Heads or Tails?

The start of a cricket game is actually 30 minutes before the first ball is bowled. The ritual of it has changed a few times over the years, but basically what happens is the captains walk out to the pitch wearing their blazers over their whites with an umpire and often a cameraman and commentator. The umpire gives the coin to the home captain who tosses the coin up in the air, and then the visiting captain calls heads or tails before the coin lands. The coin is left to land on the pitch, and then the captain who has won the toss is asked if he wants to bat or bowl.

It's an old tradition. Using a coin to make a decision has been done for at least 2000 years. Using it in cricket has dated back to at least the 1850's (The toss result was recorded in the match between Oxford and Cambridge Universities in 1858). And yet there is now some calls for it to be done away with. The ECB are going to experiment with removing the mandatory toss for the 2016 County Championship season.

There is a thought that the toss is too influential. There is a perception that there are too many matches where "if you win the toss, you win the match." Just over 50% of respondents wanted the toss to be done away with on an ABC poll.

I remember having a conversation with a friend who is a fan of most sports, but he was sick of cricket because "the toss of the coin has too much impact." As a cricket statistician, this is wonderful, as it's something that I can test. What is the impact of the toss on cricket matches. How much more often does the team that wins the toss win the match?

In all test matches, the team that has won the toss has won the match 749 times, and the team that lost the toss has won 671 times. These combined with 734 draws and 2 ties have meant that the team that wins the toss has won the match 34.7% of the time, and the team that lost the toss has won 31.1% of the time. This is a relative probability of 1.116. This means that the team that has won the toss has had a 11.6% higher chance of winning the test.

This is slightly lower than I would have expected, but it's still a statistically significant difference. (Statistically significant is a technical term that basically means that we can say that we have enough evidence that there is a difference, and that it's unlikely to be just because of randomness).

But if we delve deeper into these numbers, then some interesting things turn up. First lets break it up by home and away. This is an important distinction, as the home teams will generally be better at reading the conditions. I would have expected that winning the toss at home would provide a bigger difference than winning at home. It turns out to be so, but not by nearly as much as I expected.

When the home team has won the toss, they've won 41.8% of the time (467/1117 matches), when the home team has lost the toss, they've won 37.9% of the time (394/1039). This is a relative probability of 1.103, or a 10.3% increase in probability of winning. There are different methods of testing for significance, and this is right on the edge of being significant or not. In other words, while there's a 10% difference, if we randomly selected the results, it would be reasonably likely that we would get this sort of difference.

When the away team wins the toss, they've won 27.1% of matches (282/1039) vs 24.8% when losing the toss (277/1117). This is a relative probability of 1.094: away teams have won 9.4% more often when they've won the toss than when they've lost the toss. Again, there is a difference, but it's not statistically significant.

The reason why it can be significant with the full group, but not with any sub group is due to the smaller sample sizes.

The similarity can be represented fairly well graphically.

The result proportions for home and away are very similar, regardless of who won the toss.

Now at this point, I wondered if this was simply due to older tests, where perhaps there was less doctoring of pitches. It is an interesting idea that pitches are doctored more often now. I would have thought that if anything, the nature of pitches round the world is now more similar.

To look at this, I selected a completely arbitrary cut off point of the 1st of January 2000. Looking at matches that started after that date, I found these numbers:

Overall the team that has won the toss has won 260 out of 680, while the team that lost the toss has won 252. That's a relative probability of 1.032 ie. in the past 15 years, the team that won the toss has won 3.2% more often than the team that lost the toss.

That's an almost negligible difference.

Breaking it down to home/away it gets even closer.

When the home team won the toss they've won 46.9%, when they lost the toss, they've won 46.9%. The difference is so small that you have to go to the 4th significant figure to be able to measure it.

When the away team won the toss they've won 29.4%, when they lost the toss, they've won 27.4%. The relative probability is 1.072. Surprisingly this is much larger than the advantage for the home team, which suggests that the difference is just down to the effect of randomness rather than the effect of the toss.

Here it is visually:

Again the similarity is remarkable.

So, to assess our original question: does the toss have a major impact on the result of the match? No. Absolutely not. Winning the toss has historically only given teams an 11% higher chance of winning, and recently that's reduced to only 3.2% since the year 2000.

*picture of Bradman and Allen at the coin toss thanks to Wikimedia.

The McCullum Conundrum

There seems to be a regular pattern to cricket related chat in New Zealand. It often refers to Brendon McCullum.

A number of people want him dropped. They mention that he has only scored 1 hundred in the past 3 years. That he averages in the low 30's in test cricket and that he's too arrogant.

A roughly equal number of people want him to remain in the team, talking about how "form is temporary, class is permanent" and mentioning his successive fifties against England, his double century in India and his good captaincy.

While engaging in one of these fruitless (but fun) discussions, I noticed something surprising in his numbers. His away form has been horrible recently, but his home form has been remarkably good.

