Thats wrong, their are no joint liverpool and rugeley trains. The only service joint with a rugeley train is the crewe via stoke and that isnt all day
Basically:
Like i said before 3 tph leave london
(as other posts above will show)
The Liverpool train leaves euston as an 8 car, this splits Northampton with 1 half going back to euston
The rugeley train leaves euston 8 car, again splitting at Northampton.
This is also the same with the crewe train
(when its not joint with a rugeley train)
The only long distance 8 car train beyond Northampton is the crewe train when its joint with rugeley. Otherwise all are 4 car
Even when the crewe/rugeley are joined their are still 3tph: (on birmingham line)
1) liverpool
2) rugeley
3) crewe OR crewe/rugeley joint
Rugeley will often get 2tph but still only 3 tph going brum way leave euston
(Trains going back southbound back to london however is another story
)
Think thats how it will work