This thread has thrown up some examples of odd, obscure journeys which somebody *has* actually made. Plus there will be many more implausible trips made by non-RUK Forum punters, driven by particular family, education or work requirements.
Entertaining as it is, quoting weird examples doesn't answer the OP's question about how many station pairs have had nobody ever make a journey (or buy a ticket) between.
I doubt an exact number can be determined from ticket sales data, since some of the stranger journeys might be done using Rover tickets, meaning no point-to-point ticket was bought. And then there's Oyster/contactless in London.
But here's a "thought experiment" to visualise this concept:-
1) Imagine you have a computer with some technology which can monitor the movements of each and every rail passenger who uses National Rail.
2) Draw up a matrix, table or grid with 2500-odd rows and 2500-odd columns.
The number of rows & columns in the grid corresponds to the total number of National Rail stations (I say 2500-odd here to avoid bickering about exactly how many this is at the moment)
3) On the left-hand side of the table, label the rows with a list of all the station names.
4) List the stations in order of their annual user numbers (rather than using alphabetic or any other sequence) from least-used to busiest, or vice versa.
5) On the top of the grid, label each column with the list of stations in the same sequence - from least-used to busiest.
6) Each of the approx. 6½ million squares in the grid will correspond to at least one person making a single journey
from the station named on the left-hand side
to the station at the top of that column.
7) Choose some convenient time/date when you want to "start the clock".
8) Before starting, colour each cell / square in the grid grey. Grey means no-one has yet made that journey. (There will be single diagonal line of uncoloured cells, because a trip from one station to the same station by rail does not count).
9) Once you press the big, red, virtual START button, begin to change the colour of each cell from grey to green (other colours are available) when someone makes that journey. So if someone travels from Wimbledon to Waterloo, the square at the Wimbledon/Waterloo intersection turns green. Someone travelling in the opposite direction from Waterloo to Wimbledon would make a different Waterloo/Wimbledon cell turn green.
10) Run this exercise for as long as you like - weeks, months, a year, whatever - and watch as the grid of grey cells fills up with more and more spots of green.
11) Initially new green cells would pop up very quickly, especially in the bottom-right of the grid. As time passes the rate of new green cells appearing on the grid would slow.
12) After a convenient interval, stop the clock and take a look at what patterns you've got.
This is how I'd expect the grid would look after a reasonable period of time:-
- The top-left of the grid would still be mostly grey, and the bottom-right would have a predominance of green (assuming you’d listed stations in order quiet to busy)
- Among the "sea of grey" at top-left would be random spots of green where someone had made at least one journey (e.g. Lakenheath to Duncraig - see Post #77, or Whitley Bridge to Thurso - Post #80)
- Enthusiasts travelling from far & wide to bag celebrity stations such as Shippea Hill, Reddish South and Teesside Airport might mean more "greens" appearing at the very-least-used extremities of the grid than at less well-known places like Chapelton, Rawcliffe or Clifton (see Post #160).
- In the middle of the grid would be a large number of small, unremarkable stations located all around Britain which have a reasonable number of users (say 100,000 to 1 million p.a. like Plumpton, Pontyclun or Town Green) but likely to have most journeys to/from a limited number of local destinations, plus maybe the biggest cities (London, Birmingham etc, depending where they were) and a shotgun pattern of occasional unpredictable oddballs.
- Towards the bottom or right of the grid, where one or both stations are mid-sized, there would be a more balanced mix of grey and green. There may be some surprises here where a reasonably busy station actually had no-one travelling to another reasonably busy station in a different part of the country. Where these pairs will be is probably fairly random and unpredictable.
- There may be some suburban stations in London & South-East which see a lot of passengers, so appear in the bottom right of the grid, but where most journeys are commuter-style and no-one ever goes to obscure, far-away destinations. So there may be a surprising amount of grey in the "sea of green".
- Even at the bottom-right extremity of the grid at the busiest locations of all (London terminals and big city stations) it would not be all green. There are many busy station pairs which would not register a genuine 100% National Rail journey, such as Marylebone to Brighton, or Manchester Piccadilly to Cannon St, or Fenchurch St to Bristol Temple Meads. This is largely an artifact of the way the London terminals where built in the 19th Century.
I think what this suggests is there may be a greater fraction of "grey cells" on the grid than you might imagine by just thinking of a list of station names.
Any other odd patterns this thought experiment throws up?