A better World Cup format

As this world cup draws to a close, I've been thinking about the positives and negatives of the format.

There are quite a few of both.

Firstly the positives:

1. Everyone plays each other.
2. Not too many matches that seem like a mismatch on paper.
3. Teams that lose a couple of games early still have the chance to compete.
4. Guaranteed 9 matches for India, so the ICC get enough money to keep growing international cricket.
5. There was a match or two every day through the majority of the tournament, so that the momentum built towards the finals.

Then the negatives:

1. Not enough representation from lower level teams. The qualification was too difficult, and so the goal of making the world cup became unrealistic for most teams.
2. There were only 3 matches in the final week, meaning that the momentum was lost.
3. Dead rubbers, or similar - 3 teams were effectively eliminated with 2 weeks to go.
4. Incomplete rounds - India being 2 matches behind made the narratives and changes in fortune less obvious. 
5. Pitches were too different from how they've played over the past 4 years, meaning that there was too much of a role of luck in the event. 

The negatives are too great to mean that it's a good idea to continue with the same format in my opinion. But, the positives are things worth keeping.

So, using those positives as constraints as much as possible, and also keeping the tournament to the same length, I have come up with a format that I believe will make for a better event.

World Cup Simulation update - 5 July

Here's the latest update for the world cup simulation. I have New Zealand at 100%, but that's simply due to the probability of Pakistan getting the required run-rate being so low that that possibility never eventuated in the 50000 trials that I used. The probability of Pakistan going through is slightly lower than the probability of someone being shot accidentally by a dog running along a beach while holding a handgun in it's mouth during the next week,

The next graph is the expected points. The simulation has had the correct top 4 from the second match on, however, the expected points and the order of the teams have changed considerably

The top 4 was looking fairly likely from about match number 6 on. There was some excitement from the two upset losses by England, but Pakistan never got beyond 40% on the simulation.

The complete make up of the semi-finalists has not yet been decided, nor has the team in 5th place. Pakistan, Bangladesh and Sri Lanka could all end up 5th. 

Next I looked at the winning probability. This is getting close to the point where it can be calculated analytically without much trouble.

 The next thing to look at is the rankings. A thing to remember here is that it is all relative to Afghanistan, so everybody going up is more an indication that Afghanistan has gone down.

The order that the teams are in here is the same as David Kendix' official rankings order, with one exception - I have India ahead of England, rather than the other way round.

Finally, a little graph to show what Pakistan needs to do to make the semi-finals. They need to keep Bangladesh below the green line.

World Cup simulation update - 1 July

Here's the latest update to the simulation. The first two graphs disagree slightly, and that's because I have two different methods to calculate the expected net run rate. The first one seemed to be slightly more accurate than the second, but there was not a big difference when I tested them. (The margin of victory in cricket matches is actually really difficult to estimate - teams batting second tend to cruise to victory rather than try to win by as big a margin as possible) I decided to use both when doing the calculations. With the first method, New Zealand and India both have a higher than 99.98% probability of going through, while it's 99% for India and 97.7% for New Zealand with the second method. These seem more realistic.

The big thing to notice is the change to England's probability, and how England beating India damaged the chances of both Pakistan and Bangladesh. Pakistan's probability went down by slightly more than Bangladesh's probability because the ranking of India dropped slightly, and Bangladesh need to beat India to get through.

This graph shows expected value - not the most likely value. Those are actually different things. The expected value is the mean of all the expected outcomes. As a result, none of the teams will actually end up with the points that this shows, but they should mostly get close to it.

 It's now looking like there's a roughly 45% chance that net run rate will be a deciding factor in who goes through to the semi-finals.

If Bangladesh beat India (which is admittedly a fairly unlikely outcome), we could then see a situation where Pakistan and Bangladesh are playing for the opportunity to be level on points with New Zealand and India on 11 points. If that is the case, then (in all likelihood) the rained out match between New Zealand and India will have allowed both to progress at the expense of the winner of Pakistan vs Bangladesh.

The most likely semi-finals at this point are Australia vs New Zealand and England vs India, but these are by no means confirmed yet.

In individual matches, England effectively has a higher ranking than that, because teams playing at home get a ranking boost of 0.86 over their opponent. That's why I have England back on top in the next graph:
This one is quite different to what the book-makers have. I have England as favourites, while they have India and Australia both tied for favourite on roughly 30%. They also have Pakistan and Bangladesh at about double the probability that I do.

I used the first net run rate model for the winning probability, but the difference in numbers suggests that the bookies are possibly using a model that is more similar to the second one.

World Cup simulation update

The group stage of the World Cup is now roughly half way through, and there are 4 clear favourites to be the semi-finalists.

Afghanistan is the first team to be eliminated (they may have a mathematical possibility, but they don't have a statistical one). At this point, Sri Lanka are not far behind.

The rankings of the teams have remained fairly consistent, suggesting that the extra weighting for world cup matches is about right.

The fact that almost all the teams seem to have gone up is due to them all being relative to Afghanistan. Afghanistan do not seem to be quite as good as they were seeming to be and so they have dropped, but as they are set to 0, it's pushed everyone else up slightly.

The semi-final probability is the most interesting. 

I personally feel that this is underestimating the chances of South Africa, but we will see as the tournament progresses.

The key point on this graph is match 5, where Bangladesh overcame South Africa. If South Africa had won that match, they would be on about 40% and New Zealand and Australia would both be a lot lower.

The simulation also puts out the points for 4th, 5th and the difference between them. This suggests at the moment that there's only a fairly low chance that net run rate will come into play. However, one more rained out match, or a Bangladesh upset of Australia, and this could change dramatically. This makes the expected lines to be 9 points for 5th place, and 11 points for 4th place.

So far of the teams that I've had as favourite to win, 14 out of the 17 have won. Given the probabilities that the models assigned them, that's slightly higher than I would have expected - I would have expected there to have been 4 upsets rather than 3, but it's still telling me that my model is working quite well. That may be due to teams not always playing their best combinations in every match between the world cup, adding extra uncertainty to the results than exist inside a world cup.

It will be interesting to see if it continues to have the same success rate after the cup is finished.

Finally, applying the same system to find the probable winner gets the following results:

England are still favourites, but India are not far behind them.

Fakhar Zaman's amazing start

18 matches. That's all it took.

1 year and 45 days to go from relative obscurity to being one of the most talked about cricketers in the world. Fakhar Zaman has certainly burst onto the world stage.

I wanted to look into the context around the record, and also to see how his start compares to others.

I then will look at how well we can predict someone's eventual career record based on their start.

