19.25 hours of service Back Bay to South Station
19.25 * 60 = 1155 minutes
56 trains from Back Bay to South Station every day
1155 / 56 trains = 20 minute headways
And that's the average for the entire day -- including the off peak runnings.
From 8:00am to 9:00am, there's a train every 4.6 minutes.
That's rapid transit frequency.
That's an average you took, not an actual indicator of what the real time from one train to the next is at Back Bay. 20 minutes would be barely acceptable by rapid transit standards if it was a regular 20 minutes, all day long - but it's not. 4.6 minutes - which, again, is an average rather than an accurate indicator of times between trains - would be an excellent level of rapid transit service. Unfortunately, good rapid transit service needs to occur for more than one hour a day.
Here's all trains running through Back Bay from 6 am to 10 am, which I would say makes for a good range of times to constitute the morning peak service. Amtrak trains (all one of them) are in blue, even though neither Amtrak nor the MBCR particularly like you freeloading on those trains. I've also taken the liberty of adding the time in minutes between each train:
Inbound to South Station:
#800 @ 6:15 AM
#P500 @ 6:25 AM (10 minutes later)
#802 @ 6:35 AM (10 minutes later)
#P502 @ 6:41 AM (6 minutes later)
#600 @ 6:45 AM (4 minutes later)
#702 @ 6:45 AM (Arrives at the same time)
#902 @ 6:59 AM (14 minutes later)
#704 @ 7:04 AM (5 minutes later)
#804 @ 7:14 AM (10 minutes later)
#602 @ 7:24 AM (10 minutes later)
#904 @ 7:28 AM (4 minutes later)
#P504 @ 7:30 AM (2 minutes later)
#706 @ 7:38 AM (8 minutes later)
#806 @ 7:40 AM (2 minutes later)
#708 @ 7:54 AM (14 minutes later)
#66 @ 7:55 AM (1 minute later)
#842 @ 8:02 AM (7 minutes later)
#604 @ 8:09 AM (7 minutes later)
#P506 @ 8:10 AM (1 minute later)
#808 @ 8:11 AM (1 minute later)
#P508 @ 8:22 AM (11 minutes later)
#906 @ 8:27 AM (5 minutes later)
#732 @ 8:35 AM (8 minutes later)
#606 @ 8:37 AM (2 minutes later)
#P510 @ 8:45 AM (8 minutes later)
#810 @ 8:46 AM (1 minute later)
#710 @ 8:49 AM (3 minutes later)
#P512 @ 8:57 AM (8 minutes later)
#908 @ 8:58 AM (1 minute later)
#608 @ 9:08 AM (10 minutes later)
#734 @ 9:20 AM (12 minutes later)
#812 @ 9:27 AM (7 minutes later)
#P514 @ 9:34 AM (7 minutes later)
#844 @ 9:44 AM (10 minutes later)
#P516 @ 9:54 AM (10 minutes later)
Well, the good news is you're never waiting more than 14 minutes for a train, and most of those wait times are less than 10 minutes. Still, this is hardly a normalized, regular schedule, and the number of 1 minute later arrivals (plus the two trains arriving at the same time) makes me feel a bit worried about that average you came up with...
Well, surely the schedule in the other direction looks better?
Outbound from South Station:
#2153 @ 6:11 AM
#95 @ 6:15 AM (4 minutes later)
#801 @ 6:25 AM (10 minutes later)
#841 @ 6:40 AM (15 minutes later)
#P503 @ 6:56 AM (16 minutes later)
#P505 @ 7:06 AM (10 minutes later)
#905 @ 7:07 AM (1 minute later)
#605 @ 7:10 AM (3 minutes later)
#2155 @ 7:20 AM (10 minutes later)
#803 @ 7:25 AM (15 minutes later)
#607 @ 7:30 AM (5 minutes later)
#P507 @ 7:44 AM (14 minutes later)
#907 @ 7:45 AM (1 minute later)
#843 @ 7:55 AM (10 minutes later)
#705 @ 8:00 AM (5 minutes later)
#171 @ 8:20 AM (20 minutes later)
#609 @ 8:45 AM (25 minutes later)
#909 @ 8:55 AM (10 minutes later)
#P509 @ 9:11 AM (16 minutes later)
#2159 @ 9:20 AM (9 minutes later)
#707 @ 9:30 AM (10 minutes later)
#93/83 @ 9:41 AM (11 minutes later)
#911 @ 9:50 AM (9 minutes later)
#805 @ 10:00 AM (10 minutes later)
Ooh... ouch. That's not better at all! Especially not given the long wait times on either side of a departing Amtrak train. Odds are, anyone trying to take the commuter rail out to Back Bay is going to be waiting a non-trivial amount of time... perhaps that's why it's much less common to see? Well, that and the fact that you probably get charged for the trip.
Okay, so AM peak hour service inbound kind of sort of approximates rapid transit frequencies pretty good. Now let's check out what happens when the morning peak ends and we move into the mid-day, lunch hour and afternoon period service - we'll take another broad sample here and go for 10 AM to 4 PM.
Inbound to South Station:
#712 @ 10:03 AM (9 minutes later)
#610 @ 10:11 AM (8 minutes later)
#910 @ 10:12 AM (1 minute later)
#2190 @ 10:19 AM (7 minutes later)
#814 @ 10:52 AM (33 minutes later)
#190 @ 10:54 AM (2 minutes later)
#912 @ 11:15 AM (21 minutes later)
#612 @ 11:28 AM (13 minutes later)
#2150 @ 11:34 AM (6 minutes later)
#714 @ 11:43 AM (9 minutes later)
#P518 @ 12:19 PM (36 minutes later)
#816 @ 12:20 PM (1 minute later)
#170 @ 12:36 PM (16 minutes later)
#716 @ 1:01 PM (25 minutes later)
#614 @ 1:28 PM (27 minutes later)
#2154 @ 1:34 PM (6 minutes later)
#P520 @ 1:49 PM (15 minutes later)
#818 @ 2:45 PM (56 minutes later)
#914 @ 2:49 PM (4 minutes later)
#718 @ 3:00 PM (11 minutes later)
#172 @ 3:05 PM (5 minutes later)
#2158 @ 3:35 PM (30 minutes later)
#P522 @ 3:39 PM (4 minutes later)
#616 @ 3:45 PM (6 minutes later)
#916 @ 3:53 PM (8 minutes later)
Yeah... those are some pretty huge holes there in the schedule - and if you assume you're not going to be bluffing your way onto any of those Amtrak trains, the time table looks that much worse for it.
I could take a look at the evening peak timetables too, but I think you get my point. A statistical average doesn't necessarily reflect the true frequency. More importantly, rapid transit frequencies aren't rapid transit frequencies if the only time they happen is by coincidence, mostly during peak hours.