Win the toss win the match?

In watching this world cup, there have been 6 sides who have looked a step ahead of the others: Australia, England, India, New Zealand, Pakistan and South Africa. There have been 8 matches featuring two of those 6 sides.

Pakistan beat India. Pakistan beat New Zealand. New Zealand beat India. England beat Australia, Australia beat South Africa, South Africa beat England, New Zealand beat England and Australia beat Pakistan.

Interestingly, in 7 out of those 8 matches, the team who won the toss, won the match.

If the toss was independent, the chances of this happening are about 3.5% (9/256 for anyone who wants a more precise answer). That is very unlikely. But it is not so unlikely that it would be considered impossible.

If I throw 8 coins, every now and again it will come up with either 7 heads or 7 tails.

It made me wonder if the toss was a significant contributor to team's success, and if so, what can be done about it.

The first thing to do is to build a model to predict the outcome of matches. This is important, because England beating Papua New Guinea after winning the toss does not say much about the importance of the toss, because England would probably beat Papua New Guinea if they lost the toss too.

I decided to use logistic regression to build the model. I looked at every international match between 2 sets of competent (or semi-competent) side in the last 3 years. Looking back afterwards, I noticed that I had left out Nepal (who did deserve inclusion) but they were the only team that the ICC currently have ranked in the top 20 that I left out. I also included a few lower ranked sides in order to give a better picture of the difference between the teams near the bottom of the rankings for the T20 World Cup. So I also included the likes of Singapore, Kenya, USA and Malaysia.

I chose to use logistic regression because it has been helpful in the past for giving realistic probabilities of winning for limited overs matches. When I tested the model, it explained about 85% of the variation in results. When it said that a team had a 50% chance of winning, they generally won about 50% of the time. When it said that a team had a 70% chance of winning, they generally won about 70% of the time.

It is not perfect, but it is simple enough and close enough to tell us about the impact of the toss.

The factors that I used were the team, the opposition, and if the match was home, away or neutral.

The model suggested that the 6 teams that I listed above, along with Afghanistan were the 7 best teams. It probably overstated the strength of Afghanistan, due to them not playing at home at all, and so therefore missing out on the home advantage. Their players are so familiar with their adopted grounds that they have an advantage there that is not accurately reflected in the tag "neutral."

Once I had built the model, I could then make predictions about all the world cup matches.

In this graph, I have the modeled probability of winning on the x-axis and then the actual outcome on the y-axis. The green points are where a team has won the toss and the red ones are where they have lost the toss.

I have divided the data into 3 groups - expected loss, too close to say, and expected win. The numbers are the proportion of wins by the team that won the toss (green) or lost the toss (red).

We can see that the team that won the toss has won more than the team that lost the toss in each of the 3 regions.

This is fairly compelling that there is an advantage in winning the toss. But it is not nearly as dramatic as 7 out of 8 in the first sub-group that I looked at.

This made me wonder if there was some sort of accidental gerrymandering with the way that I selected the data. So I tried 5 groups instead of three.

This time I grouped them together, and looked at the expected number of wins against the actual number of wins.

This time I added in two parallel trend lines, and looked at the difference between them. The groups of teams who won the toss ended up winning about 1.5 more matches than the groups of teams who lost the toss.

This was interesting, but I was not sure what to read into this. So I decided to re-randomise the toss, to see what would have happened with an independent toss.

To do this I randomly assigned to each match one team as the designated toss winner. Then I redid the groups, and saw what the difference was. I wanted to know how rare a difference of 1.5 was.

It turned out to be more common than I would have expected. After 10000 trials, I found that roughly 10 % of the sets had a difference of more than 1.478, and roughly 10% had a difference of less than -1.478. For a re-randomisation, 10% is about the cut off where you say that it was likely or unlikely to have been caused by natural variation. 

This was a surprising result. I was expecting to find that there was clear evidence that winning the toss improved the chance of winning, but instead I found out that it might do, or it might be just natural variation.