Using Added Value to assess cricket performances - Part 3 ODI all rounders

Viv Richards - by Aditya Naikdesai

Growing up in the 1980's, cricket was all about three things: the mighty West Indies, Lance Cairns biffing 6's and the "Big 4" all rounders.

I remember sitting on the school bus as someone was sharing the updates of a match that they'd been listening to on the radio: Viv Richards hit a century, Malcolm Marshall took 3 wickets, Lance Cairns hit a ball onto the roof. I may have been mixing up 3 different games, but that's what every match report felt like.

Other matches were all about the battle between Imran Khan and Ian Botham, or Richard Hadlee vs Kapil Dev. Those 4 players transfixed a generation - each of them had the ability to win a match with either the bat or the ball.

Throughout history, all rounders have been both highly sought after, and incredibly rare. To find a player who was capable of playing as a batsman or a bowler was unusual. To find someone who was a star with both was phenomenal.

There are 43 players who took more than 100 wickets and scored more than 2000 runs in ODI cricket. Some of them were batsmen who bowled a bit, some bowlers who occasionally contributed with the bat, some were "bit's and pieces players." An interesting question is if any were truly all rounders. Were any players both above average batsmen and bowlers?

Using Added Value to measure cricket performances - Part 2 ODI bowling

Reid and Matthews chat before the final over.

It was the summer of 1990/91, just before Christmas. I was on holiday at my Aunty's place in Mount Maunganui. My cousin and I were sleeping in the glass conservatory, looking out over the sand-dunes. The air smelt like salt and sand.

In our little room was a little TV, on the TV was the cricket coming out of Australia.

New Zealand were playing against Australia in Hobart.

I was 11 years old, and I was enthralled.

Danny Morrison was bowling. A year earlier, he had come to speak to my primary school assembly, then signed autographs by the school pavilion. I got him to sign my cricket bat, and I tried really hard to not get it scratched off. He was my favourite bowler. Australia needed 6 runs to win. Greg Matthews was on strike. I wasn't sure why, but as nobody seemed to like Greg Matthews, I didn't either.

Morrison bowled from around the wicket, and speared a fullish ball into leg stump. Matthews drove it, inside-out, through point for four. I really didn't like Matthews now.

New Zealand vs Australia: Head-to-Head

I've heard a number of commentators say that man-for-man, Australia have better players, but New Zealand is a better team. This strikes me as a peculiar thing to say, given that there's often no analysis included of individual head-to-head.

So I've decided to do it myself, in order to see if there actually is a clear difference, man-for-man.

I've tried to line up the players by role. Both teams have players that do similar roles generally, with only a couple of exceptions.

I'm looking at their world cup so far, as well as their numbers since 1 Jan 2013 in New Zealand and Australia.

Role 1 - Slower opener

Player	Guptill	Finch
WC Average	76.00	40.00
WC S/R	108.79	93.64
2 year Average	43.00	37.00
2 year S/R	85.08	87.13

Guptill is in better form, but the 2 year numbers are very close. These are two players of similar ability who are both playing good cricket. Both tend to be slow to start, but are capable of increasing their scoring rate once established.

Role 2 - Fast opener

Player	McCullum	Warner
WC Average	41.00	50.00
WC S/R	191.81	124.48
2 year Average	38.00	40.75
2 year S/R	135.02	104.21

Again the numbers are very close. Warner has the higher average, but McCullum scores faster. Both are remarkably good at both scoring boundaries and finding singles, but both are prone to hitting bad balls straight to fielders. McCullum has shown a weakness against left-arm spin, so there's a chance that Clarke might bring himself on to bowl early on.

Role 3 - First drop

Player	Williamson	Smith
WC Average	37.00	57.66
WC S/R	83.14	94.02
2 year Average	51.08	60.92
2 year S/R	85.64	94.77

These two players are the best batsman for their team in recent times. Smith is ahead on these numbers, but it's wrong to say that Williamson is a weakness in the New Zealand side. Both manage to score at a good rate without looking like they're trying. Both also have a big impact on their team's chances of succeeding. New Zealand win 45% of the time when Williamson scores under 40 and 62% when he scores 40+. Australia have won 53% of the time when Smith's scored under 40 and 86% when he's scored 40+.

Role 4 - Innings builder

Player	Taylor	Clarke
WC Average	30.16	29.00
WC S/R	63.06	92.94
2 year Average	46.82	23.66
2 year S/R	79.30	80.49

Clarke's had a slightly better world cup, but Taylor has produced more quality innings' over the past 2 years, averaging almost twice what Clarke has. These two are both great players, who often play roles that allow others to shine. As a result, their numbers don't truly tell the story of their contributions. Both players' numbers are also a reflection of their battle with injuries.

Role 5 - rebuild or launch

Player	Elliott	Watson
WC Average	37.83	41.20
WC S/R	107.07	107.85
2 year Average	44.76	36.82
2 year S/R	94.63	94.70

A really interesting role in modern cricket is the number 5 batsman. Their role is sometimes to steady a rocking ship, and other times it's their role to attack, and build on the foundation of the players above them. It is difficult to separate the ability of Watson and Elliott to do this role.

They also both have a role to play with the ball as the extra bowler:

Player	Elliott	Watson
WC Average	34.00	74.00
WC E/R	8.5.0	6.72
2 year Average	25.88	101.50
2 year E/R	6.56	6.37

Elliott has been more expensive, but has also broken partnerships quite regularly.

Overall, it's really difficult to separate these two with bat and ball. I'd probably back Elliott as a batsman, but Watson with the ball, despite his numbers not being as good.

Role 6 - Agressive batsman

Player	Anderson	Maxwell
WC Average	38.50	64.80
WC S/R	109.47	182.02
2 year Average	41.77	33.42
2 year S/R	125.96	125.13

One of the dangers of comparing players like Anderson and Maxwell based on statistics is that they are often asked to do different jobs. Against South Africa, Anderson's job was not to come in and score at a massive strike rate. His job was to play sensibly and carry the innings through. Over a longer term it's difficult to separate Anderson and Maxwell. Both are capable of being absolutely breathtaking with the bat.

Both play quite different roles with the ball, so I'll look at them later.

Role 7 - Wicket-keeper batsman.

Player	Ronchi	Haddin
WC Average	14.60	42.00
WC S/R	125.86	157.50
2 year Average	38.88	41.11
2 year S/R	128.84	111.11

Haddin has had a much better world cup, but it would not be difficult to argue that Ronchi has been the most effective death batsman in the world in the past couple of years.

They're also difficult to separate with the gloves. Both are solid keepers who have made a couple of key mistakes, but in general, they've done the job required of them sufficiently.

