I’m flying from NY to SC to see the show. Actually, I am flying in then driving 200 miles. It’s a vacation!!!

Also relevant to the cost per mile is the total cost to attend vs amount of disposable income, preferably in some sort of confusing equation as well. If the cost relative to disposable income is too high, then the whole equation should be scrapped.

Thanks for pointing out to me that I could be a lot bigger nerd.

Good additions, though I miss the simplicity of something like Geof’s equation of motivation.

Your initial assessment of the equation is good. The qL term is fantastic – A short but very high quality show should rank about the same as a longer but not as good show.

What’s been tripping me up though is the distance/time term. I think the way you have it treats the two as unrelated, when it seems like they should be more intertwined. Say, for example, the show is 10 miles away. If it takes you about 15-20 minutes to get there that isn’t insane at all. But what if it ends up taking you an hour? That should increase the insanity level significantly.

So I guess there’s no notion present of how long it takes you vs. how long it *should* take you. I propose therefore modifying the distance-time relationship thusly:

d ^ (t / t_e)

Where t is actual travel time and t_e is expected travel time (and ^ represents “to the power of”). So if that 300 mile trip took twice as long as it should have, that will square the distance term. Alternatively, if it takes you half the expected time, it will squaure-root the distance term (quite handy!).

But even this model has flaws. It treats all time/expected-time ratios equally. Twice the time on a 10-minute expectation is the same as twice the time on a 5-hour expectation. I’d say that driving 20 minutes instead of 10 minutes is much less insane than driving 10 hours instead of 5 hours.

So what if we alter the time term to reflect this?

(t / t_e) ^ t_e

Or in a specific example (ignore units):

(2 hours / 1 hour) ^ 1 hour = 2
(10 hours / 5 hours) ^ 5 hours = 32

As the expected travel time increases, your percent-error alters the time term more. Though in the example both trips took twice as long as expected, the longer one will affect the insanity much more.

This also has two happy side effects: If your trip takes half as long as expected, Insanity is lowered much more if your expected time is longer (if you make it in 3 hours instead of 6, it’s eases the insanity much more than making it in 10 minutes instead of 20). Also as your expected trip time increases, small errors count less. Taking 10-minutes longer counts much more if you expect to drive for 5 minutes vs. if you expect to drive for 5 hours.

I’ll leave it to you to convince yourself of this.

So I humbly submit my modified version:

I = (d ^ [(t/t_e) ^ t_e]) / qL

Where

I = relative insanity of the trip
d = distance traveled to the concert
t = time that the trip took
t_e = time you expected the trip to take
q = quality of the artist
L = length of concert

(using two types of containment parens for clarity of reading and nothing more)

Of course each raw variable needs to have some constant kn associated with it to make the units happy and temper the equation to empirical evidence, but hey, that’s just nerdy.

(PS — Hoping this formats better than it does in “Preview” mode… Sorry if it doesn’t!)