Reduction of clock face to sporadic on Three Rivers is, I understand, making it hard for them to sustain positive traffic direction, and also hard to maintain customer confidence.
In your experience grahame, in general, are more people put off by unevenness in times or the pattern itself?
say
a) 12.05, 13.10, 14.05
would be seen as more favourable to more people than
b) 12.05, 13.10, 14.15
for example?
What an interesting question. You give me far more credit for knowledge on the topic than I have, but I will share some thoughts (which are wider than your question)
A clock - 60 minutes in the hour - is society's established way of slicing time and it's become a natural way of setting cyclic patterns that are easy to learn and follow. So for both the providers and users of a public transport services, a 60 minutes (or multiple or division thereof) element makes huge sense - in planning, pattern running, information systems, public knowing when to turn up.
BUT ... clocklface has its issues.
1. It's too granular at the very point ( services half hourly to every 2 hours) where you're likely to want to adjust:
Train every 10 minutes - 36.00 in 6 hours. Step down to every 12 minutes is an interval increase of 20%
Train every 12 minutes - 30.00 in 6 hours. Step down to every 15 minutes is an interval increase of 25%
Train every 15 minutes - 24.00 in 6 hours. Step down to every 20 minutes is an interval increase of 33%
Train every 20 minutes - 18.00 in 6 hours. Step down to every 30 minutes is an interval increase of 50%
Train every 30 minutes - 12.00 in 6 hours. Step down to every 60 minutes is an interval increase of 100%
Train every 60 minutes - 6.00 in 6 hours. Step down to every 120 minutes is an interval increase of 100%
Train every 120 minutes - 3.00 in 6 hours. Step down to every 180 minutes is an interval increase of 50%
Train every 180 minutes - 2.00 in 6 hours. Step down to every 240 minutes is an interval increase of 33%
Train every 240 minutes - 1.50 in 6 hours. Step down to every 300 minutes is an interval increase of 25%
Train every 300 minutes - 1.20 in 6 hours. Step down to every 360 minutes is an interval increase of 20%
2. It can result in very long layovers (inefficient stock use) [or tight schedules often broken] at terminal points
76 minutes in every 120 at Swindon on the two hourly / 70 minute run service to Cheltenham Spa
41 minutues in every 60 at Salisbury on the hourly / 67 minute run service to Romsey via Southmapton Central and Aiport
3. Once your clockface service frequency is below a certain level, you're likely to find specific instances where it's unfortunate. Take a two-hourly clockface service into an employment centre - if the service arrives at 08:45 for people to get to work at 09:00, it would leave back at (say) 16:55 when they finish work at 17:00 ... next rain service 18:55 if strict clock face.
Those apply to rail and road
... on rail also, clockface may interfere with services on other interval patterns, and may give rise to even worse efficiency issues due to capacity; the TransWilts being a classic example of the latter, where an hourly clockface service would require three trains - each running for 90 minutes and then parked up for 90 minutes (46 at Westbury and 44 at Swindon) because of the section of line that was singled in the last century.
... on road also, clockface throughout the whole service running times means it has be be timed for worst congestion times, and results in buses "waiting time" along the way at any time except peak - that's frustrating and expensive in operation and people's time.
Now ... if you can't practically achieve the apparent Utopia of a clockface service, what should you do?
The Severn Beach line runs on a 40 minute service - in some ways that's half-clock face as it's xx past the even hour and yy and zz past the odd hour - an elemet of a pattern that people can remember. There was some concern this wouldn't work when it was introduced, but the line and service blossomed on introduction, only stuttering as the capacity and reliabilty of the service has stuttered.
Another possible approach is to run a service (say) every hour and ten minutes if you can't get round in the hour. I've seen this on self contained heritage lines - but on a line that's part of the national network or interfaces to it, where clock face patterns are the norm, such an approach is really difficult to schedule and causes all sorts of glitches and near-miss almost-connections.
On TransWilts and on some other lines with substantial single track sections, 2 trains in 2 hours (but not at the same time in each hour) would work. Trains at 07:00 , 08:20 and then (both) every 2 hours would work operationally, the asymetric nature allowing the trains to pass each other away from the single line section, but at the cost of a reduction in simplicity and an increase in some inter-train gaps.
For certain less frequent lines which run from a junction through to a terminus, especially where the service at the junction is irregular and most passengers connect to mainline trains, I'm going to suggest that clockface could be counterproductive. On current timetable (but not necessarily when the half hourly regular service comes in) this would apply to the lines to Looe and Newquay. It might also be applied to lines as diverse as Bleaneau Ffestiniog and Whitby.
In conclusion - I suspect the best thing is to look at each line individually. Where the service is more frequent that hourly, the metrics will differ from where the service is less frequent; in those latter cases, individual tuning will come to the fore where in the former case it'll just be a question of "there will be another along shortly".
In general, number of services, at a reasonable distribution, is more important than whether they are clockwise or not. I would rather have a good spread of 14 trains per day even if each one was a different minutes past the hour than 8 on s strict 2 hour cycle.
Final note - there are strong cases for joining up services such as ones I mentioned earlier which are very inefficient ... 41 minutes or 76 minutes sitting idle in a bay platform might be usefully used on an extended route. Of course, the 41 minutes does provide time for a Personal Needs Break for the crew, so even that gets complicated and I wouldn't dare suggest Salisbury - Romsey - Eastleigh - Soutampton area - Totton - Marchwood, now would I?