Eh? Phase 2 improves the business case for the whole scheme - it unlocks the full capacity benefits of the first phase and impacts a far larger swathe of the country.
Yeah, it's Metcalfe's Law.
Value of the network is the number of connections. Cost is length of the connections.
So Phase 1 is London-Birmingham (one connection) but costs 119 miles worth.
Phase 2 is London-Manchester, London-Leeds, Birmingham-Manchester, Birmingham-Leeds (four connections) costing 216 miles worth. Even if you count the two non-London connections as half the value of the London ones, that's still a 50% better cost-benefit ratio.
The real calculation is, of course, a good deal more detailed than that - it includes the real costings for tunnels, bridges, stations etc (so not every mile costs the same), includes the benefits for the classic-compatible connections to Liverpool, Sheffield, Newcastle, Edinburgh and Glasgow, includes the through-stations at Old Oak Common, Birmingham Interchange, Crewe Hub and Toton.
But the back of an envelope that Phase 2 is about 50% more cost-benefit than Phase 1 is pretty much right.
Once we've built HS2, extensions are going to have a really good cost-benefit ratio: Newcastle, Hull and Liverpool are all going to have much better cases, because they will each be connected to a host of places on the network (Hull and Newcastle to Leeds, Toton, Birmingham and London, and to each other if both are built; Liverpool to Manchester, Birmingham and London). All three improve the case for a Manchester-Leeds link because it will then allow Liverpool-Newcastle and Liverpool-Hull links.
It's a classic network effect: adding a new place to the network links it to all the places on the network, so the number of links grows as the square of the number of nodes. If your benefits grow quadratically and your costs linearly, then bigger networks are more efficient.
Now, because of physical constraints, this doesn't work quite as well for a transport network as a data network (for a computer, you could do Manchester-Leeds via Birmingham without a problem; for a train, that would take far too long, so you need a trans-Pennine link), but it remains an important point.