Songs without Words

Two months ago, I was reading some quartets with a fellow violinist for fun.  At some point, I brought up my concept of “subway karma” – basically, that there was some quantity of good fortune I could build up (by waiting long times), and that it would dissipate at some point in the form of the train arriving immediately when I got to the station, ideally – and usually – when I really needed to get somewhere quickly.  I also threw out concept that when in a rush, the occurrence of either just missing or just catching a train was much higher than usual, and that this was somehow tied to some subway spirit’s judgment of me.

He of course told me this was ridiculous and that if I were really a scientist, I should prove it with data.  So I’ve done just that – I’ve recorded the majority of subway rides on the Red Line that I’ve taken in the past two months, notating the amount of time I waited (note that 0 = the train is right there as I enter the station and I’m able to board it; -1 = the train pulls out just as I’m entering the station – I did record the actual wait times for these, but those data are not presented here).

Here are the wait times for all the rides (n = 78), in chronological order.  I did not write down exactly what time I took each ride.

While it’s impossible to prove whether there’s a subway spirit or not, this looks pretty convincingly .. random.  No pattern of build-up and dissipation or anything like that.  But what about being in a rush?  Being in a rush was defined for these purposes as me having to get someplace at a set time, and that I was not leaving more than 5 or 10 minutes of extra wiggle-room in the estimated trip duration.  n=28 for being in a rush, n = 50 for not being in a rush.

What’s interesting here is how much more likely it is that I will catch a train just as it’s arriving at the station when I’m in a rush.  Most likely it’s something like the increased frequency – and increased stopping times – of trains during times when I’m likely to be in a rush (near or just after rush hour).  And it’s confounded by the fact that I can see people walking out of the station, or even hear the train pulling into the station, before I even enter the station, and make my own judgment about whether or not to book it.  But it’s interesting that my perception reflected a dimension of reality in this case, even if the magical interpretation is nonsensical.

Other notes: I never actually realized before how frequent the red line trains are, especially in comparison to the very long times I was accustomed to waiting on the green line.  My average wait time over this period was 2.6 minutes (here I’ve used the real wait times in place of the “-1” notation for missing a train), which makes sense given that I travel about half during rush hour (every 9 minutes per line, but I don’t care whether it’s Ashmont or Braintree so it’s every 4.5 minutes) and half during other times (every ~12 minutes per line, so 6 minutes per train) – the expected value of waiting would be 5.75/2 or ~2.9 minutes.  Weekend frequencies are lower, but I did not notate a lot of the weekend trips, because they were rarer and the “wait time” tickers are often shut off, so that it’s harder to keep track of how long I wait.  Overall, 62% of the time, I waited 2 minutes or less for the train.  Not too bad!