Mobile apps for real-time passenger information are neither approximately nor actually equal to frequency of service. (and yes, "neither approximately nor actually equal to" is the name of the character in the title of this post)
But that doesn't mean real-time passenger information isn't valuable. On the contrary, it's immensely valuable, in the right circumstances. For discretionary riders, who can vary their arrival and departure times, real-time passenger information is valuable. For passengers who have somewhere to wait before the bus or train comes (the proverbial "have another drink before you go"), it's valuable. But for passengers, particularly transit-dependent passengers, who are trying to mesh the geometry of transit with their complex lives, nothing beats frequency of service.
Consider an example: you will depart Event A at 1:00 PM, and must be at Event B by 2:00 PM. A bus route connects the two, and the trip takes 45 minutes. If the route runs every 15 minutes (or more frequently), you have a good chance of making your second appointment, possibly even if you miss one arrival (or if the trip loses some time en-route). But if the bus runs every 20 minutes? Every 30 minutes? It becomes a game of chance. You might make your appointment, or you might not. Knowing when the bus will come does nothing to change the inexorable geometry of a low-frequency transit network—you may know when the bus is coming, but it's still not going to get you to your appointment on time.
Some people might say "but you can call or text and push your appointment back!". Sure, some people can. If you're fortunate to be in a privileged position where you can dictate other people's schedules, then you're all set. But most of us simply have to be where we're supposed to be, when we're supposed to be there. So while it may help to know just how late you're going to be, that neither excuses nor mitigates the impacts.
This is why transit planner and consultant Jarrett Walker says "frequency is freedom". Sure, apps may help reduce wait time, but if a transit service is simply too infrequent to be useful, discretionary riders won't ride, and captive riders will suffer.
Additionally, the benefits of real-time passenger information really only become apparent when the information provided to passengers is accurate and reliable. This isn't a nuts-and-bolts post, so I will refrain from naming particular vendors or transit agencies, but not all real-time information is created equally.
It doesn't do passengers any good, for example, when they arrive at a bus stop just as their app tells them the bus should be arriving, only to find that the bus departed several minutes prior. Nor does it do them any good to stand at a bus stop (in the cold, in several feet of snow, in the blazing summer heat, etc.), watching an app count down from ten minutes, to five minutes, to one minute, and then back up again, with no bus in sight. When these things happen, passengers become disillusioned. They lose faith in the system. In the short-term, they give up on the bus or the train and call a cab or book an Uber or walk. In the long-term, they begin making plans that allow them to avoid transit—perhaps they even buy a car.
As as software developer, and one who works on real-time passenger information systems, I'm not going to say that apps aren't good. But I am also a transit rider, and I know there's a balance. Two Sundays ago, for example, after leaving the Conveyal TRB Welcome Party in Columbia Heights, I walked over to 16th Street to catch an S bus home. OneBusAway told me that the next bus was 18 minutes away—that I'd just missed the previous bus—and there wasn't a thing I could do about it. App or no app, I was going to sit and wait in the cold for another 18 minutes until the bus arrived. Arguably I should have checked OneBusAway before I left, but that's precisely what "frequency is freedom" means: it was late, I was tired, and I was ready to go home. Not in another 18 minutes, but now (or maybe in another 5 or 10 minutes, but certainly not 18).
Telling people to plan their lives around a transit app just isn't a good way to lure them out of their cars or endear them to transit. It's much more compelling (and leads to a much more usable transit system) when we can simply tell people "show up at a stop, and there'll be a bus in 10 minutes or less". It's also not a problem app developers can solve alone; as the cliché goes, when all you have is a hammer, everything looks like a nail. Providing reliable real-time passenger information is a good first step towards improving the usability of a transit network, and one that is often far less expensive than actually increasing frequency of service. But that doesn't mean our work is done once the app goes live; on the contrary, we've only just begun.