By John Considine
On Saturday, just before halftime in their rugby championship game, South Africa were awarded a penalty against New Zealand. It presented the South Africans with a decision to make. To take a kick at goal or to select some other option such as a kick to touch where South Africa would have the throw in to the lineout. As viewers we did not know for certain the options that were being considered. We did observe the outcome of the decision. It was decided that Handre Pollard would have a kick at goal.
It would be fair to imagine that the decision makers weighted up the probability of the successful kick for three points against the probability of a successful alternative with the reward for that alternative. Knowing the outcome of the decision, it is also fair to assume that they decision makers decided that the kick at goal gave the better expected value.
What evidence might the decision makers have considered? It is fair to assume that everyone knew the hot streak the Pollard was on in 2022. Or maybe they knew of Jared Wright’s analysis of Pollard’s 2021 attempts (see accompanying picture) or his career attempts to that point (74.6% = 191/256). But the calculation of the expected value of the best alternative option (the opportunity cost) would have been much more complicated and less precise.
The rugby union situation is not too dissimilar to situation facing a free taker in hurling. The expected return from having a free shot at the posts can be estimated. In what follows a “free shot” refers to the situation where one team is penalised for foul-play and a player from the opposing team is allowed to lift and strike the ball without interference. It does not include free-shots awarded because a player has put the ball out of the field of play (i.e. puckouts, sidelines, or 65s).
In last month’s All-Ireland hurling final, only 1 of the 17 free shots that crossed the endline plane was wide of the target. The remainder went between the uprights and above the crossbar. An astonishing 94% success rate. Success rates from bigger samples, from different weather conditions, from different venues, and different free takers tends to be lower. (A future post will consider the impact of distance and angles.)
Across all of their 2022 games in the Provincial and All-Ireland series, Kilkenny players had an 85% success rate when going for it whereas Limerick players had an 83% success rate. These “Going for it” rates overestimate the chances of success because it does not include shots that were intended to cross the endline but fell short. I have no way of knowing exactly what was in the players’ minds.
Virtually all of the Kilkenny frees were taken by one player when he was on the field of play. By contrast, Limerick have a long-range and shorter-range free takers. Not surprisingly, the short-range free taker has the highest success rate.
If we examine all 7 games in All-Ireland series then the success rate of free takers as a whole drops to just below 70%. At this success rate the expected value is 0.7 points. It is hard to see the value of any alternative exceeding this expected value. The advice to most of these free takers is probably "Go for it".
It would be fair to imagine that the decision makers weighted up the probability of the successful kick for three points against the probability of a successful alternative with the reward for that alternative. Knowing the outcome of the decision, it is also fair to assume that they decision makers decided that the kick at goal gave the better expected value.
What evidence might the decision makers have considered? It is fair to assume that everyone knew the hot streak the Pollard was on in 2022. Or maybe they knew of Jared Wright’s analysis of Pollard’s 2021 attempts (see accompanying picture) or his career attempts to that point (74.6% = 191/256). But the calculation of the expected value of the best alternative option (the opportunity cost) would have been much more complicated and less precise.
The rugby union situation is not too dissimilar to situation facing a free taker in hurling. The expected return from having a free shot at the posts can be estimated. In what follows a “free shot” refers to the situation where one team is penalised for foul-play and a player from the opposing team is allowed to lift and strike the ball without interference. It does not include free-shots awarded because a player has put the ball out of the field of play (i.e. puckouts, sidelines, or 65s).
In last month’s All-Ireland hurling final, only 1 of the 17 free shots that crossed the endline plane was wide of the target. The remainder went between the uprights and above the crossbar. An astonishing 94% success rate. Success rates from bigger samples, from different weather conditions, from different venues, and different free takers tends to be lower. (A future post will consider the impact of distance and angles.)
Across all of their 2022 games in the Provincial and All-Ireland series, Kilkenny players had an 85% success rate when going for it whereas Limerick players had an 83% success rate. These “Going for it” rates overestimate the chances of success because it does not include shots that were intended to cross the endline but fell short. I have no way of knowing exactly what was in the players’ minds.
Virtually all of the Kilkenny frees were taken by one player when he was on the field of play. By contrast, Limerick have a long-range and shorter-range free takers. Not surprisingly, the short-range free taker has the highest success rate.
If we examine all 7 games in All-Ireland series then the success rate of free takers as a whole drops to just below 70%. At this success rate the expected value is 0.7 points. It is hard to see the value of any alternative exceeding this expected value. The advice to most of these free takers is probably "Go for it".
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