Everybody knows how to play the game “Signs That Indicate How Long I’ll Stand on The Platform Before The Train Arrives.” For example, how many people are in the station? How nervous do they look? How long, historically, has it taken the damn C train to get here? Would running upstairs and taking a bus or cab be faster? Probably not! Traffic is the worst.
Still, despite years of your own data points, you understand there is no one sign that can accurately give you an answer. On a given day, a train could just as easily arrive in one minute as it could in twenty. When it comes to the MTA, the world is an eternal, exciting mystery.
And that still is true! Except now someone has figured out, on average, exactly how long you should wait for your train before submitting to an Uber, or walking, or god forbid, taking the bus. The answer? Eleven minutes.
As reported by Technical.ly, engineer Erik Bernhardsson explains this magic number in a blog post called NY Subway Math. Using oodles of data from the MTA’s open API, Bernhardsson outlines why 11 minutes, on average, is usually the point beyond which you can determine: something is seriously, mechanically F-ed, and I should get out of here. At least, that is, if you’re in a hurry. But when are we not? Basically, this applies all the time.
Here’s why: In an effort to understand whether a given wait is, as Bernhardsson accurately describes it, a “sunk cost” versus an “investment” he listened to his intuition. He thought, there must be “a T [time] such that the expected additional time you have to wait goes down as you approach T, but then goes up afterwards. Until T, every second you wait gets you closer to the next subway,” Bernhardsson reasoned. “After T, there’s most likely some random issue with the subway and you should just give up.”
Berhnardsson gives us several scenarios below: starting with the 50th percentile of wait times (the median case, outlined in blue), and moving up in increments of 10 to the worst case scenario, the 90th percentile (outlined in yellow).
Using all of those open data points that none of us would know what to do with on our own, Bernhardsson calculates that when you walk into a given station—if you’re lucky—on average, you’ll wait five minutes; if you’re not, on average, you’ll wait 11 minutes.
Then, he writes, “The interesting conclusion is that after about five minutes, the longer you wait, the longer you will have to wait. If you waited for 15 min, the median additional waiting time is another 8 minutes. But 8 minutes later if the train still hasn’t come, the median additional waiting time is now another 12 minutes.” Basically, the longer you wait, the more likely it becomes that something is seriously wrong.
And this is when we have to make a judgment about how much more time you care to sink, or can sink into the MTA and never get back. “Let’s assume you want to optimize for a wait that’s less than 30 min in 90% of the cases. Then the max time you should wait is about 11 minutes until giving up,” which, according to the chart, is the point at which the worst-case-scenario yellow line extends beyond the 30-minute mark.
So, while most will continue to use anecdotal evidence, taking in the number of frowning faces and crowds on a given platform, and trying to decipher what on earth is being announced over the indecipherable loudspeaker system, those more-well-informed with Bernhardsson’s numbers can now make a solid bet on waiting for 11 minutes (if you’re a pessimist and assume the worst case scenario) before hightailing it to an Uber that waits patiently for you above ground.
And if you live on the L train, you can use this advice at least until 2019, when, we have finally found out, the L train tunnel will likely shutdown for scheduled Sandy repairs that might last 3 years. But at that time, at least we know who to reach out to to figure out our best-case, worst-case-scenario commutes.