Robshaw's Risky Decision
A bad decision is different from a bad outcome
27 September 2015
Sometimes sport lets us witness the drama and pressure of decision making at its rawest. The World Cup rugby match between England and Wales produced one such occasion.
The match was on a knife edge. With two minutes to go, England trailed Wales by 25 points to 28. England were awarded a penalty, and the captain Chris Robshaw now had to make a decision. He could ask his kicker Owen Farrell to kick for goal and secure three points to guarantee a draw, or he could take the risky route and kick to the corner in the hope of being able to score a try and win the match.
Robshaw took the gamble and lost. England failed to get the try, and Wales won a famous victory.
So did Robshaw make a bad decision? “Yes,” said much of the media and most rugby pundits the next day, clearly he made a bad decision because England lost. But that isn’t a fair way to assess a decision. Suppose in a game of Bruce Forsyth's Play Your Cards Right you draw a 5 and are asked "Will the next card be Higher or Lower?" The best decision would be to predict that it will be higher. If the card turns out to be lower, was it suddenly a bad decision? No, because based on all the information you had, you picked the choice with the best expected outcome. You were just unlucky.
To assess Robshaw’s decision you need to look at the value of the different choices he could make, and that means looking at some probabilities. Had he asked Farrell to kick for goal, the chance that Farrell would have made the kick was high (he had been kicking outstandingly so far in the match). In those pressured circumstances a kicker of his quality would probably fire between the posts 80% of the time. What about the chance that England would get a try? The way England had been dominating set pieces, Robshaw probably felt confident. He probably reckoned he had a better than 50% chance of getting a try in those circumstances. And it must have been on his mind that just a week earlier, Japan had been in a similar situation against South Africa, and had eschewed the penalty, scored the try, and grabbed the headlines for their courage.
Meanwhile what were the payoffs for England? As things stood, at 25-28 England would get one (bonus) point for defeat and Wales would get 4 points. A successful penalty would mean both teams would get 2 points, so England would be 3 points better off relative to Wales. A try would mean England would be 6 points better off.
Robshaw’s decision could therefore be evaluated like this:
- Kick penalty: Value of outcome 3 x 80% = 2.4 points
- Go for try: Value of outcome 6 x 50% = 3 points.
On that basis, maybe Robshaw made the right decision. That was my hunch at the time, even though I didn't like the outcome. And it’s interesting that when Robshaw made the call to go for the corner, former England rugby player Jonny Wilkinson in the studio felt it was ‘not a bad decision’.
But now comes the benefit of hindsight. I’ve had time to think about it and I’ve changed my mind. England’s situation was subtly different from Japan’s the previous week.
First, the payoff for Japan if they went for the try was higher. If they won they would achieve something never done by their country before. On the other hand if Japan lost, there would be little damage, there's no 'history' between the two countries and Japan weren't expected to do well in the tournament. And secondly, Japan’s decision was made in the final few seconds of the match, so there was only a chance for one phase of play.
England, on the other hand, had nearly two minutes left. More outcomes were possible:
- Farrell kicks penalty. Wales restart. England get possession and press for a penalty or drop goal. Chance of happening maybe 20%?
- Farrell misses penalty. Wales drop out. England get possession and go for try/penalty. Chance of happening maybe 20% again.
Losing to Wales has a lot of emotional baggage, which has to be taken into account. And the result of the match also had implications for which team might top the table after the rest of the Pool matches.
All this makes the evaluation much harder, but the value of kicking for goal was probably quite a bit higher than the 2.4 points I gave it earlier, and it would probably have been the better choice.
But I say all that with the benefit of being able to think about the incident, look at the points table, listen to commentators and discuss it. Robshaw, on the other hand, had to do an intuitive calculation, make an instant decision and live with the consequences. That’s the difference between being a pundit and being a leader.
Postscript. On 5th October I discussed this and other ways in which maths and rugby overlap with Paul Grayson and Hugh Hunt in FLYING BALLS, a special event at the Rugby Fanzone. I asked Paul what probabilities he would have assigned to scoring the kick and the try. His hunch was around 70% for the kick, but only 10-20% for the try. If that's the case, it would immediately swing the decision in favour of taking the kick. Chris Robshaw might have been a victim of what psychologists call 'Optimism bias'. Here's a link about our event in Rugby: http://greenandgold.org/2015/10/07/critical-rugby-decisions-explained/