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28/09/2015 13:43 BST | Updated 28/09/2016 06:12 BST

Rugby World Cup: England Miscalculate Badly

On Saturday evening at Twickenham we saw the first game that actually mattered in this Rugby World Cup towards ascertaining where the trophy might ultimately end up...

On Saturday evening at Twickenham we saw the first game that actually mattered in this Rugby World Cup towards ascertaining where the trophy might ultimately end up.

Argentina against New Zealand in Wembley was like an entrée for what lies ahead in the tournament, but in terms of consequence, it was mostly irrelevant. Both teams will qualify for the knock out stages and be largely unaffected by their result last week. The All Blacks would still have been favourites to beat either Ireland or France in the quarter-finals, whereas Argentina would still have been roughly 50/50 vis-à-vis the same two opponents.

England against Wales was different though, and you could sense it in the ferocity. If the number of injuries serves as a proxy for the levels of commitment, this match was like nothing we've seen in the Six Nations. Yet physical commitment alone is not enough. Brawn without brain might appear macho, but it is a recipe for disaster, particularly so when margins are so fine.

With moments to go in the match, England spurned the chance to go for goal and instead opted for a try by kicking to the corner. Perhaps they were just unlucky, but probably not. Of course 'anything is possible', just like it was for Japan a week earlier, but this rationale is flimsy. As a foundation for critical decisions, it's worthless. Gamblers think in possibilities while winners think in probabilities.

This isn't the first time England have demonstrated such poor decision-making in recent years either. During the November internationals in 2012 when Stuart Lancaster and Chris Robshaw were still familiarising themselves with their roles, the same dithering cost England in two successive games. Against Australia, England lost 20-14 after turning down three kickable penalties. Then a week later, when faced with a similarly tough choice, England took so long to decide what to do, that when they finally made the call, time was up. They lost 16-15 on that occasion to South Africa. That same weakness then showed its head again this year in Dublin during the Six Nations when England opted to turn down three points towards the end of the first half. Alone this didn't cost them the game, but the result was the same. Wasted points in a match where every morsel counts.

Consider the final few minutes of England's match against Wales and the decision they faced. Kick for goal and maybe draw, or kick to the corner and maybe win. Both outcomes are uncertain so what should one do? Perhaps thinking about it probabilistically might help.

England could have opted kick for goal with a conservative likelihood of success of 85%. The turf was perfect and the weather fine so this might easily be increased. However, to score a try, an unimpeded chain of events needed to unfold. Firstly, they needed to kick to the corner accurately, to within say ten meters of the try line. Assume Farrell or Ford can do this around 95% of the time. Then they needed to win the lineout. Assume they do this 80% of the time, which is generous considering what happened at the previous lineout. Next they needed to push over the try line which isn't easy and made harder by the choice of throwing to the front of the lineout. Assume they can do this 60% of the time which is again generous. Lastly, all this needs to happen without the referee finding a flaw and awarding a penalty, or there being a dropped ball. Assume that 85% of the time they can avoid these mishaps. The product of these numbers gives an overall likelihood of success of around 39%. (0.95 x 0.8 x 0.6 x 0.85 = 38.7%). Given this, England's decision to opt for the corner looks seriously flawed. Sure a higher risk does allow for a higher reward, but we can adjust for that risk too, and the news doesn't get any better for England.

Using a concept called the 'expectation', which is a bit like a weighted-average, England's expectation from kicking to the corner was their probability of success (38.7%) multiplied by their reward (four points), which gives 1.55. On the other hand, their expectation from kicking for goal was their probability of success (85%) multiplied by their reward (two points) which gives 1.7. Of course neither 1.55 points nor 1.7 points are possible in the pools, but the logic is unwavering and England miscalculated.

Of course there is no way to know for sure what will happen, but guessing randomly is bad, and guessing emotionally is worse, blurring rational insights. As the American author Andy Rooney suggested in his 50-50-90 rule, that "anytime you have a 50-50 chance of getting something right, there's a 90% probability you'll get it wrong."