Okay, so let's get back to the football example where we can either run or
pass and the defense can guess run or pass.
So let's suppose this is our current situation right here.
We'll highlight this in red.
Okay, and so run offense versus run defense gains -5 yards, etc.
Now it turns out the mixed strategies here, this is like odds and evens.
It's 50/50 for the offense and defense.
Flip a coin whether you run or pass or play run or pass defense.
And the value is zero, you can see that.
What's your expected payoff if you're the offense against each of
the defense strategies?
0.5 times -5 plus 0.5 times 5 equals 0.
Or 0.5 times 0.5 plus 0.5 times -5 equals 0.
Okay, let's suppose you draft a running back, okay, who's a better running back.
And so the only change we're going to make is we're going to make this number better.
So in other words, if basically the defense doesn't look for
the run, we're going to gain ten yards instead of five yards.
because we have that better running back and
he can break a tackle more often than our current running back.
All right, so what does that mean?
Okay, we've got a better running offense, we should run more, correct?
Wrong!
We should run less.
Okay, it turns out the optimal strategies here are 40% run offense,
60% pass offense, which is less than 50/50.
Why is that the optimal strategy?
because you play this against both of the defensive options,
you average the same amount.
0.4 times -5 is -2.
0.6 times 0.5 is 3, so you'll average 1 yard.
Here you get 0.4 times 10 is 4 yards.
0.6 times -5 is -3 yards.
So the value is 1 yard.
So you're better off You'll average 1 yard you can guarantee then.
0 yards but you run less, now why is that?
Because the defense knows you have good running.
They'll lay for the run more and so you'll run less, but
you'll be better off because you've strengthened your team.
So don't think if you've strengthened a part of your arsenal in sports,
that you'll basically use it more.
I mean, that may not work out.
Okay, so that's really sort of a paradox that game theory sheds some light on.
Now really,
what you'd like to do is validate game theory in a empirical context.
Okay, and we'll get to that in a second when we talk about penalty
kicks in soccer.
I'm taping this right after the FIFA scandal, which is unbelievable.
Okay, I mean, maybe not unsuspected, but still unbelievable.
Okay, but basically, well,
let's talk about the Soccer example.
Well, how could we really use game theory during football?
If we could do something like Madden.
In other words, if you could list the offensive plays