning blind. Next Dilshan hit a leg glance into his thigh pad and got hit at short leg. After that Mahela summed up his match by attempting to leave the ball, but just chopping it on instead. The final wicket in the hour was Samaraweera who was out plumb lbw. He reluctantly challenged, but it was to no avail. At the other end, Sangakkara is batting as well as anyone has this test. It was said of the New Zealand team's bowling in the 80's that it was like facing the World XI at one end, and the Illford 2nd XI at the other end. It must feel like that for the Australian bowlers at the moment.

Middle drinks, Day 3: Australia lead the mini-session count 10-4

Possibly the most futile drinks break in history, Sri Lanka effectively have only one wicket left. It looks fairly likely that Australia will win now.

End of Match, Day 3: Australia win the match by an innings and 201 runs and the mini-session count 10-4

And it only took 5 balls to wrap it up. This is the first time that a team has had an innings closed to lose a match after losing only 7 wickets. It's also Australia's biggest ever win over Sri Lanka. This match would have been much closer if the Sri Lankans hadn't been struck down with injuries (4 players injured, first Kulasekera in the warm up, then Jayawardene, Welegedera and Sangakkara), and also if they had taken their chances. It was really a case of poor concentration more than anything else. Sri Lanka lost wickets straight after every break except the final lunch break. They missed vital chances in the field. Then once the Australians got on top, they made the Sri Lankans pay.

Australia weren't as clinical or as comfortable as the scoreline would suggest, but they still played a lot better cricket than Sri Lanka and thoroughly deserved their win.

The news has come in that Sangakkara is out for 6-8 weeks, so this loss will have serious repercussions for the next test and the One Day Internationals.

Does Tendulkar do badly after breaks?

A while ago I was referred on to this article about Sachin Tendulkar having trouble after having a break from cricket. I get sent quite a few Tendulkar stats articles and normally I see them as a bit of a waste of time. There are a lot of articles and most of them are poorly written and make dubious statistical claims. There are some exceptions (Nicholas Rohde's contriversial piece springs to mind), but most are either Indian fans wanting to say that their man is the greatest ever, or anti-Indian fans trying to get a reaction.

When I read Jigar's piece, however it read well, and seemed well researched. My statistics antenna picked up, however when I read through his research, and wondered how significant his findings really were.

Here is a brief summary, for people who haven't read the article: Tendulkar has scored a large number of low scores immediately after returning from an injury or other extended time away from the game.

Jigar's theory was that SRT needed some time to get back to top form, and the troubles against New Zealand were simply because he hadn't been playing enough.

But I wanted to know if the numbers that he had provided were significant. The more I looked at them, the less certain I was. I needed a statistical tool to assess the significance.

To do this in a non-cricketing environment, the first call would have been to look at a confidence interval. Find a 95% confidence interval for the scores where Tendulkar was coming off a break, and, if his actual mean lay outside that, then we could say there was a significant difference. The only problem is that means and standard deviations don't really work with cricket. Not outs make things complicated. I've tried to develop a cricketing equivalent to standard deviation, but have yet to be successful.

My next port of call statistically would be to get an informal confidence interval based on median and inter-quartile range. The problem with this is that again not out's become very tricky to deal with fairly. If a batsman come in with 8 runs to win and scores 2*, how do you count that?

So I had to use a technique that I had heard about, but hadn't actually used myself previously: randomisation.

The idea with this technique is to see if a particular sample fits within the normal range for something. I attended a lecture where it was explained how it was used to test the distribution of berries in a forest and various other conservation related topics. The way that I approached it was this:

Jigar had taken out 47 innings that he described as being shorty after a break. So I looked at those 47 innings and found their batting average. Then I took a random sample of 47 out of the 773 international innings that Tendulkar had played (he's played since I started working on this) and found the batting average of the sample. I took 1002 samples (I intended to take 1000, but forgot to clear my first two test samples before running the program) and looked at how they were distributed.

The 47 innings that came after a break had an average of 41.8.

Here is a graph of my results (I grouped them by the nearest 0.25 of a run).

We can see that the idea of a set of 47 innings having an average of 41.8 isn't particularly unusual. There are a number of samples that were in that region.

We can also see that the distribution looks normal. I calculated the mean and standard deviation of the averages and looked to see how it fitted. Here's the graph of the distribution:

Given that it is so well modeled by a normal distribution, we can use the mean and standard deviation to decide if we can make a call.

The mean of the averages is 49.41. (this is slightly higher than Tendulkar's career average across all formats of 48.68, but close enough to use). The standard deviation was 8.24.

If we were able to make a call that Tendulkar was badly affected by a break, we would expect his average in matches where he has had a break to be at least two standard deviation lower than the mean. This would require the average to be lower than 32.2. Instead his average in the 47 innings that Jigar mentioned was 41.8. It is lower, but we can't really claim that it is significantly lower.