Here's what I mean. He has played exactly the same number of tests both home and away. In 41 tests at home McCullum has scored 2531 runs at a respectable average of 41.49. However, in 41 tests away he has scored 2153 runs at a much more pedestrian 29.90.

That's a fairly significant difference, but it wasn't always like this. Up until the end of 2010 his numbers were fairly similar. It's only since then that things have changed.

	Home			Away
Year	Matches	Runs	Average	Matches	Runs	Average
2004-2010	29	1669	37.93	27	1563	36.34
2011-2013	12	862	50.71	14	590	20.34

His career progress in terms of home and away is visually quite interesting.  Here are a couple of graphs to show the difference:

If we break it down by year we also see something interesting:

We can see that there has been a big difference in average per year at home and away from 2011 onwards.

This isn't due to the teams that he has played either.  In that time McCullum has played Zimbabwe, England, South Africa and West Indies both home and away, and has played against Pakistan at home, and Sri Lanka, Australia and Bangladesh away. There is no particular difference in the strength of his opponents at home and away in that time.

I also looked at a weighted 7 match average. This is where I look at an average for 2 games either side of a match, and 3 games either side of a match and average those two averages. It's a reasonable guide to the form that a batsman is in, and it normally covers 12-14 innings, so it is a reasonably reliable guide.  Again I broke it up into home and away.

We can see here that his career was tracking along similar lines for a long time, but then they started to split. The latest weighted average is at just over 57 for home matches, and just under 16 for away matches.

If McCullum was able to replicate his home form away from home, there would be no more questions asked about his place in the side.

I wondered if part of the difference was due to where he batted. He has moved around the order a bit recently, and wondered if he was more likely to play in positions that didn't suit him away than at home.

However I quickly checked his averages at different positions options, and found that there was a significant difference in his average at home and away for every group of batting positions. As an opener he averages 51.80 at home and 32.13 away. Batting from 3-5 he averages 37.40 at home and 30.57 away. In the lower order (6-9) he averages 41.26 at home and 27.72 away.

The question then remains as to what he can do about it. How does he become good at batting in conditions he can't practice in?

One option is to play a season of first class cricket as an overseas player.  He has played 3 matches in his career as an overseas pro, in 2007, and was quite successful, but picked up an injury doing so.

The difficulty is finding somewhere that takes overseas players, and plays their first class cricket when NZ is not playing, where the standard is high enough to be useful. Martin Guptill played second division cricket in England, and dominated, but that did not translate to his test game improving significantly.

Given that he's captain, it makes it more difficult for him to be able to find time to play in England also. But that does bring another question. Is the difference due to captaincy? Are the difficulties of captaining a side on tour affecting his game?

This is a difficult question to answer initially, as he wasn't captain at the start of his career when he was going well, but he also wasn't captain all the time when his away form started to dive. I first of all looked at the over all numbers, which are quite different. When he was not captain, he averaged 39.11 at home and 32.55 away. When he is captain his numbers are truly astounding. His home average is 59.85, while his away average is 15.18. However, if we just look at the matches where he was not captain since 2011, his averages are 44.30 at home and 23.50 away. It seems as if the impact of captaincy is exaggerated due to the fact that he is captain at a time where he is already struggling away from home. Also his away matches as captain have been against South Africa, England and Bangladesh. McCullum has struggled against left-arm spin at times, so Bangladesh, with 3 left arm spinners, is hardly the best tour option for him personally. (Just under half of his dismissals as a captain have been to left arm spin bowlers) Also England and South Africa are two of the more difficult places to tour.

If Brendon McCullum can find his form away from home, he is capable of becoming one of New Zealand's greatest ever captains. He has at his disposal probably the most solid batting line up New Zealand has ever produced combined with what is turning into one of the most lethal opening bowling attacks ever.  It may be worth playing a tour without him, in order to get him to play some serious first class cricket overseas and allow him to improve his away game.

Tearing down the strongholds

Last year I looked at the fortresses, the grounds where the home teams dominate. The article is here

Over the past couple of months there have been matches at 3 of the top 4 grounds in this list.

NZ was beaten by South Africa in Wellington.
Australia lost to Sri Lanka in Hobart
and this morning West Indies crumbled horribly to lose to Australia at Arnos Vale.

South Africa should probably be glad that they didn't schedule any ODI matches in the Sri Lanka series at Newlands.

Where batsmen flourish

This year has seen a shift in the usual trends for where people score runs in test matches.

Traditionally India and the West Indies have been the best places to bat in. While at the other end of the scale has been England, New Zealand and South Africa.

Most countries have had batting averages around 30, with Australia, Bangladesh, Pakistan, Sri Lanka and Zimbabwe all having a historical average between 30 and 31.