Role 8 - Bowler who bats

Player	Vettori	Faulkner
WC Average	41.00	14.66
WC S/R	164.00	176.00
2 year Average	15.66	44.25
2 year S/R	123.68	114.56

Faulkner and Vettori have very different styles, but can both be very effective. Vettori has rediscovered his batting form of 2008-2012 in this world cup, during which time he was one of New Zealand's best batsmen as well as being an outstanding bowler. Contrastingly, Faulkner hasn't found his rhythm since returning from injury.

Role 9 - Right arm opening bowler

Player	Southee	Hazlewood
WC Average	27.13	20.85
WC E/R	5.57	4.19
2 year Average	28.97	20.44
2 year E/R	5.53	4.37

Hazlewood has the advantage here numerically, but some of that is due to Southee having a role bowling at the death. I don't think many selectors would pick Hazlewood over Southee, regardless of the difference in their stats.

Role 10 - left arm opening bowlers

Player	Boult	Starc
WC Average	15.76	10.20
WC E/R	4.41	3.65
2 year Average	22.09	14.37
2 year E/R	4.58	4.34

Starc and Boult probably been the two best bowlers in the tournament. They both offer different things. Starc bowls into the pitch with a high arm action that causes the ball to bounce higher, but it also gets less movement and arrives to the batsman later, despite the quicker speed through the air. Boult bowls over his front foot and tends to bowl more deliveries along the wicket than into the wicket. As a result, the ball swings more and arrives at the batsman faster. (Ed Cowan, after facing both, commented that Starc might bowl 5-10km/h faster but you have a lot more time to face the ball. Boult certainly feels faster.)

It's difficult to separate them, but not impossible. Starc has been the premier white ball bowler in the world recently.

Role 11 - 3rd seamer

Player	Henry	Johnson
WC Average	-	24.66
WC E/R	5.00	5.43
2 year Average	19.00	25.15
2 year E/R	4.26	5.04

Henry has only bowled 8 overs this world cup, as he wasn't even in New Zealand's original squad. His first 5 overs included 2 maidens and conceded only 9 runs against South Africa. He went the distance in his next 3 overs, but even then, a large proportion of his runs came through edges and mis-hits. Johnson is a master with the red ball, but hasn't had the success recently with the white ball that he had earlier in his career. It's still difficult to complain about an average of 25 and taking a wicket every 5 overs.

Role 12 - 4th seamer

Player	Anderson	Faulkner
WC Average	16.21	23.00
WC E/R	6.45	4.90
2 year Average	22.69	26.57
2 year E/R	6.42	5.45

This is a slightly more difficult comparison, as Anderson generally bowls at the death. His economy rate here is outstanding, and he's taken a lot of wickets. However, taking wickets with bad balls isn't necessarily a trait that is repeatable. Faulkner looks like a better bowler, despite his numbers not being quite as dramatic as Anderson's.

Role 13 - Spinner

Player	Vettori	Maxwell
WC Average	18.80	36.20
WC E/R	3.98	5.83
2 year Average	35.12	32.91
2 year E/R	4.10	5.24

Vettori is in a different class here. It's probably the only place where there's a clear difference in quality between players doing similar roles in the two teams.

Overall it's really difficult to separate the two teams. Both have a team full of good players in good form. They have players doing similar jobs, often in similar ways.

I don't think I can honestly say at this point which team has better players. The more you look at this match, the more mouth-watering it becomes.

Updated QF prediction chart

In my previous post I ran a simulation to find out potential quarter-final places. I received some criticism for having England so low, and Bangladesh so high, but events over the past 48 hours have shown that the respective probabilities of the two teams qualifying may not have been so far off.

The program that I wrote to do the simulation was corrupted when my computer crashed and I foolishly hadn't saved it, so I've written a different one to re-calculate. This time I made a couple of modifications. I moved from an additive model for run rates to a multiplicative one, as that seemed to be more sensible (teams are realistically a % better than other teams, rather than a fixed number of runs better. We would expect the margins to blow out more in terms of runs on better batting pitches than on difficult tracks).

I also slightly reduced the standard deviation of the simulation by moving it to one quarter of the mean rather than one third. This again made the results seem more sensible. There were too many teams scoring over 400 or under 100 previously.

Here are the new results. This table shows the probability of each team qualifying in position 1, 2, 3 or 4 in their group, and then the total probability of qualifying. Again I have not factored rain into this, and with Cyclone Pam heading towards New Zealand that may be a little optimistic.

Team	1st	2nd	3rd	4th	Quarters
New Zealand	1	0	0	0	1
Australia	0	0.976	0.024	0	1
Sri Lanka	0	0.024	0.9725	0.0035	1
Bangladesh	0	0	0.0035	0.9965	1
-	-	-	-	-	-
India	1	0	0	0	1
South Africa	0	0.976	0.024	0	1
Pakistan	0	0.017	0.664	0.1165	0.7975
Ireland	0	0.007	0.312	0.1405	0.4595
West Indies	0	0	0	0.743	0.743

The potential group results look like this:

Group A

NZ Aus SL Ban	0.9725
NZ SL Aus Ban	0.024
NZ Aus Ban SL	0.0035

Group B

Ind SA Pak WI	0.5295
Ind SA Ire WI	0.1985
Ind SA Pak Ire	0.1345
Ind SA Ire Pak	0.1135
Ind Pak SA WI	0.011
Ind Pak SA Ire	0.006
Ind Ire SA WI	0.004
Ind Ire SA Pak	0.003

The three interesting potential quarter final match-ups to watch for here are

SA vs Aus	4.7%
Ind vs SL	0.35%
Ire vs Ban	0.02%

In reality the probabilities of Ireland vs Bangladesh and Australia vs South Africa are higher, as they are both much more likely if rain starts to fall.

South Africa vs Zimbabwe - things to watch for

Here are 5 things I'm going to be watching for in this match.

1. I really enjoy watching Elton Chigumbura. He's the sort of player who plays to win the match, rather than playing to have a good average. He gives himself the difficult jobs, and then puts everything into them.

2. Will Zimbabwe get Amla early. The Zimbabwean attack is quite suited to most New Zealand grounds, but if they don't get Amla early, then they will struggle to get him at all.

3. Quinton de Kock - can he rein his game in against the slower paced (but subtle and tricky) opening attack of Zimbabwe.

4. Brendan Taylor - Has he regained his touch that made him one of the best batsmen in the world in 2011.

5. South Africa's movement off the ball in the field. De Villiers has made it clear that he wants to see his team moving around more off the ball, like the New Zealand players do. This will be a chance to see if his talk has worked.

