T20 World Cup Group 1 permutations

After the first two sets of matches in Group 1 of the Super Eights all four teams still have a chance to advance and all four teams still could fail to advance, though in Sri Lanka’s case that would be unlikely. The last round of matches sees the West Indies face New Zealand and England face hosts Sri Lanka. For Sri Lanka, almost any result is enough. A win will guarantee that they will top the group and even if they lose they can still advance if the West Indies fail to hammer New Zealand. If England win they will probably be in the semi-finals and might even top the group if they win by enough. A defeat will not necessarily eliminate England, however. It will depend on the result of the other match. The West Indies can can not ensure a place in the semi-finals even if they beat New Zealand, but they can put some pressure on the other teams to get a result. But they are out if they lose, as are New Zealand. The Kiwis are in the most dire position, needing both to win and get some help from elsewhere.

It gets interesting in the specifics though. Whilst a Sri Lanka victory and a West Indies victory is simple enough (they both advance), if England and the West Indies both win then they and Sri Lanka will all be on four points at the top of the table and the group winner and runner-up will be decided on Net Run Rate. Sri Lanka have a comfortable lead right now, but a loss to England will obviously eat into that. England can realistically top the group if they win by a decent amount and in theory the West Indies can as well, though it will take an incredible win.

For England to top the group they have to beat Sri Lanka and hope that the West Indies don’t win by enough to top their NRR (which would be unlikely). The first situation is the most straightforward, Sri Lanka’s NRR right now is: \frac{304}{35.2} - \frac{303}{40} = 1.029 and England’s is \frac{313}{38.5} - \frac{327}{40} = -0.115. (NB: The decimal values for overs are not ‘true’ decimals, but the usual cricket notation for fragments of an over. That is: ‘38.5’ = ’38 + 5/6′.) Unfortunately, the way NRR is set up means that it can’t be said that England need to win by x runs or with y balls to spare; the required margin of victory will actually vary with the first innings score. If England bat first and score x and Sri Lanka then score y the equation (and I’ve set it up as an equation instead of an inequality because England technically only need to draw level; the next tiebreak is head-to-head result) for England to overtake Sri Lanka is \frac{313+x}{58.5} - \frac{327+y}{60} = \frac{304+y}{55.2} - \frac{303+x}{60} (bearing in mind that the sides are considered to have used their full overs even when bowled out and that England are assumed to win since otherwise the analysis is irrelevant). This solves out to a linear equation that gives Sri Lanka’s maximum score, y, for a variety of English scores, x: y=0.969x - 16.5. This works out to a 20-25 run margin for likely scores.

It gets a little bit more complicated if Sri Lanka bat first though. Then it becomes a question of England needing to knock the runs off in a certain number of overs. If Sri Lanka score x then the overs, y England have in which to get the total is given as: \frac{313+x+1}{38.5+y} - \frac{327+x}{60} = \frac{304+x}{55.2} - \frac{303+x+1}{40+y} which works out to: y=\frac{28.8(\sqrt{x^2+618x+95500}-0.369(x+331))}{x+315}. (As much as I’d like to say I worked that out by hand, it would not be true.) This is a more complicated graph, but it actually has a happier result. It is quite flat for reasonable run totals and the quantised nature of the run chase gives us a handy result: for any Sri Lankan score between 101 and 205 (inclusive), England will have 17.2 overs in which to chase it if they wish to better Sri Lanka’s NRR. There is the caveat though that if it is close then England could hit a boundary for the winning runs and possibly get over the line with an extra ball used. For totals of 100 or fewer England will have 17.1 overs and for totals of 206 or greater England will have 17.3 overs, but in the first instance it isn’t likely that Sri Lanka will score so few and in the second instance it isn’t likely that England will chase that many even in twenty overs.

That’s for England and Sri Lanka and England are safe if they can get above Sri Lanka. But the the West Indies are still in the mix with a win. The easiest scenario for them is that they win and England lose. That will guarantee them the runners-up position. They can also finish second if England win narrowly, though and if England manage to drag Sri Lanka’s NRR down far enough the West Indies could even top the group. The problem for the West Indies is that right now their NRR is very low. It’s well behind Sri Lanka and pretty far even behind England. Even if England win by only a very small amount and only increase their NRR by a small amount, the West Indies will need to win pretty comfortably to catch them. The other possibility for them is that England hammer Sri Lanka and bring Sri Lanka’s NRR within range, but that will likely require another comfortable victory for the West Indies. They also have the slight problem of playing first, so they will not know what they need. Getting their NRR back to parity would be a good way to make England (and Sri Lanka to a lesser extent) sweat a bit though. To do that they would need to win by about twenty runs \frac{308+x}{60} - \frac{294+y}{55.2}=0 \Rightarrow y=0.928x-8.24 or with about two and a half overs to go \frac{308+x+1}{40+y}-\frac{294+x}{55.2}=0 \Rightarrow y=\frac{15.7(x+347)}{x+294}. It certainly can be done, though it won’t guarantee anything. They’d need a much more convincing win to have a chance to top the group though. Either England or Sri Lanka will have a NRR well into the positive range and for the West Indies to get their NRR that high would be a massive effort.

What they will be hoping above all is that England lose. And If the West Indies win and England lose then the West Indies will finish as runners-up. If the West Indies lose, however, they are out even if England also lose. They would actually be level on points with England and New Zealand, but their NRR is already worse than New Zealand and would of course go down even farther. This is actually New Zealand’s only chance of going to the semi-finals. Right now their NRR is only a little bit worse than England’s and there is every chance that a win could send them above England or even close enough that a subsequent English loss would send their NRR under that of the Kiwis. Like with the case of the West Indies it is hard to calculate what they need as they don’t have a clear target, but the closest thing is probably England’s current NRR (although England can actually raise it with a loss if the loss is in a super over). Still, for New Zealand to go past England on NRR would put a lot of pressure on England and the equations to do that are (defending): \frac{322+x}{60} - \frac{323+y}{58.5}=-0.114 \Rightarrow y=0.981x-6.59 and chasing: \frac{322+x+1}{40+y} - \frac{323+x}{58.5}=-0.114 \Rightarrow y=\frac{18.83(x+324.4)}{x+322.3}. They could do this relatively easily by winning by about ten or eleven runs or by chasing a target in 18.5 overs. Their chances should certainly not be written off.

Sri Lanka can get through and top the group with even a reasonably close loss. If they get within 20-25 runs of England in a chase or make England take more than 17.2 overs to chase down a target they will very likely win the group. They could theoretically be knocked out if England pass them and the West Indies beat New Zealand by enough to pass them both, but the odds are against it.

England can top the group by beating Sri Lanka by more than 25 runs or chasing down Sri Lanka’s target in 17.2 overs or quicker. A win of any type will probably be enough to advance though the Windies could knock them out with a comfortable win over New Zealand. They can advance with a loss if New Zealand win, but very narrowly.

The West Indies can advance if they win and England lose. They can also advance if they beat New Zealand by about 25 runs/three overs and England win fairly narrowly. If they thrash the Kiwis they will have a chance to even top the group, but it is very unlikely.

New Zealand can advance if they beat the West Indies comfortably and England then lose. But anything else will send the Kiwis out.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s