In regards to the ending counterpoint that a goaler has no chance of saving a ball to the top third of the goal anyway:
A high ball should have a higher risk of missing the goal entirely. So the better you can predict the keeper, the lower and safer shots you should be able to take.
This was the point I was going to make. Even in this most recent world cup, we saw plenty of outright misses by shooters. Better to put it on frame and force the keeper to a save then to risk missing outright.
If I were the shooter I'd visibly flip a coin before walking to the penalty point. I'd try to equally scan both sides of the goal, and do a neutral run-up that hopefully wouldn't give away which side I picked.
This would neutralize most mindgames, statistical analysis and self-doubts.
Players have a stronger foot. But it's not particularly difficult to use that foot to strike the ball to one side or the other. It's a different technique, but it's one that every professional footballer has inevitably mastered.
The gambler's fantasy is a fantasy when you're trying to use it to predict a coin flip, not what another human will do. The penalty kicker has to make the same decision after looking at all previous results, and also may be making decisions about where to kick based on the direction of the previous kicks.
If the kickers attempt to second-guess the "this side is due for a kick" behavior by goalies, the goalies can try to second guess the kickers by knowing that they are intentionally trying to avoid even distributions over a moving historical window. It's the classic endless paper-rock-scissors strategy discussion.
It's not, because the direction the penalty taker chooses is not a random event. It may not be the optimum strategy, but it's not the gambler's fallacy.
Watch the second half of kicks in the most recent World Cup, you can see that some kickers seem to wait for any indication of the direction of the goalie taking a dive in a particular direction.
At the level these guys play, they kick so fast it is difficult for the goalie to get to the far reaches of the net even when they guess correctly, so I can see why they jump early. In this situation, the bigger goalies definitely have an advantage. Changing the direction you jump randomly isn't going to help much.
One counterintuitive piece of game theory trivia is that, in equilibrium, penalty kickers should kick to their weaker sides more often than their stronger sides.
In equilibrium, you should be indifferent to the goalkeeper's strategy, and if you're better at kicking to the left, that means you should kick to the right more, not less.
This comment left under the article, which is supposedly bullshit, says it all:
"Justin • 16 hours ago
I have played goalkeeper for almost 30 years, and this article makes no sense. We are not randomly guessing which way the kicker is going. For important matches, you're going to study the other team's kickers penalty history. Most players have a direction they feel more confident kicking to. You pick that direction if the info is available. If not, I always found that even if a kicker was trying to convince me of one direction, his eyes would always give away the true direction right before the kick. Most kickers need to do a visual check of their intended direction right before striking.
I'll tell you what never in 30 years influenced my decision: the direction of the previous kicker."
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[ 1.8 ms ] story [ 28.9 ms ] threadA high ball should have a higher risk of missing the goal entirely. So the better you can predict the keeper, the lower and safer shots you should be able to take.
This would neutralize most mindgames, statistical analysis and self-doubts.
If the kickers attempt to second-guess the "this side is due for a kick" behavior by goalies, the goalies can try to second guess the kickers by knowing that they are intentionally trying to avoid even distributions over a moving historical window. It's the classic endless paper-rock-scissors strategy discussion.
https://www.youtube.com/watch?v=wLlBIJekQTc
At the level these guys play, they kick so fast it is difficult for the goalie to get to the far reaches of the net even when they guess correctly, so I can see why they jump early. In this situation, the bigger goalies definitely have an advantage. Changing the direction you jump randomly isn't going to help much.
In equilibrium, you should be indifferent to the goalkeeper's strategy, and if you're better at kicking to the left, that means you should kick to the right more, not less.
"Justin • 16 hours ago I have played goalkeeper for almost 30 years, and this article makes no sense. We are not randomly guessing which way the kicker is going. For important matches, you're going to study the other team's kickers penalty history. Most players have a direction they feel more confident kicking to. You pick that direction if the info is available. If not, I always found that even if a kicker was trying to convince me of one direction, his eyes would always give away the true direction right before the kick. Most kickers need to do a visual check of their intended direction right before striking.
I'll tell you what never in 30 years influenced my decision: the direction of the previous kicker."