Wednesday, 30 September 2015

Pool of Death Permutations

Rugby World Cup 2015's Pool A, the "Pool of Death" took a dramatic turn at the weekend when Wales beat England 28-25 with the England players turning down a likely draw in the form of a kickable penalty in the dying minutes in favour of a lineout that failed to produce a winning try (I'm hoping to do a post analysing that decision soon). The top two qualify from the group and with 4 relevant matches left any of the big three (England, Australia and Wales) can still make it but the various bonus point permutations are mind boggling. Don't worry though, I'm here to help!

The games left are, in order:
  • Wales Versus Fiji (Who are all but out) on Thursday 1st
  • England versus Australia on Saturday 3rd
  • Wales versus Australia on Saturday 10th
  • England Versus Uruguay a little later on Saturday 10th.
England failing to pick up all 5 points against Uruguay is widely agreed as vanishingly unlikely and makes modelling significantly more complicated so I've taken that as a given, everything else is still to play for. Wales are favourites to beat Fiji but whether they're going to get the try bonus point is still very much up for debate (Australia missed out with 3 tries, England nicked it with a last gasp 4th try) and an upset is still possible. The other two games could go either way.

In order to easily visualise who qualifies based on the various results I've created some cut out and keep charts, there are 6 in total, one each for the range of points Wales could take from their game against Fiji (4 or 5 being the most likely).

The result (in match points terms, not score) of the England versus Australia game is along the top Wales versus Australia game is down the side. England winning their game is the left portion of the chart, Australia the right. Wales winning their game is the top portion of the chart, Australia the bottom. Draws in the middles

 Most cells contain the names of the 2 teams who will qualify. Cells that just say "points" indicate both qualifiers will be decided based on points difference (discussed below), where a cell has a team and "point" that team has qualified and second place will be decided on points difference.

 Wales get 5 points from Fiji

Wales get 4 points from Fiji

Wales get 3 points from Fiji
Wales get 2 points from Fiji

Wales get 1 point from Fiji
Wales get 0 points from Fiji
In the event of teams finishing equal on points the first tie breaker is the winner between the two tied teams, if that game was even then points difference (from all group games) come into play. In the event of a three way tie the points difference (again from all group games) becomes the first decider.

An interesting, but almost certainly irrelevant, consequence of this is that there are certain situations where after losing to England and being level on points with them it may become in Australia's interest to allow Wales a bonus point in order to put the three teams level on points which means the first tiebreaker is skipped and gives Australia a chance to qualify top of the group (In theory facing an easier opponent in the quarter finals).

The Fiji Bonus point, who benefits and when

A big topic of conversation after the Wales versus Fiji game, assuming Wales win, is likely to be Wales' winning bonus point or lack thereof, but how important is it and to whom?

If you closely compare the 2 relevant tables you'll see that out of the 256 possible outcomes 18 of them are affected by the Fiji bonus point, all of which require Australia to beat Wales and England to manage at least a draw with the try bonus point. Listed below is what they mean for each team.


In the event England get the draw with a bonus point and Wales can't manage at least one bonus point against Australia then England will qualify at the expense of Wales. 3 other outcomes turn from England needing to qualify on points difference to automatic qualification but these are somewhat offset by 2 similar (If less likely) outcomes that go in the opposite direction. As explained below England are in good stead if it comes down to points difference so this isn't likely to change an awful lot

The only other outcome change that England are interested in that would be altered is a 4-2 win to England and a 5-1 win to Australia against Wales which would turn from Wales and Australia qualifying to England and Australia qualifying. Wales missing out on the bonus point would be good news for England but nothing to get excited about.


In the event of an England win over Australia and an Australia win over Wales it's going to become a scrap for bonus points, most likely between Australia and Wales. 13 of the 18 outcomes that are changed are in favour of Australia (the other 5 being neutral). For england outcomes that change from teams automatically qualifying to teams qualifying on points difference even but for Australia they are all beneficial, changing from needing to qualify on points difference to automatic qualification or from crashing out to being able to qualify on points difference. Australia are the big winners if Wales miss out.


Still safe if England lose but otherwise losing to Australia just became fraught with danger and getting the remaining bonus points will take on new impotence.

Who has the advantage if it comes down to points difference

Probably England, having beaten Fiji by a reasonable margin, losing narrowly to Wales and having at least drawn with Australia (which they have to if it is to come to points difference) they will already be set up reasonably and will go into the Uruguay game knowing exactly what they need to do, while Australia and Wales have played the weakest member of the pool when qualification coming down to points difference seemed relatively unlikely so have balanced gaining a favorable points difference against resting players and avoiding injuries, England, if needed, will go all out and unless Uruguay (who only have 4 days turnaround before the England game) dramatically rise to the occasion I would expect England to get what is necessary.

Between Wales and Australia I'd give it to Australia, who did better against Uruguay and will have (Probably, if it's come to this) beaten Wales yet lost to England. This could change depending on the margin in Wales versus Fiji.