On whether to take two points or to go for a try when awarded a penalty within 20m of the opposition’s line.
Practical application
At GIO Stadium in Canberra last night the Raiders twice opted to take two points when given a penalty inside the Knights’ defensive 20m. We ended up losing by two points. Is it possible to say whether, in probability terms, it would have been better for us to have gone for tries when given these two penalties?
Problem
When it comes to a decision about whether “to take two points” (the false assumption being that the kicker will not miss) or to go for a try, there are five variables:
the clock (eg whether it's useful to run the clock down, thus depriving the opposition of the ball etc); the scoreboard (the current state of play); the probability of succeeding in 'taking two'; the probability of scoring a try; and the probability of converting the try if scored.
For the purpose of this exercise let us ignore the clock. Where the scoreboard is concerned, let’s consider the best option across the whole season rather than at any particular point in any particular game.
Let us assume that:
on average, there are two penalties received per game within 20m of the opposition's try line; there are 26 rounds, that means 52 penalties in a season (N=52); the success rate for the side's kicker (Goal Kicking Conversion Rate - GKCR) is 80% from anywhere inside the 20m line, whether from a penalty or a try conversion attempt; GKCR = 80%; (Jarrod Croker's current all-time conversion rate is 81.46%); and x% = the success rate for scoring a try when that option is taken.
With a GKCR of 80%, the decision to ‘take two’ on every one of the 52 occasions would result in 84 points over the season.
To be calculated
We are looking for the smallest value of x that would result in >84 points in the season if the try option was exercised every time (52/52).
Method
Let x be the success rate for scoring a try when that option is taken.
Let pTRY = the percentage of times a team goes for the try option when given a penalty in the opposition’s 20 metre line – a percentage between 0 and 100.
x = (pTRY(52) x 0.8 x 6 points) + (pTRY(52) x 0.2 x 4 points)
Let us set pTRY at 30%:
x = ((0.30 x 52) x 0.8 x 6 points) + (0.30 x 52) x 0.2 x 4 points x = (15.6 x 4.8) + (15.6 x 0.8) x = 74.8 + 12.5 x = 87.3
87.3>84
QED
Conclusion
Across a full season, if the probability of scoring a try from a tap penalty from within the opposition’s 20 metre line is 30% or higher, this would be the preferred option (ie better than opting for attempting two points from a penalty shot at goal).
This does not account for the potential ‘value’ of absorbing time with a slow penalty; and it assumes an 80% Goal Kicking Conversion Rate across the board.
The 30% figure is a global guide. It does not account for the position on the scoreboard at the time, or the assessed strength/weakness of the opposition, or whether someone might be in the sin-bin, or the preference of the crowd watching on.
For a couple of reasons the 30% figure is a little conservative, or higher than it need be to make the try attempt preferable. For one thing, it results in 3.3 more points than estimated for the penalty kick option. For another, the proof here does not allow for the fact that, even if a try is not scored from the six tackles after the tap re-start, the attacking side may be in a strong field position for its next set of tackles; or the opposition may drop the ball in playing their set. Whereas, if the penalty kick has succeeded, the opposition returns to the half-way line and kicks deep into ‘our’ territory.
Simpler proof
80% of 2 points = 40% of 4 = 26.7% of 6 = 1.6 points