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I'm not sure I'm reading your formula correctly. Is that ln|e^((S-Q)/Q)|?

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No, that would evaluate merely to (S-Q)/Q.

It's ln(e * (|S-Q|)/Q)

-AF

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Okay, good. How'd you decide on that?

If I were in math class, I'd write the whole thing as

Ps = Q/T * (1 + sign(S-Q)(1 + ln|(S-Q)/Q|)

To make it easier for people who are less familiar with math notation, maybe two formulas for the different signs?

If you program, you may wanna try writing a program that calculates your actual EV with various chip stacks in various sized tournies, using the trick that your odds of coming in second are the sum of your odds of coming in first in a tourny without player i times the odds that player i wins.