Ulster says… Maybe

After last Friday’s wonderful display in Ravenhill, Ulster have 19 points, and are sitting pretty on top of their pool. However, with a trip to the daunting Stade Marcel Michelin to come, where the home side have won 38 on the spin, they aren’t too confident of finishing there.
To rub salt into the wound, the Brethren, despite being the best runner-up to the tune of two points over Embra and three over Quins, appear to be outsiders to reach the last eight, as home games to London Samoa and away games to Connacht are slightly easier to navigate than away to the Bananamen.
However, given we are Maths nerds, and measure our self-worth in Fields Medals and not girlfriends, we’re going to try and quantify exactly how likely they are to become the third Irish province in Sunday’s semi-final draw, which will see Saracens get the home semi-final they need to guarantee a Twickers sell-out in May.
There are 4 ways Ulster can make it:
1.       Beating Clermont
2.       Losing by <7 with Quins not scoring 4 tries
3.       Losing by <5 and scoring same amount of tries as Clermont
4.       One or more of Toulouse, Quins, Cardiff and Embra losing
Options 2 and 3 are too hard to work out, and pretty unlikely anyway, so lets concentrate on 1 and 4.
Beating Clermont: According to the bookies, who are generally right, Clermont have an 85% chance of winning the game. This seems absurdly generous to us, so we are going to bump it up to 95%, and put some sneaky money on Les Jaunards to help heal the pain of the inevitable thumping. So Ulster have a 5% chance of winning.
One or more of Toulouse, Quins, Cardiff and Embra losing: This is easier to work out – unless all 4 win, Ulster are through. Therefore the probability of Ulster going through down this route is [ 1 – the probability of all 4 winning ].
Again, using the bookies as a benchmark, the probabilities of winning are as follows:
·         Toulouse (A Gloucester) – 70%
·         Quins (A Connacht) – 79%
·         Cardiff (H Racing Metro) – 90%
·         Embra (H London Samoa) – 83%
These all look reasonable, except the theory that Toulouse are most likely to choke. Toulouse tend to chug along in third gear for most of the pool stages, but rest assured they will crank it up if they need to. Let us bump that up to 90%.
So the probability of all 4 winning (assuming independence, for all you pedants out there) is  [90% * 79% * 90% * 83% ] = 53%. Therefore, Ulster have a 47% chance of qualifying, no matter what happens in France.
Taking into account that all 4 games could go against them, but they could win in Clermont, which has a probability of [ 5% * 53% ] = 3%. So, Ulster’s total chance of qualifying is … 50%! Given that Options 2 and 3 must have some positive value, we make Ulster slightly better than 50-50 to go through.  Hooray!  You heard it here first!  But still, talk about being on a knife edge.  The moral of the story is that it’s better to have the points in the bag than have a nerve-shredding must-win-or-lose-by-less-than-five-with-equal-tries game.
Let keep our fingers crossed that Disraeli’s nonsense about statistics doesn’t get proven right. Again.
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4 Comments

  1. Dunno much about gambling but is there not a bookie/market somewhere taking bets on Ulster going through or going out? How do your implied probablities compare?

  2. There might be … a potential arb if you the odds are beter than evens as well…

  3. Looking at the infrequent nature of Clermont's home defeats and the irregularity of Ulster's away wins you may have to apply deterministic chaos theory to this one lads! Certainly with Ferris' form and a pretty (not in a good looking way) huge pack (surely one of the biggest bopping eights in irish rugby history) they will be looking to create plenty of demented molistic/demonistic chaos in France. Add the varied talents of Pienaar directing that brawn about the park, they have become a bloody good team and are capable of doing this irrespective of other results…..

  4. ……theoretically anyway.

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