Maths Question. I'm seriously, you guys.
 

Rather than think about the probablity of a goalie saving a penalty (which I think over-complicates things), would it be sufficient to consider the goalie's available radius against the goal size in the two instances to get a sense of the advantage? If so then perhaps it becomes a trivial problem that even I could manage if I could remember any of my maths from all those hundreds of years ago.

Yes. By moving 2 yards forward, he decreases the effective surface area of the goal from 192 sqft to 133 sqft.

What about instances where the height of the ball stays below, say, 3 feet? This is probably true for a majority of penalties.

The geometry of the net changes taking away the top stuff, and some of the sides.

To put this in perspective, say if he has a wingspan of 6 feet, he'll have a body surface area 'between the tips' of about 8 by 6 or 48 square feet. He'll cover around 6/20 of the net, or about 30 percent. Standing in the net normally, he'd cover about 25 percent. So I'd expect to see him about 20 percent more effective.

Regulation is 8x24. 2 feet out that becomes 6 2/3rds feet by 20 feet. Corner to corner is now 21 feet, as opposed to 25 and a third.

Which keeper?

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