please empty your brain below

I always think of the East London line as the I-don't-go-anywhere-useful line.

Surely a better denominator would be number of possible journey segments? So a line with two stations would have two journeys - A-B and B-A. A line with three stations would add B-C and C-B and so on. So rather than dividing by s - the number of stations, you would divide by (2s-2). No idea what that does to your figures. And you'd have to make allowances for branches and the circle line.

Maybe it is that the deep level are busier but were more expensive to make...because of the demand for the route. It has an odd logic to me.

OK Alan, I like a challenge.

Here's the table ordered by "passengers per line segment", not "passengers per station"...

Victoria: 10.7 million
W & City: 9.6 million
Jubilee: 4.9 million
Northern: 4.1 million
Bakerloo: 3.8 million
Central: 3.7 million
Piccadilly: 3.4 million
District: 2.9 million
Circle: 2.5 million
H & City: 1.7 million
Metropolitan: 1.6 million
East London: 1.5 million

So, no change to the order, but the two shortest lines (Waterloo & City and East London) nearly overtake the line above them.

Of course the deep-level tubes don't tend to go as far into the suburbs, hence all Victoria line stations are busier than, say, the District or Met lines. Doesn't mean these lines don't get busy in the centre.
More importantly there's double counting of stations going on where the shallow lines share stations. Hence the Victoria line runs every 90 seconds and the Circle every 8 minutes. How about passengers per train km?

I feel better knowing that.

I catch the East London Line every morning from Whitechapel to Canada Water. It is true that I can always get a seat, but this is made up for by the remainder of the journey, which is one stop from Canada Water to Canary Wharf on the Jubilee, in which I am luck if I am not crushed to death.

The East London line is much more useful than it used to be, now that it has two additional interchanges with other lines (DLR at Shadwell, Jubilee at Canada Water) as well as the long standing interchange at Whitechapel (District, Hamersmith & City, and historically Metropolitan but not at the moment). When they finish stage 1 of the extension and extend it to Highbury and the Victoria Line to the north and variably Crystal Palace and West Croydon to the south, I think it is going to be very busy. (When they discussed the possibility of running trains all the way to Purley, they nixed it because they believe the line would then be too busy). It's a shame they can't manage an interchange with the Central Line at Shoreditch, but a new deep level station there would probably cost as much as the rest of the project on its own.

Number of passengers per train would be a much more accurate measure of busyness.

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