With digital, as long as the signal hits a minimum threshold then you'll get just as good a picture as if you're getting max threshold signal. This means that "the picture looks okay" isn't really any sort of reliable guide.
There are ways of checking signal level, but you need a bit of background first to help work out what the results will mean.
Your TV has a basic signal level meter for two measures: Strength (S) and Quality (Q). The most important thing is quality. This is a measure of the difference between the peak signal and the noise level picked up and/or introduced in all aerial systems. You'll know this more commonly as Signal to Noise ratio (SNR).
The signal direct off the aerial connection itself is the the best Quality (best SNR) your system will ever see. No amount of boosting will ever improve it. This is why getting the right aerial and having it set up properly is important. Everything after this point will either reduce the signal Strength (amplitude) or increase the noise and so reduce the Quality (SNR).
Cable length, passive splitting and cable joints are all forms of resistance. They will reduce Strength but won't reduce the Quality.
Poorly shielded cable and active amplification will both introduce noise. This will reduce Quality.
Amplifying the signal after it has lost Quality will increase everything by the same rate, and that includes the noise in the signal. It will also introduce its own noise as well. This means you end up with a "louder" signal but worse SNR. This is why set-back boosters behind the TV don't fix reception problems.
They're okay for compensating for the loss from any splitting they have built in. The extra amplification is useful too for offsetting the cable losses in the next run to another TV. However, this relies on there being a healthy SNR to start with that can cope with a bit of a reduction.
Bringing this back to the TV metering, the Strength reading doesn't need to be that high; 50-60% is generally fine. Quality though needs to be higher. 70-80% as a base level, but higher is better.
The average TV though will measure optimistically. You'll have to take some of the readings with a pinch of salt.
The way to check how much margin you have to play with is to introduce a bit of level reduction in the form of some signal attenuation. This could either be a bunch of pass-through connectors with fixed level attenuation values. They'll be available at 3, 6, 9, 12, 15 etc and 10, 20dB values. You stack them together to make larger values. Alternatively, a variable 0-20dB attenuator can be used, but it's less precise as these things don't have a graduated scale. Either will work though for what we need.
Starting with the signal from a strung mux, say for BBC1 or ITV in SD, check the TV metering. This is usually best accessed through the manual tuning menu. If you have 70-100% for Quality, and 50% or more for strength then get the attenuators for the next stage.
With either the fixed attenuators, or the variable set at 75% of the dial rotation, introduce 15dB of attenuation and check your meter readings and picture. If your Quality level hasn't dropped or is showing no more than a reduction by 10% then the signal is fairly healthy.
If after attenuation your still at 50% or more signal strength then you might even be able to get away with passive splitting.
Should you wish to use an amplified splitter at the mast head, then look for something either in the 10-15dB range or one with a variable level adjustment.
Regarding power, if you consider for a moment that a masthead amp is designed to live outside, up on the aerial mast, right next to the aerial itself, then you'll probably have worked out for yourself the problems of getting power to that location. For this reason, masthead amps have a solution worked out already.
The answer is something called a phantom power supply. This uses the coax cable itself to carry power up to the amp at the same time that 5he cable is carrying signals down. The two things don't interference with each other.
A power brick has in and out aerial connections and a cable with a mains plug. Folk often confuse these with some kind of signal booster. It normally lives behind the TV.
My only concern with your plan is using a phantom power supply with that length of cable. Theres going to be a drop in voltage over an 80m run, and that might be enough to reduce the voltage so the masthead amp doesn't work.
Can you get a point somewhere along the cable run so that the powered bit of coax isn't so long?
