Optimal sock purchasing strategies

| Comments (5) | Overthinking
Most of my running socks are Wigwam Ironman Ultralites, but I recently tried some of the Injinji Tetrasoks, which seem to be the preferred choice of a lot of the ultra guys. The Tetrasoks are more like gloves for your feet than socks: each toe is in an individual pocket, thus at least theoretically preventing blisters between the toes. Takes a little getting used to, but they're pretty comfortable, actually.

Anyway, this creates a new problem in terms of laundry: ordinarily, any pair of socks the same color make a pair, but tetrasoks are chiral, so if you just pick a random pair of socks you have a 50% chance of having two lefts or two rights, neither of which is very useful. So, with ordinary socks it's likely optimal to have all your socks the same because that minimizes your search cost (no matter what your laundry strategy is). However, the situation with tetrasoks is more complicated. Let's say that you have a pile of laundry and you pull items out one at a time. If a sock matches a sock you've already seen you pair it up. If not, you put it aside waiting for a match. If it takes time X to figure out what color each sock is, and tiem Y to tell whether it's a left or right sock, then if X > Y, then you want to get all socks the same color: you just have a working pile of socks (either left or right). When a sock comes in it's either the other side, in which case you pull a sock off the stack and put the pair away. If it's the same side, you put it on the stack.

On the other hand, if Y > X, it's a little trickier. You need to maintain a separate pile for each color. If you only have one of each color, then you only ever incur X, since the second of each color must be its match. On the other hand, if you have more than one of each color, then you incur Y + X because you need to know both which pile to look in and whether a sock is a match or just more of the same (this can be partially optimized when you've already paired up all but one pair of a given color, at which point you go back to incurring X for that color). So, the breakeven point here depends on how many different colors of socks the manufacturer makes. Injinji only makes three colors of this sock (white, black, tan) so it probably makes the most sense to buy all one color.

Extra Credit: Is the situation the same if you just throw all your socks in the drawer and then try to pick out socks later? Scanning for colors isn't the same as deciding what color something is...

UPDATE: Apparently this is a problem many others are concerned with as well.

5 Comments

Black socks? With sneakers?

I nearly had a heart attack when I saw the headline; I had replaced "sock" with "stock" and thought you had gone off the deep end with some bullshit market prediction mechanism.

I have never been so glad that a blog post was about socks.

For cycling, I wear all Under Armour black low-cut socks. They're quite comfortable and effective. When it gets to really cold temps, I switch to a taller, thicker UA sock.

I wonder about 1 pair each of all but one color, and N pairs of the remaining color. Then you have a fast success if you happen see two matching socks for most of the colors, otherwise you search. Perhaps this works best when you have an at-a-glance overview of a substantial fraction of the total clean laundry, and the socks themselves are readily distinguishable from the background laundry.

Educated,
Wouldn't it be simpler to keep pairs of socks *together* through washing and drying? Try those mesh zipper sacks that women use for washing lingerie (to keep bra straps from tangling). Surely Mrs. G can find them for you.
At worst -- if all your socks are the same color OR you can't tell the colors apart -- you will need as many sacks as you have pairs of socks. They're cheap. :-)

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