There are two major errors in statistics: saying too much or saying too little. This situation looked like one that had the potential to put egg on my face no matter which way I went. There was not quite enough evidence to be very confident that the toss made a difference, but there was also enough evidence to be quite confident of that fact.

I wanted to try one more test before I decided that I didn't know what to say.

This time I picked 60 random innings from any match in the past 3 years. I applied the model to that innings, and then grouped the innings and found the difference between the two lines. I repeated that 1000 times.

This time I found more like what I was expecting.

Less than 1% of the randomly selected innings had the impact of the winning the toss as high as it has been in the world cup. Interestingly, the teams that lost the toss actually had a slight advantage (1.7% of the time losing the toss had an advantage of 1.478 or more matches)

This tells us two interesting things:

Winning the toss seems to have given teams an advantage in this world cup, and it does not normally give teams any advantage whatsoever.

I wondered if that was due to the dew factor. It can often get harder to bowl as the match wears on due to dew in the gulf states. But that does not seem to have been the difference. Winning the toss was roughly as much of an advantage in the daytime as it was in the nighttime.

The biggest single factor seemed to be Dubai International Stadium. Matches there seemed to be much more toss dependent than almost anywhere else.

And that is where the final is being held.

Given that, the toss is likely to give an advantage to whoever wins it. Or perhaps it will revert to type, and there will be no advantage.

Assuming that the toss should be factored in, my model has the following probabilities for the final:

If Australia win the toss: Australia 67%, NZ 33%.

If New Zealand win the toss: Australia 30%, NZ 70%

Neither team is 100% or 0% in either scenario, but there's clearly an advantage.

Now it will be up to the players to see if they can overcome it.

Is it game over if you lose more than 2 wickets in the powerplay?

I recently observed this conversation on twitter:

It immediately made me wonder if Aakash was correct. Do you lose if you are more than 2 wickets in the power play of a T20 International.

I decided to find out. I felt that it was probably best to only look at situations where a team had batted first, as there is not any external scoreboard pressure (or lack thereof) interfering with the batsmen's mind sets.

I looked at every match where there was a result inside 20 overs (I ignored matches that had ended in a super-over or bowl-off) and looked at how many wickets down the team were after 6 overs. I didn't count "retired hurt" as a wicket, despite there being a change of batsmen and the batting team losing momentum similar to when a wicket falls.

Once I did that I came up with some quite interesting numbers.

Wickets Down	Wins	Loses	Winning %
0	41	18	69.5%
1	74	48	60.7%
2	52	51	50.5%
3	11	36	23.4%
4	5	10	33.3%
5	0	3	0%

It's fairly clear here that losing wickets early hurts the probability of winning. This is not really a surprise, often teams bat their best batsmen at the top, and the subsequent batsmen have to take fewer risks if there are not many wickets left above them. However while there are a lot of incidents of teams losing 1 or 2 wickets, our sample size is quite small for the other number of wickets. I've graphed it, adding in a 95% confidence interval. This indicates what range we can expect the actual winning probability to lie in per wicket loss: The shorter the line, the more reliable the data.

We can clearly see the trend here. But we also notice the huge gap between being 2 down and being 3 down. There does seem to be a difference between losing 2 wickets or losing more than 2 wickets.

Accordingly I broke it down into 3 groups. Less than 2 wickets, 2 wickets or More than 2 wickets. Here's how that looks:

Roughly teams win two thirds of the matches where they lose less than 2 wickets, half of the matches where they lose two wickets and about a quarter of the matches where they lose more than 2 wickets.

I also broke it down further by team, and this holds true for almost every team. The only team that has won more than half of their matches when batting first and losing more than 2 wickets in the power play is Ireland. (Interestingly Ireland has the 4th best winning record of any team batting first, and then they are not far behind Pakistan, Sri Lanka and South Africa).

Sri Lanka win just under 80% of t20's when they lose 2 or less wickets in the power play, but 20% when they lose 2 or more wickets. England win just over 60% if they keep their wickets in hand, but only 20% when they lose 3 or more in the power play.

With the World T20 getting underway, how the teams approach the first 6 overs could be a fascinating thing to keep an eye on.