Martin Guptill and the form myth

Every season there seems to be a cause célèbre among NZ cricket fans. In 2013 the call was that Brendon McCullum wasn't scoring enough runs, and needed to be dropped. In 2013-14 it was that Peter Fulton wasn't scoring enough runs and needed to be dropped. This season the overwhelming majority of cricket talk in New Zealand has been about one man: Martin Guptill. Apparently he isn't scoring enough runs and needs to be dropped.

In either calls to Radio Sport or comments on the Vietchy On Sport facebook page there have been at least 21 players suggested as being a better option as an opener than Martin Guptill. People have suggested different ways that he might get injured in order to get him replaced in the squad.

But the opinion that Guptill's significantly out if form is not just confined to the uninformed public (I consider anyone that suggest Michael Pollard, Peter Ingram or Kyle Mills as replacements for Guptill uninformed). There have been a number of the country's sports journalists join in. In a quite well written and balanced piece, Andrew Alderson noted that Guptill "struggled for form." Charlie Bristow talked of Mike Hesson needing "to handle Martin Guptill's stuttering form." Mark Geenty commented that the top order was carrying "significance and concern." Guy Heveldt said that Guptill is "under immense pressure to find some form before the World Cup begins." Daniel Richardson said that Guptill is "out of touch", "has done little to inspire confidence" and that his "form is a concern."

David Warner vs Rohit Sharma

Over the past couple of days I've been called a troll, a Jonathan Agnew fan and even an Australia on twitter, because I have a position that is somewhat different from others on the David Warner vs Rohit Sharma incident. The problem is that a nuanced view doesn't fit neatly inside a 140 character window, and so my views have been missinterpreted. Part of that is because people seem to have very absolute views on the matter, when I don't think what happened is really very black and white.

First of all I'll talk about my system of ethics with sledging and other play, and what I consider acceptable, then I'll look at the Warner-Sharma confrontation specifically.

Sledging is an attempt to get a psychological advantage over another player. For me this is part of the game. However, there are limits to what is acceptable. Some examples of forms that are acceptable (in my opinion) are fielders encouraging the bowler in a way that the batsman can hear and that might get into a batsman's head. For example "That's 4 dot balls in a row now" "He's got no idea about the short one" "Look at how he's holding the bat with his bottom hand, I reckon his coach will have words with him about that afterwards. It's causing him to push the bottom of the bat in. I reckon a half volley outside off will see him nick out here." These comments make the batsman doubt either their technique or their form, and can cause them to play false shots.

Likewise batting advice to the batsman is acceptable, even if it's not always genuine. The below example (about 1:20 in) where Hadlee gives Botham some advice on how to play his bowling is a classic. Botham may well have been late on the shot because he was thinking about what Hadlee had said and had anticipated a different delivery.



I f the fielding side feel that the batsmen are doing something underhanded, such at taking a run when the ball was dead, they are entitled to express their displeasure to them.

The more interesting questions are what is unacceptable. Here is my list:

Threats of violence that don't involve the playing of the game. For example "I'm going to break your ribs with the next ball" is acceptable. Likewise "If those close fielders stay there, I'm going to still play my shots and they will get hurt." Both of these, however, need to be in context. A bowler/batsman shouldn't be randomly threatening violence willy-nilly, but in the heat of an exchange they are fine. "I'll see you in the car park afterwards and smash your face in," however is not acceptable.

Racial slurs are not acceptable. They are not acceptable directed at a player or spoken about a player. There's a story about some things that Shane Thompson said to Wasim Akram and Waqar Younis to try and goad them into bowling short at him (rather than yorkers) that are totally unacceptable things to have been said on a cricket pitch.

Abuse for the sake of it is unacceptable. This includes most (but not all) send-offs. There can be time for a witty send off, provided it is brief and concludes an ongoing conversation. Prolonged send-offs, especially abusive ones, are completely unacceptable.

Likewise abusing someone to get under their skin, without there being any relation to the game or without it being in the context of an ongoing conversation is not on. The way that Fleming subjected Smith to a torrent of nastiness when he arrived at the crease may have helped New Zealand tie the series, but it was not something that New Zealand fans should be proud of.

There are other difficult situations, but generally it is fine to sledge, provided it is done in a way that has a purpose, and doesn't cross the line into pure abuse.

Now lets look at the Warner-Sharma situation. Here's my summary of what happened, as far as I understood it.

1. Rohit Sharma was slightly outside his ground, as he's entitled to be.
2. David Warner threw the ball towards the stumps.
3. The ball was very wide of the mark, and (only just) missed Sharma, and then evaded Haddin.
4. Sharma and Raina then proceeded to run an overthrow.
5. Warner thought that the ball had deflected off Sharma and got angry that they ran an overthrow contrary to established protocol.
6. Warner told Sharma that he was unimpressed
7. Sharma said something to Warner in Hindi. Warner speaks a few words of Hindi and didn't understand the full message but was upset by what he did understand.
8. Warner shouted at Sharma to speak English.
9. Sharma repeated his message in English as the umpires separated the players.

The one key point here is number 2. David Warner is a fantastic fielder. He has produced a few blinding run outs from direct hits. One of the impressive things about his fielding is just how often he hits the stumps. Given his ability, the fact that he missed the stumps by about 3m from close range is peculiar. The fact that he almost hit Sharma was concerning. How off target it was can be seen by the fact that Haddin stepped twice, then dived full length, and still didn't get to the ball.

He thought that he had hit Sharma with the throw, and that, therefore, Sharma shouldn't take a run. He didn't appologise for hitting Sharma, which would normally happen. It makes me wonder if he was aiming to hit Sharma with the throw. For me that is the key thing that was wrong with that incident.

What Warner said after that was in keeping with his understanding that Sharma had taken a run he would not normally be entitled to take. Sharma speaking Hindi successfully got in the head of Warner, and I don't have a particular problem with that. Warner's reaction, likewise, was totally understandable in context. The only issue, and it's a big one, was if Warner deliberately tried to hit Sharma with the ball.

If (in the opinion of the match referee) he did, then it would be a level 2 offence and he should be banned for a couple of games. Instead Warner was charged with a level 1 offence for "using language or a gesture that is obscene, offensive or insulting." As he had been found guilty of a similar offense within the past 12 months it was automatically raised to a level 2 offense, but he received the minimum fine for that offence, of 50% of his match fee.

The thing that I don't understand is how he was found guilty of that at all. As far as I can see he didn't abuse Sharma, and he didn't use any offensive gestures that I could see. If Sharma had spoken to him in English, then asking him to "speak English" would have been offensive, but given that Sharma didn't actually speak English, it was a perfectly reasonable request (despite not being delivered in a particularly reasonable manner). In the verbal altercation, Warner and Sharma acted equally badly, but not nearly badly enough for a charge.

