So, much ado has been made about the 1-game lead that the higher seeded team enjoys in the 5-game series, so I thought that in order to make better decisions for next year's league, we should have a concrete idea of just how valuable that one game lead.

Assumption: Each team is equally skilled - They have a 50% chance of winning each match.

Expected value of the conference semi-final with no home-field advantage:

Top seed: 0.5 * 1000 = $500
bottom seed: 0.5 * 1000 = $500

Expected value of the conference semi-final with home-field advantage:

Top seed: 0.6875 (top seed will win 11/16 times) * 1000 = $687.5
Bottom seed: 0.3125 * 1000 = $312.5

Value of the 1-game lead: $187.5

There is of course more to it. For example, having the higher seed means that you don't have to play the wild card match. How does having to play the wild card match affect your equity?

Top seed value from the wild card match:

0.6875 * 250 = $171.86

$171.86 - $125 = 46.86

However, the top seed in the wild card match simultaneously forfeits some of their expected value from the semi-final match when they fail to win the wild-card round:

0.3125 * 312.5 = $97.65

46.86 - 97.65 = - $50.79

You lose $50 dollars in equity there.

Then there's the fact that having the homefield advantage gives you a better chance at going on to the conference final, though here the calculations get more complicated since there are more variations as to who will be the higher seed.

Assuming that you are the 1-seed.

You gain $187.5 immediate value from the one game lead in the conference semis.

Multiplying this by 2.5 ($2500/$1000) gets you $468.75 value of the 1-game lead in the conference finals

But you also have to take into consideration that it lets you get from the semis to the finals 18.75% more of the time, so

2500/2 + 468.75 = 1718.75 is your expected value from the conference finals with the home field advantage

so you get 0.1875 * 1718.75 = $322.27

Beyond that you have a better chance of getting into the overall championship, where your expected value = 0.5 *5000. So instead of having, before the conference finals, 0.5 * 0.5 * 5000 =1250, you have 0.6875 * 0.5 * 5000 = $1718.75 equity there, for an increase of $468.75

So, in conclusion, looking at the value of having the one seed:

a) You do not have to play the wild card game, and avoid a $50.79 loss in equity there.

You have an 18.75% greater chance of winning the semifinals, for an expected value of $187.5

c) You have an 18.75% greater chance of winning the semifinals and thus moving on to the finals, and that greater chance of moving on has a value of $322.27 from the finals, and $468.75 from the overall championship.

So roughly, assuming my caculcations are correct and that I haven't made any huge logical errors (again, this was all just thrown together so I would appreciate someone double-checking), the value of the top seed is roughly $1000 in equity.

Okay...you know too much math. I don't wanna play you.

I actually made a pretty big mistake in the thing about the wild card game, it's actually plus EV if you just take the conference semi-finals into account, and I didn't extrapolate beyond there.

OK I think I am bleeding out of my ears now. Were'nt you the basis for "Good Will Hunting"?

I had to stop reading..............


Although I like the comment "this was all just thrown together"

C'mon - bunch of lazy bums. No one has double checked his calculations?

I somehow feel inadequate after reading this post

My Father is a structural engineer....so he knows more about math than everybody in this forum knows combined...

He says that these calculations are dead on.


I am very impressed and that is a feat since 1/4 of brain fell out of my ears while I read this post.