Assuming that's true or thereabouts, we can already say that a one-hour show must be affected somewhere between 10% (if the impact 20% in the first half-hour and 0% in the second) and 20% (if it's 20% in the first half-hour and then that same 20% in the second). Both of those extremes are definitely not true; most shows airing out of huge lead-ins drop at the half, but they still drop to a level that's ahead of where they'd be with no lead-in.
So here's the table:
|Amazing Race Fall 1||1.99||2.82||3.41||3.14||+1.42||+0.32||23%|
|Amazing Race Fall 2||1.71||2.47||3.03||2.68||+1.33||+0.21||16%|
|Amazing Race Fall 3||1.40||2.35||3.30||2.45||+1.91||+0.11||6%|
|Amazing Race Spring||2.15||2.71||3.41||3.05||+1.26||+0.34||27%|
|Criminal Minds: Suspect Behavior||1.75||2.09||3.71||2.40||+1.96||+0.32||16%|
|Criminal Minds: Suspect Behavior #2||2.18||1.84||3.77||2.25||+1.58||+0.41||26%|
|Lie to Me||1.23||1.37||3.31||1.55||+2.08||+0.18||9%|
I was surprised how few hourlong shows actually had the kinds of drastic differences in lead-in I'm looking for. One thing that's certain here is that, among this rather varied sample of shows, there's a much wider range. The newer shows are typically much more helped by the big lead-ins, while veterans Castle, Criminal Minds and Lie to Me see only small increases from bigger lead-ins.
So this didn't teach us a whole lot, just that the veteran shows with established audiences are closer to that 10% minimum and the newer shows are closer to (if not above) the 20% maximum. Though the average is 18%, I'm still tempted to go closer to the middle of the range at this point.
First, let's look at the only "qualifying" show that really got a lot of airtime after a wide variety of primetime lead-ins. That was ABC's Castle, which aired after the fall cycle of Dancing with the Stars, then The Bachelor, then had one episode (the one used for "small" above) in December after enormous flop Skating with the Stars, then got the hugely-rated spring Dancing.
Even this one's not very helpful, because Castle is so much stronger during the spring Dancing season that it seems pretty evident the show got "truly" stronger rather than just following its lead-in. Just comparing all the airings after the fall Dancing and The Bachelor, the show lost about 18% of the decrease in lead-in... about on par with the average above.
Since there's a disproportionate quantity of new shows in the average above, some of which drag the average way up (in particular the Blue Bloods episode that aired after a repeat of Criminal Minds), I think I'll say that one-hour shows are affected by 1/6 of the change in lead-in. That ~17% change seems to be right in the middle of the veteran shows which are usually lower and the newer shows which are usually higher. I'd kind of like to do more like 1/7 to separate it more, but 1/6 is closer to the average and seems to give new shows (which are often the ones that get "new" lead-ins) a fairer shake. Perhaps I can revisit it with a fresh set of 2011-12 data, because the hour-long shows are so all over the map that it would be tough to have much confidence in any number. When we look at some of the shows with local programming lead-ins, perhaps that will shed some more light.
As I said before, there just aren't enough two-hour programs to test this, so what we have is: a program will change by 1/5 of its lead-in's change if it's a half hour and by 1/6 of its lead-in's change if it's an hour. To connect these with an equation, we come up with 1/(4 + 2*Length), where Length is the number of hours the show runs. That means that a ninety-minute show is affected by 1/7 of its lead-in's change and a two-hour show is affected by 1/8.