User blog comment:RobinCarr/Proposal for New Presentation of Fusion Success Probabilities/@comment-5039776-20120825074718/@comment-5116140-20120825151200

<< Are we certain the probability is an arithmetic and not geometric mean? >>

We are certain, but that's a really good question as your proposal of the GM is also symmetric and idempotent, in that for both the GM and AM we have

P(p,p) = p (idempotent)  and P(p1,p2)   = P(p2, p1), symmetric

The confirmation is really the full relationship involving the crystal fee to guarantee success. Note the crystal boost fees are not from the Dino Fusion File, but only appear inside the fusion chamber itself. (emperical)

The two relations, P= (p1+p2/)/2 and Boost Fee = 10 + Failure%

explain all the emperical crystal boosts perfectly.

Neither the GM nor any other measure of average can do that.

Indeed, the two relationsships provide an explicit derivation for P(p1,p2) as seen next.

Faliure % = 100 – P(p1,p2) = Boost Fee – 10

so

P(p1,p2) =  110 – Boost Fee  = 110 – Fee(p1,p2)

so

P(p1,p2) =  110 – Fee(p1,p2)

Since the table of crystal fees show arithmetic progression along each row, we have a solid derivation. Good question! I had removed the derivations as "too much"

Thz for keeping me on my toes.