This, of course, assumes that the opponents
always get the tossup if your team negs. Also, you're
not only adding the points for getting the bonus on
the "10+B" side, you're also subtracting the points
if your team doesn't get it. This is double
counting.
Let's say Q is your probability of getting the tossup,
q is their probability of getting the tossup after
you fail, B is your bonus conversion, and b is their
bonus conversion. Points are counted relatively, so
every ten points they get is equivalent to you losing
ten points.
You get the tossup:
10+B
points (your TU points + bonus conversion)
They get
the tossup:
-5-10-b (your neg, their TU points
and bonus)
Expected value of any TU/bonus
pair, assuming you always get the chance to buzz (or
not) first:
= Q(10+B)+q(-5-10-b)
What if
you don't know your own probability of getting it
right? Then you have to choose between these two
scenarios.
Correct: 10+B
Incorrect: q(-5-10-b)
I don't know
what this proves other than that negs are worse the
correct tossups :)