Work out the probability that my odd socks are specifically targeted by sock stealing gnomes. I have 43 odd socks, and 18 matching pairs, true story.  Obviously the probability of loosing a sock is greater if it is a matching pair, than an odd pair - I am less likely to wear odd socks, so they just remain safely in the drawer.  
But if such a bias hypothetically did not exist (i.e. I selected socks randomly from the entire pool each time), and despite not knowing the original number of pairs I started with, is it possible to get the probability of having such a ratio (43 to 18) or worse?  
 A: Monster math:  say you start out with a large number of pairs, $N$.  Sufficient so that the probability of a sock getting lost is roughly constant over the period (may be a poor assumption).  Let $p$ be the probability of a sock getting lost on a given day (constant and independent of all other socks), and let $d$ be the number of days.
How many odd socks do I expect to have at the end?  Well, let $X_i$ be the indicator variable for the $i^{th}$ pair.  Then $$E[\text {odd}]=2\times N\times (1-(1-p)^d)\times (1-p)^d$$
Similarly, the expected number of matching pairs is $$E[\text {matching}]=N\times (1-p)^{2d}$$
Example:  $p=.001, N=100,d=365$ .  Then $$E[\text {odd}]\approx 42.46
\quad\&\quad E[\text {matching}]\approx 48.17$$
This does not match your data especially well.  
On the other hand, taking $p=.002,N=100,d=365$ gives
$$E[\text {odd}]\approx 49.93
\quad\&\quad E[\text {matching}]\approx 23.19$$ 
Which is a pretty good fit to your data!
So, it seems that the model is very sensitive to the initial assumptions.  Hard to say much more without some way to narrow down the process.
Remark:  if you want a more physical model, where the probability of a sock getting lost increases over time as the total number of socks decreases, then I'd just sample it.  
