My experience is more that the actual traffic delays are fairly consistent from one day to the next, maybe 3-5 minutes variation at most.
I would say it is unpredictably predictable - there are patterns you can seen and understand but they don't happen consistently enough to plan around. Like SteveinSelby I used to catch the bus to work most days and recorded all my trips, with professional interest as the main part of that journey was on my employers that I helped schedule, and whilst the morning was very reliable as it was before the morning peak the afternoon trip was at the start of the evening peak and was quite variable (anything from 5-mins early to 30-mins later). I could often predict in the morning what the afternoon would be like (weather, time of year, day of the week, special events) or during the day (motorway issues) which would require customers to be able to work out which one of half a dozen timetables depending on such factors (BST vs GMT, Schooldays vs School Holidays, Wednesdays as Colleges & Unis finish early for activities and now Mondays & Fridays with home working holding down commuting) would be both unattractive and confusing.
The big killer at the moment are roadworks, they are always popping up (often with little to no notice) and can often have outsize impacts - there have been lots of discussions on here about the impact works have had in Nottingham and Long Eaton and we had a set of temporary lights pop up on a main road covered by one of our major routes and buses were losing 30-60 mins on every trip with no warning.
The problem is that this only works if the operator does everything else on time. But all the other issues that the bus operator can control get added on to that traffic- drivers not pulling on to the stand until departure time being a favourite. And that then causes the delays to escalate as everyone for the next bus arrive and so you end up 10-15 late.
But those same level of delays can accrue out of operator control just as easily (wheelchair users, difficult customers or complicated enquiries, roadworks or unexpected demand) can all delay a bus by a couple of minutes at one point that can escalate into significant delays by the end of the trip. I used to drive occasionally to work, largely to allow me to stop at the supermarket on the way home, and a couple of minutes difference in when I left could cause a 15-min delay on arrival as I would be much further back in the building queue.
I really don’t agree that traffic is all that unpredictable. I think operators hide behind traffic delays as an excuse for quite a lot.
I have trip by trip analysis for 4 different services on my desk at the moment, whilst a couple do have some trips that are consistent issues that offers an obvious fix on all of them there are significant inconsistencies day to day (there is one where it is alternating on the same trip between "on time" and "late" almost every day through a week, the next week being all on time and the third week dropping back to the alternate days pattern).
It does depend somewhat where you are, big cities are more unpredictable but their peak period extends over a significant period of time whilst small towns have more predictable traffic but over much smaller windows so minor delays or changes can have huge impacts on running time (that 2 or 3 minute discussion around the best ticket to buy or the slight delay taking the bus out for the start of the trip can really cascade). We had one route that had 3 trips leave one end of the route over an hour window but their arrival at the other end was spread over 90-mins (we had two trips leaving within about 15-mins of each other but one took 45-mins and the other over an hour and was always 10-mins late, the depots suggestion was to just start 10-mins earlier but I pointed out if we did that we would avoid all the traffic and arrive 30-mins early - finding that sweet spot can be quite difficult in these circumstances).
