Penalties. A “free” goal in a regular game, but in a tense shootout in the World Cup it could make or break your chances to win the trophy. So imagine this. You’re standing 12 yards from the goal, you need to make this or your team goes home, you have an entire country on your back, where do you aim?
Now first instinct, the top corners, thinking its the hardest for the goalie to get to, but let’s break it down using statistics.
This is a diagram made by me:
red: minimal effort needed for save(red lines mark wing span of goalie)
yellow: 50/50 requires good power to make, assuming goalie goes the right direction
green: high probability of making(assume a make for calculation purposes)
As you can see the corners, to no ones surprise are the best outcome, but which corner to aim at?
I claim aiming for the bottom corners is better than aiming for the top, let’s break it down:
When going for the top you have many things to worry about, for starters its common sense that shooting an aerial ball will be harder to aim than shooting a ground ball(because you have the “support” of the ground, and there is no force of gravity acting upon the ball). There is also the concern of hitting it too high or too low, when hitting to the top corners, let’s say this is your stats:
50%: getting it in the box(score) expected score:1
25%: hitting outside the goal(miss) expected score:0
25%: hitting below or to the yellow side of the box(50/50) expected score: 1/2
(these seem like bad stats, but remember it is much harder to shoot in the air rather than on the ground)
Doing some math calculations(counting and probability is actually my favorite math subject) we see that the expected score is 5/8, meaning there is a 5/8 probability that you make it.
This is not a great percentage in a high stakes game so let’s check out the other case, aiming for the bottom:
Now for this case we don’t have to worry about hitting too low because unless your hitting into earth’s crust(which is an such an impressive feat that it definitely deserves a goal) there’s nothing lower you can hit, and since you are never taking the ball too high off the ground so we don’t need to worry about hitting too high:
So let’s say these are your stats:
85%:hitting in the box(goal) expected score:1
10%:hitting outside of the goal(miss) expected score:0
5%: hitting to the yellow side of the box(50/50) expected score 1/2
Doing the calculations your expected score is 7/8 meaning there is a 7/8 chance of making.
So let’s sum it up, a 5/8 chance of making(top corners), and a 7/8 chance of making(bottom corners), well the obvious pick is the bottom corners(these numbers will obviously vary slightly depending on the strength of the goalie and strength of the shooter)!
Additionally, when picking which side to pick, you may want to go for the goalie’s non-dominant hand because he may have less power and/or control in that hand.
Evidence, and a real-world example shows this. Harry Kane arguably the best current-day penalty shooter aims for the bottom corners the majority of the time!
Summing it up, next time(if ever) you’re shooting a penalty, going for the bottom corner is the smartest choice.
Thanks for reading, and enjoy the World Cup!
DON'T BLAME THE MATH 