If the ICC Code of Conduct was applied correctly here, either Warner would have been charged with deliberately throwing the ball at Rohit Sharma or he wouldn't have been charged at all.

Where does Kane Williamson sit?

The first time I met Brendon McCullum was when he and I were both on the same flight from Miami to St Kitts in 2012, and we both had to wait about 2 hours in for our flight. I introduced myself to him, and he graciously put down his golf magazine and chatted to me for about 30 minutes.

After the flight, while we were both waiting for our bags (which took forever), he found out that we were staying at the same hotel, and so he offered me a lift there, provided I didn't mind going via the training ground. On the way to the ground, he got a phone call from John Wright asking if he was likely to be able to play the next day. At this point he had been travelling for 37 hours, without much sleep, and certainly did not look like he was going to be good to play. He said as much to Wright and then found out that Taylor was injured, and Kane Williamson was going to be standing in as captain.

After he hung up, McCullum couldn't contain his disappointment with that decision. He said something along the lines of "it's not that he's not capable of leading the side, it's more that he's not established in the side yet, and he's still learning his game. He doesn't need the pressure of being the captain-in-waiting to go with it. The kid is so good. He's either going to be the best batsman we've produced since Martin Crowe, or the best batsman we've ever produced, and it's our job to manage him properly to allow him to be great."

Williamson scored 9 off 17, but New Zealand went on to win the match, due largely to a good spell from Southee and Oram, and some suicidal running between wickets from the West Indies.

However the claim that Williamson could be our best ever batsman has stuck with me. Yesterday he completed an epic (but certainly not chanceless) innings of 242* to take New Zealand from a position of some trouble to a being in the box seat.

Since my conversation with McCullum, Williamson has gone on to be quite impressive with the bat. In the past 2 and a half years he has averaged 50.28 in tests and 49.25 in ODI's. In the matches before McCullum's pronouncement he had averaged 36.05 in tests and 35.75 at a strike rate of 83.85 in ODI's.

He's only 24, and there's still plenty of time left, but if his career was to end today, he would still be considered one of New Zealand's best ever batsmen. Here are his numbers, first in tests:

Name	Innings	Runs	Average	Completed innings per hundred
KS Williamson	71	3034	45.96	7.33
LRPL Taylor	113	4631	45.40	8.50
MD Crowe	131	5444	45.36	7.06
MH Richardson	65	2776	44.77	15.50
GM Turner	73	2991	44.64	9.57
AH Jones	74	2922	44.27	9.43
B Sutcliffe	76	2727	40.10	13.60
SP Fleming	189	7172	40.06	19.89
BB McCullum	159	5870	38.87	13.73
CD McMillan	91	3116	38.46	13.50
JG Wright	148	5334	37.82	11.75
BJ Watling	49	1578	37.57	10.50
JV Coney	85	2668	37.57	23.67
NJ Astle	137	4702	37.02	11.55
JDP Oram	59	1780	36.32	9.80

There is an important omission here, JF Reid only just missed out on this table, as he only played 19 tests, for an average of 46 and centuries per completed inning of 4.67. However I decided to make the cut off 20 tests to allow for diversity in conditions, and a sufficient sample size, and then noticed that Reid had missed out after that.

Ranked by completed innings per hundred, Crowe is still slightly ahead of Williamson, but if we look at the time since my conversation with McCullum his conversion rate has come down closer to 6.5.

In ODI's batting average isn't always the best way to measure success. Someone that scores 60 off 100 balls every match will have a fantastic average, but they will not be helping their team as much as someone who scores 45 off 40 every match. To counter that some statisticians use a statistic called batting index to measure success. This is basically the average multiplied by the strike rate then divided by 100. If we sort by batting average, Glen Turner is ahead, and Williamson second, but by batting index, Williamson pulls clear. Here are the top 15:

Name	Runs	Average	Strike Rate	Batting Index
KS Williamson	2045	43.51	80.67	35.10
LRPL Taylor	4580	41.26	82.55	34.06
L Ronchi	557	29.31	109.43	32.07
GM Turner	1598	47.00	68.05	31.98
JD Ryder	1362	33.21	95.31	31.65
MJ Guptill	2953	37.85	80.20	30.36
RG Twose	2717	38.81	75.40	29.26
MD Crowe	4704	38.55	72.63	28.00
BB McCullum	5200	30.05	90.56	27.21
SB Styris	4483	32.48	79.41	25.79
NJ Astle	7090	34.92	72.64	25.37
CL Cairns	4881	29.22	83.76	24.47
PG Fulton	1334	32.53	72.77	23.67
RJ Nicol	586	30.84	75.51	23.29
SP Fleming	8007	32.41	71.40	23.14

Sometimes it can be dangerous to look at a players's career based on their final average. One of the all time greats in my mind was Sir Frank Worrell who averaged 61 before his 30th birthday, but then he was convinced to come back as a specialist captain, and he averaged 41 after that. As a result it can be better to look at batsmen at the same stage of their careers.

Here's a list of the NZ players who went on to average over 40 after 71 innings:

Name	Runs	Average
Williamson	3034	45.97
Jones	2910	45.47
Turner	2952	45.42
Crowe	2948	45.35
Taylor	2868	42.81
Sutcliffe	2616	40.25
Fleming	2476	36.41

Again we see Williamson at the top. However, this time it is not so clear. If he had been dismissed for 30 instead of 242* in his last innings, he would have been on 2822 runs and his average would have been 42.12 which would have put him 5th in the list on both counts. A better picture might be to look at a graph of the career progression around that mark.

Here's the runs scored and averages of the 8 top averaging batsmen in their 60th to 80th innings:

We can see the impact of the last innings, but we can also see that there is a trend here that this innings was just a part of.

It is still too early to say that Williamson is our best batsman since Crowe, let alone that he is our best ever, but he is certainly in the conversation.

Preview ODI 3, New Zealand vs South Africa, Seddon PArk, 2014

NZ will need to overcome ring rust today

One of the reasons Mike Tyson was such a champion boxer was that in his early days he had fantastic defence. As a result, he was able to fight every 6 weeks rather than every 3 months (like most heavyweight boxers do) because he wasn't getting hurt in the ring. Fighting so regularly meant that he never got "ring rust." Ring rust is a condition where boxers miss out on the little details that make a big difference. An uppercut that connects with the right timing, on the right part of the jaw, knocks someone out. An upper cut that lands slightly to the left or the right of that, or arrives 1/4 of a second later hurts the opponent, but doesn't finish the fight.

