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.

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.