## Thursday, February 12, 2009

### Considering Dating Pools

This XKCD comic got me thinking this morning. I agree that the quantity of prospects might increase as one gets older. However, what is there to be said about the quality of these prospects? I drafted the following chart to help with this discussion.

There are a few things to note about this graph. First, the shape of the curve f(x) is such that f'(x) < 0; for some initial age A to A + E, f''(x) > 0; from A + E to infinity, f''(x) < 0. This first derivative expresses that people are exiting the dating pool (by marriage, death, etc.). The second derivative states that they do so at an increasing and then decreasing rate (a lot of people exit around 23-30, while fewer exit from 40-50). The area under the curve is the total number of prospects in your non-creepy range.

Suppose you are x years old (where x > 26). What can you conclude about your prospects? I'd suggest that those to the right of the dashed line are probably lower quality prospects. Probably. There are certainly some who have not yet married because they were focusing on their careers or traveling the world. But most are simply the leftovers.

If we were to adjust the original XKCD findings to include a qualitative measure, we would essentially eliminate the area to the right of the dashed line. However, a portion of those to the left are low quality as well. This could be illustrated by shifting the entire f(x) curve down.

Now let's think of this in a dynamic sense. Every year, your x moves one notch to the right. But, a batch of new prospects (NP) enter your non-creepy range on the left [recall that we are ignoring those entering on the far right because we already know they are low quality]. Of these new prospects, a portion of them are low quality, NP(LQ), and as such are above the red curve (but below the black curve). The rest, however, are average quality, NP(AQ).

At the same time, a portion of the average quality prospects who had entered the dating pool in earlier years exit the pool (again, by marriage, death, etc.). Let's call them EP(AQ). The question, then, is whether NP(AQ) is greater than, less than, or equal to EP(AQ).

I think some back of the envelope calculations would support the original XKCD hypothesis. Even adjusting for quality, your non-creepy dating prospects increase until around middle age.

So don't feel bad if you are single on Valentine's Day. Unless you are middle aged or older...

[HT: Angela]

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## 2 comments:

The tail has to be fat or possibly bi-modal because of the death of spouses clustering around the higher ages. I guess a firm definition of creepy would be helpful in determining the relevence of this comment.

XKCD's definition of creepy is

(AGE/2)+7.

This lower bound implies that the upper bound is

2(Age-7).

I cut off the tails on both ends past these points. It probably would have been helpful to label these points, but I figured I'd wasted enough time already. haha

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