Here is this year's table:

Host Country	Matches	Average	Strike Rate
England	7	37.05	54.86
India	3	35	55.07
U.A.E.	3	34.94	42.85
Bangladesh	4	34.7	50.59
Zimbabwe	3	32.92	48.05
Sri Lanka	3	31.25	47.22
New Zealand	2	29.87	45.62
South Africa	5	26.66	52.01
Australia	4	25.71	50.1
West Indies	5	23.41	42.96

India has remained near the top, with a lot of runs scored at a good rate in the 3 matches there, but England has moved from near the bottom of the list to the top. This is perhaps because neither Sri Lanka or India had particularly penetrating bowling attacks, and as a result England prospered significantly.

West Indies also swaps ends. This is in part due to no matches being played in Antigua this year, and most of the matches being played on new grounds. Providence stadium averages a full 10 runs per wicket less than the Bourda 8km up the road.

It will be interesting to see if England continue to be a good place to bat, and if the West Indies continue to be a graveyard.

"England vs India" vs "India vs England"

In a series where one team wins comfortably, it can normally be expected that that team would score the most runs. I was interested to see that in the England India series in England that was not the case. In fact, Duckworth and Lewis decided the result of every game except one, and as England was always batting second, they had to score a lot less. England actually faced 421 less deliveries than India, that is about 1 and a half innings normally.

** Trivia Alert **
This was the second ODI series this year where a team got clean swept despite scoring more runs than their opponents - It also happened in the West Indies tour to Sri Lanka.
** Trivia over - back to statistics **

Despite playing shorter innings, England relied on the boundaries less than India, instead getting their runs inside the field. They ran about 58% of their runs, while India ran about 54.5%.

However If we look at the series in India, the results are reversed. India still ran about 54.5% of their runs, but this time England only ran about 51% of their runs. Each series the team that relied the most on boundaries lost the series.

The activity rates were interesting too. In England it was England 0.64, and India 0.54. In India it was England 0.45 and India 0.56. It is interesting, because the difference between the two teams at home and away was largely the running between wickets and fielding. Both of them scored a similar number of boundaries in either series.

It leads me to question if it is harder to judge a run in home conditions or away conditions across the board, so this was the next thing I looked into. Here are some numbers from the last 10 years:

team	run runs (rr)	run outs (ro)	balls faced (bf)	rr per ro	bf per ro
home	119488	682	275772	175.2	404.4
away	117718	746	281803	157.8	377.8

Now this is a quite significant difference, about 10%. It certainly brings up questions for further analysis. It would be interesting to see if this is true for other modes of dismissal, and which teams have the biggest difference between their home figures and their away figures.

Tigers at home, Pussycats away

It has been said that the Indian team were tigers at home, and pussycats away. The idea was that to beat India in India was a real achievement, but beating them away was in a similar class to beating Zimbabwe or Bangladesh. Now this is obviously an exaggeration, but the current series between India and England looks like two completely different teams to the previous series in England.

England have gone back to their recent history of being rubbish at One Day Cricket (won less than 44% of matches against test playing nations in the last 10 years) and India look like champions again.

So the question arises, is there a statistical difference between their home and away performances?

Over the last 5 years, England have won 27 home matches against test opposition and lost 21, giving a home win/loss ratio of 1.28. Away from home they have won 18 and lost 26, giving an away win/loss ratio of 0.69. Quite different. India have won 34 and lost 17 at home giving them an impressive home win/loss ratio of 2. Away they have won 33 and lost 30 (much better than the stereotype) with a ratio of 1.1. This means both teams are roughly twice as good at home as they are away.

So who are the most 2 faced teams? Here is the list of all teams, and their percentage better at home than away in the last 5 years against test teams:

Team	W/L Home	W/L Away	% change
New Zealand	1.61	0.36	347
Pakistan	2.25	0.75	200
Zimbabwe	0.36	0.16	125
England	1.28	0.69	86
India	2.00	1.10	82
Bangladesh	0.75	0.44	70
Australia	2.25	1.70	32
South Africa	2.90	2.44	19
Sri Lanka	1.36	1.20	13
West Indies	0.53	0.48	10

The big surprise for me was the first team. New Zealand have been appalling on the road, performing worse than West Indies or Bangladesh. But at home they sit in 5th place.

Breaking it down a bit, New Zealand score at 5.78 at home, but only 4.8 away. A difference of almost 1 per over. The days of New Zealand being a place were regularly defended are long gone.

Team	RPO Home	RPO Away	Difference
New Zealand	5.78	4.80	0.98
India	5.79	5.25	0.54
Zimbabwe	4.67	4.14	0.53
England	5.40	5.06	0.34
Pakistan	5.30	5.00	0.30
South Africa	5.70	5.44	0.26
West Indies	4.97	4.86	0.11
Bangladesh	4.46	4.55	-0.09
Sri Lanka	4.90	5.10	-0.20
Australia	5.22	5.45	-0.23

In fact the transition in New Zealand's home scoring rates has been phenomenal. Before 2004 there had only been 2 seasons where NZ scored over 5 rpo at home, Since then they have scored at over 5 every year, and scored over 300 at least once per year. The days of the low slow NZ ODI pitch is long gone.