Who are the most reliable 6 hitters

I noticed that the ICC have set up a new game, where you need to pick a player who is going to hit a 6.

This is an interesting option, as there are not many stats out there for how reliable batsmen are at hitting 6's. We know how many 6's a player has hit, but how regularly they hit them is another issue. For example, Aaron Finch has hit 21 sixes in the 9 matches he has played in the last 2 years. However those 21 sixes came in just 4 innings. In the other 5 matches he didn't hit any. Once he gets going he really starts to pepper the boundary. In comparison, Ziaur Rahman from Bangladesh has hit 10 sixes in the 11 matches he's played in that time. However he's hit those 10 sixes in 6 matches, meaning there are only 5 that he hasn't hit a six in. In other words Finch has hit more sixes per match, but Rahman is significantly more reliable.

As the ICC game is about either hitting a six or not, the most important stat is their reliability, not their sixes per match.

To help out anyone who is playing that game, I've compiled a list of the 6 hitting reliability of players who had played 5 or more matches in the last 2 years. I've listed everyone who has hit a 6 in 40% or more of the matches.

If you want to join my league - here's the link.

Player	Matches	Sixes	Innings with a 6	P(hits a 6)
SE Marsh (Aus)	5	5	4	80%
DR Smith (WI)	9	16	6	66.7%
Yuvraj Singh (India)	11	21	7	63.6%
MDKJ Perera (SL)	11	14	7	63.6%
AM Rahane (India)	5	4	3	60%
SR Watson (Aus)	14	30	8	57.1%
RR Patel (Kenya)	14	17	8	57.1%
MJ Guptill (NZ)	14	15	8	57.1%
HD Rutherford (NZ)	7	9	4	57.1%
MN Waller (Zim)	7	5	4	57.1%
Gulbadin Naib (Afg)	11	12	6	54.5%
Ziaur Rahman (Ban)	11	10	6	54.5%
MEK Hussey (Aus)	11	8	6	54.5%
Mushfiqur Rahim (Ban)	13	11	7	53.8%
BB McCullum (NZ)	17	26	9	52.9%
KA Pollard (WI)	17	25	9	52.9%
DJ Bravo (WI)	19	18	10	52.6%
MN Samuels (WI)	16	26	8	50%
MJ Lumb (Eng)	12	13	6	50%
R Gunasekera (Can)	8	4	4	50%
JL Ontong (SA)	6	6	3	50%
MW Machan (Scot)	6	4	3	50%
CH Gayle (WI)	15	26	7	46.7%
DA Warner (Aus)	15	22	7	46.7%
LMP Simmons (WI)	11	12	5	45.5%
MR Swart (Neth)	11	12	5	45.5%
DA Miller (SA)	11	7	5	45.5%
AD Hales (Eng)	20	18	9	45%
AJ Finch (Aus)	9	21	4	44.4%
Ahmed Shehzad (Pak)	16	14	7	43.8%
Mahmudullah (Ban)	14	12	6	42.9%
Mohammad Shahzad (Afg)	14	11	6	42.9%
Asghar Stanikzai (Afg)	7	5	3	42.9%
LJ Wright (Eng)	19	20	8	42.1%
DT Johnston (Ire)	12	9	5	41.7%
Shakib Al Hasan (Ban)	12	7	5	41.7%
Mohammad Hafeez (Pak)	25	20	10	40%
GJ Bailey (Aus)	20	16	8	40%
F du Plessis (SA)	15	11	6	40%
RS Bopara (Eng)	10	10	4	40%
NJ O'Brien (Ire)	5	2	2	40%

CricketGeek Player Profiles: Samuel Badree

© WICB Media - Pal Pillai

I had intended to write a profile on Badree before the tournament started, but school work got in the road. Samuel Badree is possibly the most under-rated player on the planet right now. While his Trinidad and Tobago team mate, Sunil Narine has attracted all the headlines with his funky hair style and mystery deliveries, Badree has avoided the attention, despite also taking wickets and not conceding many runs.