It doesn't matter how much you spar in the gym, or hit bags, you can only fix ring rust by time in the ring.  Often when you watch a boxing match between two top fighters, the first 2 rounds tell you very little about the way that the rest of the match will go, they only tell you who is the rustiest.

In this series, New Zealand have been rusty. Very rusty. The bowlers have not bowled the right lengths consistently. The fielder have missed at least 4 catches and 3 run outs. The batsmen have hit the ball to fielders rather than into gaps, and thrown away good starts.

South Africa, on the other hand, were playing 5 weeks ago. They look refreshed and eager. The bowlers have been (generally) hitting good lengths, and the batsmen have (generally) made the most of the starts when they have go them.

It's hard to suggest anything different is going to happen in Hamilton today. Amla had two lives before he got to 20, then he cashed in. His technique looks totally unsuited to opening the batting in New Zealand conditions (especially pre-Christmas), but his hand-eye co-ordination is so good that he dominates when he gets the chance. If New Zealand give him more opportunities through poor fielding, then he will (in all likelihood) do exactly the same in Hamilton.

Hamilton tends to be a difficult place to start batting. Matthew Hayden described it as the hardest place in the world to see the ball. However, he also carried his bat for 181 in a match there.

In the last 10 years about 59% of top order innings in Hamilton have scored 25 or less runs. That's on a par with the overall average (61%) but the interesting thing is that in the innings where a batsman reaches 25, they go on to do better. The overall average is 52.22 (so they get another 27.2 once they get to 25). The average in Hamilton is 58.35 (an extra 33.35). This is actually a very significant difference. Of the 132 grounds that have hosted ODI's in the past 10 years, only 5 have had more then 5 games and a higher average once a player gets to 25.

As a result, making the most of early chances is vital. It's where New Zealand's rustiness could come back to haunt them. Although, there is one thing that will work in their favour: the weather.

It is likely to rain in Hamilton today. As one of only two inland cities in New Zealand, it's one of the easiest places to forecast the weather for. The game is likely to get a small shower during the first innings, a small shower near the start of the second innings, and then be curtailed by rain. With the overhead conditions, both captains will probably want to bowl first, and that is likely to be an advantage. However, the rain is likely to mean that batsmen will have to re-start their innings after they get started, so the normal Hamilton pattern might not play ball.

Betting tips.

If I had $50 to bet on this match, here's where it would go:

1. $10 on NZ to win at $2.45

It's almost always a better idea to bowl first in an ODI, especially when there's a breeze and cloud cover. This is simply because of winning the toss

2. 2 x $10 Over on any South African batsman that gets to 25.

They all have such good hand eye co-ordination that once they get to 25, they are likely to score more than 60. Watch the live betting, and go over whatever line the TAB offer.

3. 2 x $10 Under for any New Zealand batsman that gets to 25.

They are all looking so rusty, that it feels likely that they will throw it away. Other than Luke Ronchi.

(All odds accurate at time of writing from the NZ TAB)

Match 2, NZ vs South Africa preview

Trent Boult may be a key player in match 2

We now have a little more information about Bay Oval, and what it's all about.  We also have seen both teams play.  And really, we don't actually know much more.

Here are some things that I noticed, and some battles to look forward to.

1. Trent Boult vs Quentin de Kock.  de Kock is a good batsman, in good form, but he looked somewhat clueless against Boult, and it looks like he will need to develop a better plan as to how to bat against him.

2. Vernon Philander vs Martin Guptill. Guptill looked completely out of form in the first game, but that's at odds with how well he played in the CPL just recently. Often a batsman looks out of form when a bowler is bowling in places that makes it difficult for him to score.  I think that is what actually happened in the first match. It will be interesting to see if Guptill has managed to figure out how to get some runs off Philander's bowling.

3. Kyle Mills vs Hashim Amla. If Mills plays in this match, it will be interesting to see if he can repeat the dose against Amla. Mills bowled 21 deliveries to Amla, and he managed to only score 12 before getting out. And those 12 mostly came from streaky, un-Amla like shots. Conventional wisdom would say that Amla's too good to repeat that performance, but Mills is a very crafty bowler, and his successes against Chris Gayle say that he is capable of targeting a player and really getting on top of them.

4. Brendon McCullum vs Morne Morkel.  McCullum backs himself to dominate anyone, but he has always found Morkel a difficult bowler to face. Morkel got him in the first match, and McCullum will not want a repeat in the second.

5. Jimmy Neesham vs Dale Steyn. Steyn will be particularly grumpy with the way that Neesham approached their confrontation in the first match. Neesham didn't look phased by the great bowler at all. It will be interesting to see what lengths Steyn bowls to him today.

Betting tips.

If I was betting $50 on this match, here's where it would go:

1. Total match run outs $10 on over 1.5 at $2.80
There were non in the first match, but there were 3 close calls, and that was without the sort of scoreboard pressure that normally brings about run outs. McCullum sets fields trying to get run outs, and ABdV has been working hard on getting the South African fielding back to where they were in years gone by.

2. South Africa top run scorer $10 on AB de Villiers at $5.00
de Villiers has a phenomenal record in the second match of a series. Over the past 3 years he's only had 2 times that I could see that he's hit less than 50 in the second match in a series. He's hit 3 centuries and 2 not out fifties.  He's also got the wood on most of the New Zealand bowlers.

3. New Zealand top run scorer $10 on Tom Latham at $7.50
Latham looked fantastic, and would have been likely to got a big score other than a piece of bad luck against Duminy.

4. Hashim Amla runs $10 on 0-20 at $2.55
I think opening against a line up featuring (at least 2 of) Mills, Southee and Boult is a very difficult prospect.

5. Head to Head $10 on New Zealand at $2.60
New Zealand are a better team than they showed in the last game.  Look for a big step up.

All odds are from NZ TAB and are accurate at time of writing.

Match preview 1st ODI NZ vs SA, Mount Maunganui,

The circular Bay Oval, Mount Maunganui

The countdown to the World Cup finally feels like it's started for real. South Africa are touring New Zealand for 3 ODI matches that are more a means to an end than an end in themselves.  Both teams say that they want to win these matches, and the players who get on the field definitely will.  But they are both aware that the real target is the World Cup.

Surprisingly this match is being played at Bay Oval in Mount Maunganui. It's the 4th ground in the Northern Districts area to hold an international match, and is not going to be used in the World Cup.  However, it is in New Zealand's fastest growing region, and is likely to be a place where a lot of international cricket will be played in the future.  It is also on the east coast, so it is a lot less likely to be rained off in spring time than somewhere like Auckland or Wellington.

