The poor logic of long goal kicks

You see it all the time. A team gets into oppo half, is awarded a long shot at goal.....they miss and momentum is reversed. Looked at in terms of probabilities the long goal kick is an all or nothing proposition. And given the chances of success are probably no better than 50% outside the 10 metre line.....the expected result is .5x3=1.5 points. And when you miss a long one a good line clearance or dropout negates field position. But kick the ball out deep in the 22 and several possibilities emerge. The outright try via a maul or backline move, probably 40% of the time....giving a probable return of say 3 points. Or quite often the chance for another kick in a much better position ... with a probable return of 1.2% or so. So the combined probability of going for the lineout is 4 points vs a probability of 1.5 for the long kick. The long kick should only be tried at the conclusion of the half or deep into the game when the time taken is a useful additional consideration.

Mozart

In essence I am against kicking at goal when - 

*   before the last five minutes of a game unless the winning margin of the team after the kick will result in a more than 7  points;
*  when there is a penalty awarded when one of the opposing team members has been carded and in such cases a scrum near the tryline or a kick to the corner is more advisable.
The NZ teams rarely take kicks at goal early in matches -  but the SA teams do.  I think the NZ teams are wiser in that regard,       A lead of 7 points is much better than one of 3 points - simple logic.  

Nice discussion. I very seldom think the kick at goal is the best option. You always hear commentators saying a team has left three points on the field, because they didn't take a kick at posts. Well, kicks are also not a guaranteed success. Especially long range ones. Even "sitters" get missed often enough. Sure, time remaining and points on the board play a part in weather a kick at goal is the right or wrong option . However, as Moz has mentioned, even if you don't score a try off the resulting line out from a kick to touch, or you manage to lose possession, chances are, you will still be in your opponents half and in a position to score points.. 
There are some factors that can't be measured with mathematics though. Things like a momentum shift or the psychological impact of a long range penalty sinking putting pressure on opposing players to change tact slightly for fear of giving away a penalty in a kickable position. Also, if your forwards have lost a couple of balls on their own line out in the game already, the odds of securing the ball may make the line out option unfavourable. 
It would be very interesting to see the actual stats on say all 2017 Super Rugby games, and check what percentage of attacking line outs have resulted in the scoring of a try. That said, one would have to assume that is something that team management have scrutinised extensively.
For me, as a general rule, take the kick to touch and the attacking line out.  

Too true Mike. it comes back to a point I have made many times. NZ teams have a mental edge over most opposition. A kick for touch for the resulting line out and a potential try is positive thinking. Our teams tend to have a negative mind set, which I feel often leads to them taking the conservative option. 

Mike is right about the NZ tactics....they play aggressively for a turnover deep in their 22, accepting the penalty if they are tagged. It's smart play. The really dumb manouvre is to concede the yellow in defending an inevitable try....something we do too often.