Narine looks special. He holds the ball in a strange way. He flicks his wrist when bowling off spin. He turns it both ways. When he is bowling drama is in the air. It's totally absorbing. Badree is almost the opposite. He does get some turn, both ways, but it's not particularly exaggerated.

Badree is instead the master of line and length. He has enough variation that the batsman can't settle down, but enough consistency that if they wait for the bad ball his whole spell might have gone by and they've only had one ball to hit. For a leg-spinner that is exceptional. Narine is someone who you can't take your eyes off. At the end of a Badree over it is hard to remember anything happening. He bores the batsmen into submission. And he does it well.

His boringness is part of why it has taken so long for him to reach international cricket. He played his first match for Trinidad and Tobago in January 2002. It took until June 2012 before he made his international debut. 10 years is a long time to wait for a call up, particularly in the West Indies who seem to go through spinners faster than Hollywood celebrities go through spouses. In that time there have been 25 other players bowl at least 10 overs of spin for the West Indies.

He's only played 5 T20 internationals, so it is hard to draw much from his statistics in the international game, but he has played a lot of matches for Trinidad and Tobago, and his record for them is remarkable.

Career Economy Rate - minimum 100 overs

The most important question is really how many runs does a bowler concede.



We can see that he is unmatched in this arena. He is so miserly that if Daniel Vettori bowled 3 overs per match, and Badree bowled 4 overs per match, Badree would still average less runs per match than Vettori. Or Steyn, Ajmal, Swann, Malinga, or anyone else with an economy rate over 6.2.

Career Bowling Index - minimum 100 overs

The bowling index is found by multiplying the runs per ball and the runs per wicket. It is one of the best guides to the effectiveness of a bowler.



This time Badree is second. He's got the second best bowling index of anyone who has ever played, and the only one ahead of him, Narine, is yet to suffer second year syndrome, when he has to adapt to players figuring him out. There are a lot of very good bowlers behind him in this list.

Career bowling Contribution: - minimum 100 overs

Every wicket is worth about 5 runs to a teams total. So I subtract 5 runs per wicket, and then work out the economy rate. For more info see this post:



Again Badree's numbers are better than anyone else.

An argument can be made, of course, that it's one thing to succeed at the lower level, against players who are not very good against spin. How does he go against higher class opposition.

To answer this I looked at just his statistics in matches against teams with a heritage of spin, or from an area known for spin bowling. Generally a player who has grown up in one of these areas is likely to have developed a better technique against spin bowling. The teams that I have counted as good against spin are Guyana, Deccan Chargers, Ruhuna, Mumbai Indians, Chennai Super Kings, Bangladesh A, India A.

Against these teams he has bowled 36.5 overs and taken 8 wickets for 202 runs. That's an economy rate of 5.48. Worse than his career average, but still remarkably good. Of the bowlers who have bowled more than 100 overs, only Sunil Narine has a lower economy rate.

Likewise if we only look at his numbers against international teams he has bowled 35 overs, (some for West Indies, some for T&T in tour matches) and taken 7/182. That's a economy rate of 5.2. This would put him ahead of Narine, despite only counting matches against international teams.

Before the match Australia said that they were going to try and target Badree. That resulted in both of their openers ending up back in the shed. Bowling to Sri Lanka is a different prospect to bowling to Australia, but going by current form it seems unlikely that even the might of Sri Lanka will have an answer to scoring quickly off Samuel Badree.

He might be boring, uninspiring and easy not to notice, but his numbers are remarkable. At the end of the day a bowler's job is to take wickets and not concede many runs, and this is exactly what Badree excels at.

Group 2 Net Run Rate calculator

Here is a net run-rate calculator for group 2 of the World Twenty 20.

There are two possible scenarios where net run rates (nrr) will come into play. Firstly if India and Pakistan both win then there will be a 3 way tie between India, Pakistan and Australia. Nrr will decide 1st, 2nd and who goes home in this situation. The other situation is if Australia and South Africa both win. Here Australia will go through as the top qualifier, and it will come down to nrr to decide which of South Africa, Pakistan and India go through.