As there has never been an international at the ground, there are some aspects that are hard to predict. A par score for the ground really has not been established at this level, and almost all of the players will go in without too much baggage (positive or negative) at the ground.

There were a number of warm up matches played there, and we can tell some things from those.

Firstly, bowlers that tend to bang the ball in were punished.  It seems that the fuller the pace bowlers bowled, the better they did. Secondly the scores were all over the place. Some teams were scoring 300+ while others were struggling to pass 150.  Also, the spin bowlers took lots of wickets but (with two exceptions) went for lots of runs. The two exceptions were Daniel Vettori and local boy Jono Boult (brother of Trent)

The ground is an interesting shape, particularly given it's name of Bay Oval. It is a perfect circle. The boundary is 68m from the centre of the pitch in every direction. This means that it has a straight boundary of 79m and a square boundary of 67m. This obviously favours players who are good at playing the hook, cut and scoop shots (which probably explains why bowlers who bang the ball in get punished).

I've looked through the records of the players at similar shaped, coastal grounds in the past 3 years and there are three names that feature at the top of the list: de Villiers, McLaren and well ahead of all else, du Plessis. The top New Zealand name is Williamson (who is not playing) followed by Neesham.

If I was looking to make a couple of bets, I'd look at putting some money on both du Plessis and McLaren to be top scorer. While it's guaranteed that at least one of these bets will fail, I think it would be a sensible move to cover both.  At time of writing, du Plessis is paying $4.50 and McLaren is paying $26 to be top scorer at the NZ TAB. I think this is good money for both of them. du Plessis has gone past 90 in 5 of his last 9 ODI innings. That's compelling form. I'd look at McLaren for a different reason.

The ball is likely to swing at Bay Oval. It's overcast, with showers likely. The tide will turn at about 11:00, an normally the ball swings around the turn of the tide (either just before or just after). Trent Boult grew up in Tauranga so this is his home ground. If he starts getting the ball to go round corners (as he can) he is almost unplayable. In the matches at the Champions League T20 when the ball swung, he was almost unplayable. To go with that, Kyle Mills has been a beast at similar grounds in recent times. He's averaged 11 at an economy rate of under 4. To back that up, in one of the warm up matches (for Auckland against Afghanistan) he took 2/14 off 7 overs. Mitchell McLenaghan is not in such form, but he has a good record against South Africa, and the ability to hurry up batsmen.  I think it's actually quite likely that New Zealand will take early wickets, and South Africa will need to rebuild. That will create a platform for someone like McLaren to succeed.

As far as New Zealand's batting goes, it is a bit difficult to make too many predictions.  Despite his game being suited to grounds like this, Brendon McCullum has never really been successful at this sort of ground. Neesham is opening for the first time, so that will test his technique more than coming in at 6 does, especially against Steyn, Morkel and Philander (Steyn has the second best figures at grounds like this, after Mills, with an average about 18 and an economy rate just under 5). The other interesting selection is Dean Brownlie. Brownlie is particularly good off the back foot, and has had some success against South Africa, but in every large innings that he has put together, he was dropped early (often more than once). If he gets started, he might be worth putting some money on for NZ top scorer, but I certainly wouldn't back him until he made it to 25.

The other thing to watch out for in this match will be the rain.  There may be some showers early on, but it's quite likely that there will be some serious rain in the evening. This means that there is a reasonable chance that the game will be called off early, and Duckworth-Lewis will need to be used.  I'm a big fan of the Duckworth-Lewis system, but it does hurt teams with good batting depth.  The two teams in world cricket that it works against the most are these two. As a result, the team that bats first is likely to have a slight advantage if it rains.

If I had $50 to bet on this match, I'd suggest these:

1. AB De Villiers to outscore Hashim Amla $10 at $1.92
2. Total match run outs over 1.5 $10 at $3.00
3. Faf du Plessis top South African scorer $15 at $4.50
4. Ryan McLaren top South African scorer $5 at $26.00
5. Whoever bats first to win the match $10 at what ever the odds are post toss.

(all odds from the NZ TAB at the time of writing)

Maxwell joins Pringle

One of the matches that got me hooked on cricket was this one in Hobart in 1990, when Australia needed 2 runs to win going into the final over, and Chris Pringle bowled a maiden (assisted by a slightly dubious non-wide call early in the over).

Today, Glenn Maxwell has joined Pringle in the required last over maiden club by bowling Australia to victory in similar circumstances.

It was an incredible effort from Maxwell, but unfortunately, with the history of both Pakistan and of matches held in the Emirates, there is a sniff of suspicion about it.  I really hope that every player was making a genuine effort, as the result is a storybook one.

Winning an ODI from the front

Is Cook the captain to correct England's ODI ship?

There have been a lot of debates recently about the role of the top order in an ODI. Is it more effective to come out swinging or is a more cautious approach more appropriate?

Until 1992 the expectation was that the top order's job in an ODI was to see off the new ball, and scoring at 3 an over was fine. If you look at the great opening bowlers of the 80's you will see that most of them had economy rates near 3.5 rpo. Then in the 1992 World Cup something wonderful happened. In the 10th match, New Zealand were playing South Africa, and one of New Zealand's premier batsmen, John Wright, got injured. In came Mark Greatbatch. Rather than playing the traditional openers role, he took advantage of the fielding restrictions and scored 68 off 60, including hitting Allan Donald back over his head for a 6 that landed on the roof of the stand. From this point onwards, New Zealand's approach changed, and the first 15 overs were seen as the best time to score quick runs.

In the 1995/6 Australian tri-series, Sri Lanka took that tactic to the next level. Kaluwitharana and Jayasuriya batted like whirlwinds and not long later they helped take their team to victory in the World Cup. At this point the world really stood up and took notice. The dashing opener was now the in thing. New Zealand had Astle, Australia had Gilchrist, India used Sehwag, Pakistan opened for a while with Afridi. An attacking opener had become as much a part of the game as using a spin bowler in the "boring middle overs."

But recent changes to the game, such as the different fielding restrictions at the end of the game and 2 new balls have meant that some people have questioned if going for it at the outset is such a good tactic now. Is it a better idea to keep wickets hand and "go harder, later."

The majority of this discussion has come out of England, where the roles of captain Cook, Bell and (before he dropped out of the game) Trott have been coming under increasing scrutiny. Are they batting too slow? Are they putting too much pressure on the players coming in after them?

This led me to have a look at the role of the top 3, in the past 2 years. What I wanted to know was what had the biggest impact on a team winning, the openers batting a long time, them scoring a lot of runs or them scoring at a quick run rate.

The first thing that I did was I got a list of the scores when the second wicket fell in each match in the past 2 years, and the outcomes of the matches.

