## January 13, 2010

### Reader Submitted Math Problem (It Has To Do With Dating, Trust Us)

When we received this email from our reader, Jeff, we freaked out. His note is like if a TI-84 calculator and the VH-1 show Tough Love collided. There's A LOT of math involved, so all of you Mathletes out there, this one's for you:
Hi Shmitten Kitten!

I'm a big fan of the blog. I've been living and dating in Philly for about nine years, so it's nice to hear about things from the other side. I recently read about a guy in London, Peter Backus, who used the Drake equation to figure out how many potential girlfriends there were for him in London. As an engineering grad student, my natural reaction was to replicate this for myself using Philly census numbers. I thought you might find it interesting. Feel free to skip the math and go right to my conclusions at the end. Here comes the science:
Potential girlfriends = (C_p * C_a * C_g * C_s) * (F_e * F_h * F_o * F_p)
C_p = Population of Philadelphia = 1,448,394
C_a = Fraction of age appropriateness (25-34) = 0.148
C_g = Fraction of women = 0.535
C_s = Fraction that are single = 0.92
F_e = Fraction that are college grads = 0.2
F_h = Fraction that I find attractive = 0.07
F_o = Fraction that finds me attractive = 0.07
F_p = Fraction with a personality match = 0.1

C_a : The census reports this range and since I'm 33 it was a convenient number to use
C_g : Use 0.465 if looking for a b/f (sorry ladies). These numbers are for the entire population, likely closer to even for given age range
C_s : I couldn't find marriage numbers for age ranges so we'll go with 8% married/engaged for this age range
F_e : Since I've been in grad school forever, this seems like a reasonable criteria to set for me. The fraction of Philly with a college degree is 0.172 but it's likely higher for the given age range, so I went with 0.2. The number for a high school degree is 0.712
F_h & F_o : The original paper used 1/20 but here I'm using a number closer to 1/15, which is possibly overly optimistic.
F_p : 1/10 seems reasonable here
Plug all that in and round to an integer and it turns out that there are 10 potential girlfriends for me in all of Philadelphia. (Bonus nerd joke: if we use F_h = 0.125,F_o = 0.125 and F_p = 0.128, the answer is 42). Anyway, the point to all of this was to suggest that you should schedule some more speed dating sessions because it's rough out there and some of us need all the help we can get. Seriously, I did the math.
Whoa. Gulp. Wow. Exclamation point!

Amanda said...

Ladies, it's worse for us. Using the same criteria but looking for a fellow, the number is only 7.8. Seven point eight! Seven dudes and maybe a midget. How depressing.

Yes to more speed dating please.

Anna said...

I plan to do more when Spring Fever hits.

It's gonna be AWESOME!

melanie said...

It's hard out there for a grad student. Solidarity, bro.

Blue Light J said...

42. Heh.

Paul said...

Jeff,

Doesn't this assumes independence for all the parameters (which can't be right). You need a propoer bayes net my friend.

jeff said...

When possible, each estimate is preconditioned by the variables that appear to the left. I figured that was too much detail to put in. I already left out the integrals after all.

bianca said...

The answer is always 42 ;)

Hooli said...

This kind of just made my day...

Phoebe said...

I am not a math person, but did I just read this correctly: Jeff's 33 and the age appropriateness max is 34? Really? Two years older is just TOO old? Seems a bit limited.

Otherwise, this was highly entertaining!

jeff said...

The age appropriate range was chosen only by looking at the ranges for which the census provides data and then choosing the one range that included my age. I guess I should have changed "age appropriateness" to "age-range inclusive"

Anonymous said...

being a word nerd i have no idea what i'm talking about, but i'm pretty sure i'm part of the F_o. math nerds are seXY.

Jon K said...

I can say that I think I now understand why I'm dating someone that lives in another state. It's just a matter of odds.

Alexandruh said...

I saw this on reddit.com. as a math major, i think its awesome.

SophiaAP said...

Wow. This is the best thing I've seen all day. Somebody tell this guy he has a date if he's ever passing through DC.

Fuck My Dating Life said...

I second more speed dating, I need some blog material. :) (PS excuse the mass responses to your blog about to happen, I'm working and catching up on EVERY ENTRY EVER).