There are some instructions inside the frame, but you may need to scroll around. Once you type in some number the net run rate will automatically change on the right. Again you might need to scroll to see it.

Law 23 and Steven Finn

Here is a snippet from Law 23, Part 4:

"vi) the striker is distracted by any noise or movement or in any other way while he is preparing to receive, or receiving a delivery. This shall apply whether the source of the distraction is within the game or outside it."

The conditions for a dead ball are quite clear. The batsman has to be distracted. If the batsman is not distracted, then the ball should not be declared dead.

The test is not "does the umpire think that the batsman should have been distracted." The test is "was the batsman distracted."

The timing is also interesting. When is the ball dead? A possible argument is that the ball should be declared dead immediately once an umpire feels that the batsman is likely to be distracted. However that's not the test. The test is if the batsman was distracted. The ball also does not have to be declared dead immediately once an incident has happened. See for example Tom Smith's description of how to rule on an injury:

"Example 4
The ball has been hit into the outfield and the fielder, in attempting to stop it, falls and is in obvious pain through a serious injury.
Before calling Dead ball, the umpire should look to see if the ball is continuing towards the boundary. If it is and it will reach the boundary almost immediately, he would not call Dead ball as once the ball crosses the boundary it is going to be dead anyway. By delaying the call he will neither be depriving the batting side of a boundary nor unnecessarily delaying getting attention to the stricken fielder"
(Smith, 2003, p.167)

It is completely within the consistent ruling of Law 23 to see what happens, and then call the ball as dead if necessary.

Which brings us to the Steven Finn breaking the wickets with his leg. The correct ruling here is that the umpire should see if the batsman was distracted or not before calling the ball dead.

If the batsman hits the ball for 4, or 2, then it should not be a dead ball, as the batsman was clearly not distracted. If the ball goes down the leg side for what would have normally been called a wide, then it should be called wide, not dead ball, as even if the batsman was distracted there was no opportunity for him to play a shot to it.

In the South Africa test where the precedent was set the first three were not called. It was only once Graeme Smith approached the umpire saying that he found it distracting that the umpire started to call it dead.

In the Super 8 match James Franklin did not make any such complaint, as as a result the law was applied incorrectly.

Incorrect interpretation of this rule cost New Zealand significantly in the last game. It would be crazy if it continued to be ruled incorrectly throughout the rest of the tournament. This is not something that the MCC Laws sub-committee needs to look at. The law is clear, and just needs to be applied correctly.

World T20 Statistics

Here is a list of tables of some different statistics from the World T20. I have separate tables for the Group stage, the Super 8's and the overall data. Interestingly the batting numbers are reasonable similar, but the bowling numbers are significantly different. This is possibly a reflection on the strengths of the teams that missed out on the next stage, Bangladesh, Ireland and Afghanistan all have strong bowling line-ups and while Zimbabwe's strength is normally more about their batting, it didn't really fire in this tournament.

All of these are statistics that I have worked out previously, although I had to modify my DL partnership formula to reflect the nature of T20 cricket. I decided to use a score of 147 as an expected score as it's 56.6% of 260, and 56.5% is the resources left in an ODI match shortened to 20 overs.

I will try to update these regularly throughout the tournament.

Best innings:

For more info on how this is calculated see this post:

Group stage
Super 8's
Knockout Stage *
Overall Tournament

Best Partnerships:

Here I take into account the teams situation at the start and the teams situation at the end. Effectively these are the partnerships that have made the biggest contribution to their team's score. For more information see this post:

Group stage
Super 8's
Knockout Stage *
Overall Tournament

Contribution made by bowlers:

Every wicket is worth about 5 runs to a teams total. So I subtract 5 runs per wicket, and then work out the economy rate. For more info see this post:

Group stage
Super 8's
Knockout Stage *
Overall Tournament

Activity rates:

This is the runs a batsman scores per delivery that doesn't get hit to the boundary. I explain this in more detail in the glossary:

(minimum 10 balls faced)

Group stage
Super 8's
Knockout Stage
Overall Tournament

*I have reached my page limit on this platform, so these pages are in a different format.

