When the order for 810s was announced it was said that 'They will almost always run in pairs' - believe that when it happens!
I can't find the fag packet I wrote it on the back of, but the "simple"/ "simplistic" maths looked something like this when I tried to work it out in my best crayons:
If you assume that the Long Distance High Speed (LDHS) trains effectively work a half hourly Sheffield - London - Nottingham - London - Sheffield diagram let's say that covers a "fast" and a "slow" to both Sheffield and Nottingham then that's *roughly* eight hours (Sheffield - London "fasts" are just over two hours, Nottingham - London "fasts" are just over ninety minutes, but the "slows" obviously take a little longer), plus you'll need maybe fifteen minutes between journeys, so let's call it a nine hour round trip until the train that left Sheffield is back again?
Nine hour diagrams, with trains every half hour... that's eighteen diagrams... there are thirty 810s on order... leave three to one side for spares/ maintenance and the resultant twenty seven units are enough for nine diagrams to be doubled up and nine diagrams to be run as single units.
I'm not saying that the units will be running Sheffield - London - Nottingham - London - Sheffield diagrams, just using it as a shorthand way of counting up the durations. Obviously there are different staff/ depots/ roles etc (or at least there have been during the period of some services being HSTs and some Meridians). BUT, if you did run nine hour diagrams then the trains arriving into London around 08:30 would also be leaving London around 17:30.
So you could arrange it so that the nine diagrams that were doubled up were the nine arriving into London at (say) 07:45 - 10:00 and therefore the nine departing London at 16:45 - 19:00. Doubled up when/ where most needed - that'd mean single 810s at Sheffield and Nottingham during rush hour but I've got to accept that the London demand is greater.
(I'm not guaranteeing anything, but this seems a good way of focussing capacity where it's needed most, rather than complicating things with splits at Leicester or portions or anything like that - the important thing is that there should be enough to double up roughly half of the diagrams - I guess the layovers may need to be longer if the Sheffield and Nottingham services are operationally separate)