The next step was to graph it, and see what came out.

First I looked to see if there was a different relationship between the overs taken and runs scored for the first 2 wickets for teams that won and teams that lost.

We can see that there is a fairly strong relationship with both graphs.

I set the intercept of the trend lines to 0, so that the gradients are effectively the run rates.

There are a few noticeable differences.  Firstly the teams that win tend to score at a higher run rate for the first 2 wickets than the teams that lose. However when I overlapped the two graphs, this difference was not as striking visually as it is numerically. (After 40 overs the trend lines are actually only 28 runs apart)

More significantly, there's a lot more data above 15 overs on the winning graph than on the losing graph. There is also a lot more instances on the winning graph where the first two wickets have contributed 150 or more runs.

I ran a quick bootstrap analysis and found that there was a statistically significant difference between both the median number of runs scored at the fall of the second wicket by the winning teams and the number of overs that they batted for.

To highlight that difference, I drew a cumulative frequency graph. The difference in the distribution of the number of overs faced by the winning and losing teams is quite striking.

That gave me some reason to search further.  It seems that there is a statistical evidence to say that there is a difference between the performances of the top 3 batsmen of teams that win and lose.

The next question was to see which made more of an impact: the number of runs, the number of overs or the rate that the runs were scored at.

To do this I ordered the innings by each of these three variables, and then looked at how many of the 9 innings surrounding each one were won and lost. This is not particularly intuitive, but it did give me some idea about the impact an increase in the variables would have on the likelihood of winning.

First I looked at run rate:

There is a trend here, but it's certainly not a strong relationship.

It's clear that increasing the run rate that the first two partnerships score at can contribute to increasing the likelihood of winning.

The important number here is the R² value of 0.35914. The closer to one this value is, the more linear the relationship is. While it is not a perfect measure of how strong a relationship is, it is a good indication.

The next graph that I looked at was the total runs scored.

This is a similar relationship, but it is clearly stronger.

The points are generally closer to the trend line and the R² value is higher (0.44074).

The data (expectedly) thins out as the number of runs increases, as it's quite rare for teams to get to 200 for the loss of only one wicket.

The R² value is less than 0.5, so there's still more of the variation that is unexplained than explained by this relationship, but again that is to be expected, as there are a lot more factors in a game than the first 3 batsmen, and it is always possible for a game to change suddenly.

The total runs scored for the first two partnerships seems so far to be a better predictor of success than the rate that they scored at.

The third factor is the one that I found the most interesting.


The relationship between the overs batted and wins looks (unsurprisingly) quite similar to the relationship between runs and wins.

The R² value for overs is lower than the corresponding value for runs, but both are higher than the relationship with run rates.

The point where the teams are winning more than they are losing are roughly 14 overs, 75 runs and 4.7 rpo respectively. These numbers start to give us an idea about what we should be looking for in an opener.

However, I wasn't totally convinced by these graphs.  I wondered if they would have turned out the same if I had chosen to look at 15 innings or 5 innings, or some other slightly different way of looking at it.  So I decided to try looking at the winning probability for individual points.  To do this I rounded the run rates to the nearest 0.1 rpo, the overs faced to the nearest over and the runs to the nearest 5 runs.

Again these graphs were quite interesting.

Visually, the strength of the relationship is indicated by the degree to which the top of the colours bars get close to trend line.

The runs and overs graphs look like they are a better fit than the run rates graph. But we can get extra evidence for the strength of fit from the R² value again.

This time the R² value for overs was significantly stronger than it was for either the run rate or the total runs.

The lower (green) graph suggests that for every extra over before the second wicket falls, the probability of winning increases by about 1.7%

Likewise, for every extra 5 runs scored, the probability of winning increases by about 1.7%

At this point I started to feel like there was some fairly significant evidence that having a top 3 that can see off the new ball is definitely the way to go.

The rate that the top order score at is important, but it doesn't seem to be as important as the number of overs that they bat for.

This makes sense for a couple of reasons. Firstly, a cricket ball is at it's most hittable when it is about 15 overs old. At this point it's still hard enough to go quickly off the bat, it has normally stopped swinging conventionally and hasn't yet started to swing unorthodoxly. The ball is the hardest to play when it is less than 10 overs old, because the ball will swing and seam, and the edges will go to hand, rather than dying as quickly as they do later on.

When the balls are 15 overs old, the match is 30 overs in.  At this point it's sensible for teams to have their best hitters at the crease.  If they are in too much before the 20th over, the hitters are being exposed to a swinging ball that makes it difficult to time their shots.

The next bit of analysis I did was to look at those 3 marks from above (14 overs, 75 runs and 4.7 rpo) and look at the difference in the results between teams that reached these milestones and teams that did not.

The outcomes were again quite interesting:

Here fast was any innings where the first two partnerships scored at more than 4.7 runs per over, big was where the second wicket fell when the score was over 75 and long was where the wicket fell after the 14th over.

The column titled "Relative" is the relative probability.  This means that teams that have their first two wickets score at more than 4.7 rpo are 37% more likely to win than teams who score slower than that.

Again we see that the biggest advantage is when the first two wickets last more than 14 overs.  It isn't a panacea, but it is important.

The final thing I did was to look at two similar skilled options, with different approaches, and see which was best.  To do this I looked at every innings where the second wicket fell between the 7th and 14th over, and the run rate was between 4.7 and 5.3 (this puts them roughly in the 2nd quartile for scoring rates and the 3rd quartile for length). I then also looked at times where the second wicket fell between the 14th and 19th over, with a run rate between 3.8 and 4.7 (which puts them roughly in the 3rd quartile for scoring rates and the second quartile for length).  Again the more cautious approach paid dividends, although this time with a much smaller sample size.

The more attacking start yielded 9 wins and 13 losses (40.9% winning record.) The more cautious start also yielded 9 wins, but only 8 losses (52.9% winning record). The difference here, however, is not statistically significant, given the low sample size. 

Putting this all together, an ideal opener is a player who averages at least 37.5 (half of 75), averages lasting 42 deliveries (half of 14 overs) and has a strike rate of at least 78.3 (equivalent to 4.7 runs per over).  If they a compromise has to be made on one of these it should be the strike rate, as that's the least important to help the team win.

So, finally, how does Alastair Cook stack up to these criteria?

At the time of writing Alastair Cook averages 37.51 runs from 48 balls at a strike rate of 77.66.

He (just) makes two of the 3 criteria, and the one that he misses out on he is very close to, and is the least important.

England have not been going well in ODI cricket recently, but Cook's batting is not the right thing to blame. The issues are clearly elsewhere.