Quote:
Originally Posted by mrtshead
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It's not a usable definition for you, because you sense that you will be unable to make a case that your 'solution' is 'satisfying' without quantifying it.

What may be satisfying to me may not be satisfying to you. Thus we won't be able to establish a proof based on subjective expression like "satisfying" or "fun".
Quote:
[...]
matches last an average of 10 minutes, with a 95% confidence level, for both 1v1 and 5v5 matches.

I understand that as " a match will last 10 minutes in 95% of the cases".
Quote:
Players have a selection of meaningful choices to make in ship and power selection  at least equal to what is in the game now.
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Players have active click power available at least once every ten seconds in top level pvp  on average.
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Players of roughly equal skill level have roughly equal chances of winning a match, both 1v1 and 5v5, meaning the 5v5 setting has to be robust enough so that a more skilled player can balance out a less skilled player on the same team.
[...]

First of all, from the above list I can only conclude that you are currently not finding PvP in STO in any way satisfying, because the current combat, not even when limiting it to 5v5 Arena sports events, is not even close to meeting the above criteria.
Second, I ignore any subjective additions like the funny part where you reserve the right to dismiss anything just based on some subjective feeling that you can claim to have, because you obviously were just joking.
Now, a simple system that achieves your goal would be:
 Matches last for exactly 10 minutes. After that time is over, the match is ended by the engine, and dished out damage, and heal per side is compared. The side with more damage+heal in points (counting both shields and hull) wins. This satisfies the desire for an average 10 minute match duration, with 100% reliability (first criterium).
 We essentially use the system of abilities as it is now, with modifications where needed, see below. This will satisfy the desire for a diverse system and the desire for every player having something available to click at least every ten seconds (second and third criteria).
 All heals and resistance bonuses are castable on team mates and on the player's ship itself, as much as all attacks are possible to concentrate on a given target. This will mean that the numbers of damage and heal will be balanced regardless of team sizes, provided that both sides have sensible builds, stay close to each other, coordinate equally and stay awake. Thus, the system will be scale for 1v1, 2v2, 5v5, 10v10 and 1000v1000.
 The numbers for heals and attack powers (weapons, damageinflicting ablities like GW, damageincreasing abilities like CRF) are balanced vs a given number, say, 20,000 dps plus HPS for max level gear and maxedout stats set up in the optimal combination (this is just an example number, don't read too much into it). Thus, all ship and captain classes s are balanced vs one another.
(Note for any innocent bystanders just jumping into this thread: I am not proposing this system to replace the one we have. This is just an example that proves how something that was claimed to be impossible is actually possible.)
So, obviously it is not impossible to do that. Point proven.
Of course certain people will now jump up and down to show how they don't think that proves anything, or will try to move the goalpost, make lame jokes to distract from the point that was proven, or some other forum PvP that is just so tiring about this subforum. But for me, any claims that "it is impossible to balance both for 1v1 and 5v5" are just no longer existant, and I will ignore them due to the above.
As you, mrtshead, have already agreed that balancing for 1v1 as much as for 5v5 or 10v10 is a desirable goal, and were simply of the opinion that it wasn't impossible, you will of course now say that the system should balance out for 1v1 as much as for 5v5. Right?

Promote what you love, instead of bashing what you hate.