Subways routinely are: 1 late, 2 closed for repair, 3. de routed etc...

eg. today, the 6th is not operating uptown, between 9:45 last night, and 6:am next morning

You say, fine, I will take another line, but then the 2 and 3 are not operating at all due to 'tunnel repair',

You need to go to work? Your choice is go downtown, take one of the express trains to uptown, and take another downtown train.

So, your 15 minutes train ride becomes 45+ minutes. You can always take a cab, but this becomes expensive to do regularly, plus during rush hour it is hard to catch one.

NYC's subway runs 24hrs in theory only. It is always a whack-amole game if the train is 1. late, or overcrowded, your 2. station is closed, 3. the whole line is not running that day, and My least favorite: 4. Tain strands you for a while, because "there is traffic ahead", or some accident happen.

Just as the article mentioned, I noticed I had to start leaving early to make sure I make my soccer games in time (they are in brooklyn). In case the usual route has issues (which happens about 25-30%% of the time during weekends).

It's a cascading failure issue. Toronto has the same problem, on a smaller scale. What I see here:

Step 1: a train gets delayed for a minute somewhere on the line. A dozen common reasons exist- someone becomes ill, mechanical issue, debris on the tracks, etc.

Step 2: Because it's rush hour, there's minimal buffer time between trains so the train behind it must also stop (and the one behind it, and the one behind it, etc). Even a 60 second delay of one train can back up the whole line.

Step 3: Because a train is late, there's more people trying to get on and off, which makes it take more time per station. As well, with more people per train, there's more human-related delays per train. The additional delays mean "go to 1".

With large enough buffers between trains, the system is stable- the problems get smoothed out. With small buffers, like during rush hour, the system can get into a feedback-loop total system failure. A 30 minute trip becomes hours long.

So, first thing that's helpful to know in answering is that there is actually a schedule for the subway. For example, here's the one for the A line:

http://web.mta.info/nyct/service/pdf/tacur.pdf

At least back in 2012 or so, when I cared, the A train did keep reasonably close to this schedule (effectively genuinely on it when it wasn't rush hour). It definitely does not keep to this schedule now.

Now, do New Yorkers actually know this schedule? Well, sometimes, actually: while trains do come every few minutes in Manhattan, any specific train comes much more rarely, up to about every 20 minutes for the A train I linked above. This matters if you can't afford to live in Manhattan, or even if you live far away: for about a year, I commuted regularly from 181st St. to Fulton St. on the A, and you better damn well believe I had a specific train I wanted for that trip.

But even for those who don't, if the train gets too far off schedule, you start getting delays, because the trains cannot handle the throughput. Maybe for those commuting within the Midtown area, you know that a train will come every 3-5 minutes, but if the train that would normally take you is still 15 minutes away, then you've got at least a 12 minute backup of extra people who are going to be on that platform. Not only does that mean you won't manage to get your normal train (because you won't be able to reach the platform); it also compounds, since it'll cause people to enter and exit the trains more slowly. There are also many times when trains join or split from sharing the same track, and scheduling delays can change a smooth swapping of a switch back and forth to a traffic jam as controllers try to figure out whether it matters more to give the E or F priority on such-and-such a segment given that the nearest D and C trains are in such-and-such a place. You get this same kind of thing on your compute with disk seeks: it may not seem like a big deal if a read request shows up a millisecond late due to bus contention, but if it means that the drive head has just moved past the data you want, you're gonna have a long delay while it sweeps back, and that in turn may mean that other requests get delayed and so on.

So: yes, the schedule matters even if you don't know the schedule; but it still causes problems even if you want to think of it purely as "bandwidth."

Running slower than it is supposed to or broken down frequently. So, the trains still come every 3-5 minutes, but it takes (for example) twice as long to get there sometimes (track problems causing them to run trains slower than normal, or just being stopped for an arbitrary amount of time). So you end up 20 minutes late to your job. So if you absolutely have to be there on time, you have to leave 20 minutes early (at least).

And in my experience there is no cell service when you’re in the tunnels, so you can’t even let your work know there’s a problem.

One train leaves. The next train is due in 5 minutes but doesn't come for 15 because of equipment problems, a medical emergency, etc. Now there are three trainloads of passengers trying to get on to that train. Some won't get on till the next train or the train after that, and the trains get more delayed as people squeeze on. In the end, people are half an hour late to work.

It’s not about the train showing up late, it’s about the train taking a long time to go from stop to stop. People are spending more time on the train due to how slow it’s moving.

THe keyword here is “supposed”. I don’t have regular experience with NYC subway, but used to ride Toronto subway everyday, which is the subject to the similar problems. The trains do arrive every 3-5 minutes on weekdays, but then something happens (security incident on a train, unauthorized person on a track level, fires, signal problems, or - the most horrible - “personal injury on a track level”, the language for someone falling in front of the arriving train - intentionally or not. Then everything stops for tens of minutes, or hours in worst cases, stations get overcrowded, buses get sent to operate on the route, taxis and Uber’s are impossible to get and so on. Things like this push average delay times up, not the uniform slowness of the trains throughout the day.

They're late because they're moving slower and randomly-but-frequently stopping between stations.

The trains are frequent, but so are unscheduled stops. Even as a tourist, you don't have to take many rides to get familiar with announcements that start with "We are being held momentarily..."