This NYT taxicab thing is stupid (Or, how I know the NYT has never interviewed for McKinsey)

If you live in New York, read the NYTimes, or read any bloggers who like fun econ-y facts, you've probably heard about this study done by the Taxi and Limousine Commission to track customer pickups using GPS.

From the NYT:

It is a question that taxi-seekers in New York often ponder: Is there some kind of secret formula for where to find a cab in this town?  Turns out, there is.  A new mobile application allows would-be riders to see a map of nearby street corners, ranked by the number of taxi hails they attract at that hour, on that day of the week.  The most popular corners to catch a yellow cab in Manhattan can now be pinpointed, at any hour of any day of the week, thanks to a record of 90 million actual taxi trips that have been silently tracked by the city.

OK, so far so good, so this data can tell me where most people take cabs from.  But then the article goes on to say:

On a Saturday at 11 p.m., it is easier to hail a cab on the nightclub-and-bar-filled Lower East Side than at Grand Central Terminal. Columbus Circle gets more passenger pickups than the Port Authority bus station. And make sure you are in the right neighborhood: taxi rides are 25 times as likely to start in the West Village as in Washington Heights.

The problem with this is that it's not true. 
What determines ease of hailing a cab is not just the number of cabs, but also the number of people trying to hail.  In other words, if you're alone in an area of the city where a cab comes every 25 minutes versus standing on a street corner with 25 other people where a cab comes every minute, your chances of hailing a cab in a given minute are the same: 1 in 25.  Therefore, just because there are more pickups on the Lower East than by Grand Central doesn't mean it's easier to hail a cab there.  What we care about for ease of hailing a cab is the ratio between the number of available cabs and the number of people looking for cabs.  On average, between very busy areas and very slow areas, these ratios are likely to be similar, because cab drivers themselves optimize, moving to new areas whenever the probability of getting a fare times the potential fare is higher than where they currently are.

 It gets worse, because a scientist gets in on the nonsense (he's a computer scientist, not an economist, so I forgive him--although not the NYTimes for quoting him):

“You always argue with your friends about it — I think you should stand on Sixth, I think you should stand on Seventh,” said Blake Shaw, a doctoral candidate at Columbia University who oversaw the data analysis for CabSense. “To be able to say you’re 50 percent more likely to get a cab on Seventh, that’s unique.”

Again, just because there are 50% more cab pickups someplace does not mean you are 50% more likely to get picked up--not if there are 200% more people waiting for those 50% more pickups!  But no matter, the Times has everyone from Gawker ("60th street is objectively the best place in Manhattan to catch a cab," they say) to Tyler Cowen ("There's also a new iPhone application that tells you where to stand to maximize your chances of getting a cab") lauding the study's potential, without anyone stopping to point out that the write-up is completely misleading.  To be fair to Cowen, he does talk about the equilibrium and optimality of it all, but he doesn't take the time to question the premise that an app that tells you where the most people get picked up cannot tell you the best place to get picked up yourself.

The joke about McKinsey in the headline comes from the fact that a common management consulting interview question focuses on whether a cab driver is likely to make more money at the airport, where the fares are high, but so is the wait for a customer, or in the city, where customers are plenty but fares are low.  The answer, after some other assorted calculations, is that the two are likely to be equal, because cabs will move to the airport until their expected payoff is equal to what they'd get by staying in the city.  Therefore, in equilibrium, the last cab making this decision (the "marginal" cab) should be indifferent.  What you as a potential cab hailer want to look for, to really determine ease of getting a cab, are those out-of-equilibrium situations, where for some reason the number of free cabs is greater than the number of people trying to hail should warrant.  This can happen on streets that open cabs use as thoroughfares to get to busy areas, for example, but where there aren't actually any customers waiting.  It can also happen at places where there is about to be or has just been a big swell of customers, and the cabs are there waiting, or haven't moved on yet.  An iPhone app that could identify these phenomena would be something worth celebrating.  Until then, this is just an interesting heat map of where people are, that says nothing about where you should be.