What's the loss of effective output, with a worn chain? I was just bought a new fine ultegra chain for 10 speed road race bike. This is actually the first new chain for this not so old bike. I am a fan of statistics, measuring power with a power unit on my time trial bike, and so on.

Let's focus on this worn chain. 

It ran for about 1000km, so worn you nearly can do a 270-360 degree bow with it. How much effect are you losing between a completely new chain and a worn but (which is the point of comparison) accurately cleaned and re-oiled chain?

I mean, look at a cleaned oiled chain, fitting well with the current sprockets and not skipping cogs. Where is the power going away against a new firm, chain?

How do I measure?
Can I proof any other important winnings?

And (which I may have to point out) together with which kind of use.. I mean, the differences in a low-efficient 200km tour may be negligible compared to a 30km Time Trial where one may average 350 watt in 40 minutes.
This extensive IHPVA article about chain drive efficiency shows a model of how you might empirically test the losses, and describes the efficiencies of a new chain. Their test suggests that lubrication and chainline matter very little, while chain tension is of significant importance.