So it’s day two. And I’m back. So this project has lasted longer than any diet I’ve ever tried…

I mentioned yesterday my hypothesis about the time distribution of SMS message replies, and to prove that my mind turns the trivialist of matters into mathematical models here is the expansion of that idea.

Let’s say that at 12:00 you send a text message to a good friend; not a deep and meaningful ‘we need to talk’ message, just a genial ‘how’s your day?’, ‘fancy a pint later?’, ‘Do you realise you had asparagus in your teeth when I saw you yesterday but it was funnier to not mention it at the time?’ or some such. The sort of text that you would expect a relatively quick reply to. Now at 12:10 let’s say you send another message of a similar nature to a different friend, before the first friend had replied to the first message. At 12:15 your phone makes that little Pavlovian jingle to indicate you have a message. Before you read it (and assuming it’s a reply from one of the two previously mentioned friends), which of the two do you think it is most likely to have come from?

My hypothesis says that it is much more likely to come from the second friend than the first friend.

To explore this idea lets make some assumptions to make it easier to reason about the situation. Let us assume that the messages sent are such that the receiver would be highly likely to reply ‘as soon as they are able’ – it’s not a message that requires a lot of time to consider and reply to, it doesn’t require the receiver to do a lot of work before replying for example.

We also assume that the receiver is ‘predictably lazy’ – when they receive a message they may wait a while before replying due to procrastination tendancies, but they will still reply as soon as they ‘get round to it’ – we assume they won’t reply at some random time that afternoon determined by little more than whimsy.

In that case we assume the only reason that a reply is not received ‘instantly’ (minus the time needed to receive, absorb, and construct a reply) is that the receiver is currently unable to reply for some reason – they are in a lecture, at work, walking home from town, performing some street theatre or whatever – or are being lazy.

I put it that the probability distribution of a reply diminishes over time – in the first minute we might reasonably expect a noticable probability of a reply, there is less reason to assume a reply will come in the 17th minute – if they haven’t replied in 16 minutes, why should we suppose they would reply in 17? The longer a reply doesn’t come the more we must assume there is a reason they are not replying sooner (being in a lecture, laziness) and so the less we should expect a reply the next second, or the next minute.

In the example above therefore, at 12:15 it has been only 5 mintues since you sent a message to friend two, but 15 since you sent one to friend one. Therefore, by this hypothesis, you must assume there is a greater chance of friend two having replied.

I have personal anecdotal evidence in support of this theory, though of course I’m more than likely to suffer from confirmation bias. If I could be bothered, or if the results would actually have any kind of bearing on my, or anyone else’s life I might conduct a more formal experiment. But, you know, meh.

Till tomorrow, I hope.

Mark