CricketGeek Player Profile: Elias Sunny

In July this year, Elias Sunny became the first person to be named man of the match on debut in two different formats when he took 5/13 against Ireland at Stormont. It was another notch in what has become a stellar start to his cricketing career. He also took 6/94 on test debut.

Sunny is a slow left arm bowler, but he bowls with quite an open action, so the ball comes from a slightly different angle than an orthodox left-arm spin bowler. This has given him an ability to get left handed batsmen out with more regularity than most left-arm spinners. He also turns the ball quite sharply, and tends to bowl a slightly different length than most orthodox spinners. These combine to make him a real danger man for teams playing against Bangladesh.

His different angles mean that he's likely to be a particular threat to batsmen who have not faced him before, although he has shown the ability to get out some batsmen repeatedly, notably compatriot Mahmudullah, who he has dismissed a number of times in domestic cricket.

His international T20 record is remarkable, averaging 12.22 with an economy rate of 5.50, but that is somewhat artificial, given that he has only played against Ireland, the Netherlands and Scotland. However his overall T20 record is still very good, and includes being the local player of the Bangladesh Premier League. Here is a graph of his career averages.

We can see he is settling in to an average of under 20, and an economy rate close to 6. If he can translate that to international cricket he will be a massive asset to Bangladesh, and could be part of the catalyst that they need to go to the next level.

This tournament is likely to be a good litmus test for him. We may get the chance to see if he has just had a good start, or if he really is as good as his figures would indicate.

CricketGeek Player Profiles: Glenn Maxwell

Glenn Maxwell is an exciting young allrounder from Victoria. He is a very quick scoring batsman and a handy off-spin bowler.

His recent form has been very impressive. He had a reasonable BBL for the Renegades, played a couple of games for the Delhi Daredevils, but then really shone for Hampshire in the Friends Life t20 in England.

He had the 8th highest batting index in the competition, with an average of 44.75 and a strike rate of 175.49. To add to that he took 7 wickets at an average of 25.5 and an economy rate of 7.56.

He has proven to be particularly good at hitting boundaries, scoring roughly on boundary every 5 balls. He's also developed a reputation as a great fielder.

Here are a couple of graphs of how his career t20 averages have shaped up recently.

His batting averages are going up, and generally his bowling averages are going down. This is exactly what should be happening for a quality player in his breakthrough season.

But the ultimate proof of his rise is that the Australian selectors have opted for him ahead of Dave Hussey, the highest run scorer in t20 history. How he goes in that role will be interesting. The one thing that his opponents will probably be aware of is that he has tended to get out to off-spin early in his innings. That's not exactly a good weakness to have in Sri Lankan conditions, but it also might be something that the selectors feel is just an anomaly.

CricketGeek Player Profiles: Jeevan Mendis

When talking about Mendis, the first name that comes to mind for modern cricket fans is Ajantha, the mystery spinner. For slightly older fans, there could be a number of players thought of, as there have been over 30 players called Mendis play first class cricket in Sri Lanka (and one Gehan Mendis play 366 first class matches in England). The subject of this profile, however is Jeevan Mendis.

At schoolboy level Mendis was a star with both the bat and ball for the prestigious St Thomas' School. He got a call up to play in the Under-19 team, and he continued to shine, having respectable averages of 51 with the bat and 13 with the ball.

It has taken him a while to become a regular player for the national side, but he is starting to establish himself now. In his recent domestic T20 matches he's averaged about 30 with the bat and about 24 with the ball. If he can keep this ratio up in the international level, he could become an indispensable bits-n-pieces players, like Albie Morkel, Scott Styris or Abdul Razzaq.

He relies more on placement than power with the bat, but he has a good reverse sweep, so he has the ability to create headaches for the fielding captain by hitting the ball to unusual places. He bowls leg-spin, but with a slightly unorthodox grip that make it difficult to read him out of the hand. Accordingly he should be the sort of bowler who can get out the tail quickly, which might be a very useful skill in the first game for Sri Lanka. He might not be a bad player to have in your fantasy team for the match against Zimbabwe.