Aldaron, jrrrr, I can't argue with that premise. I personally believe that these decisions should be made on fun and even the status quo should be factored in. Changing the metagame after all... is a Game Designer's decision and not a gamer's decision. Your arguments reflect my argument during the Wobbuffet discussion.
Nevertheless, I feel that double team can contribute to the game. Without testing, we have removed an entire aspect of this game perhaps unfairly. We add not only double team to the metagame, but a host of new attacks like Vital Throw, Odor Sleuth, Foresight, and all the Pokemon who can benefit from these attacks. We open up the metagame to new counters, new strategies, and new pokemon, as opposed to closing out all chances of counters and possibly adding a setup turn to already overpowered pokemon like Lucario or Gyarados (Wobbuffet -> Encore). A larger metagame does not necessarily mean a better one of course, which is why I'm open for testing and not for an immediate unban. While I'm unsure how to go about testing something like that properly, I do feel that the mechanics of Double Team have changed enough to warrant at least a test... in comparison to Advance anyway.
Perhaps most important about Double Team... it is an opportunity to provide strict control of probabilities on your team. "On the average" estimates (like what I've been doing), are great for the long run, but on the day to day battle you rarely will actually have a long enough battle for you to reach the average.
Indeed, battles are short enough that significant deviation from the average is possible. The analysis required for these kinds of short term is less trivial but still doable. It adds a significant complexity to the game that simply does not exist now. Adding double team adds the management of probability to the Gameplay, and clearly more skilled players will manage probability better than less skilled players.
Finally, as for Obi's point about the tournament formats... perhaps double team isn't appropriate for a classic single elimination tournament. It does make the end result more unreliable. Nevertheless, what we have here right now is the Shoddybattle ladder, and a large enough set of games is played on it to make these rare occurrences truely rare. I can think of a few tournament formats that would be better for Pokemon anyway... considering how luck is a big part of it. (IE: Round Robin, Swiss format, etc. etc.)
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Obi, here are my calculations that you requested. For a single turn of Cosmic Power vs Double Team...
For each turn... with 1 boost..
1. 6.25% of the time you take 2x damage (Critical hit), 93.75% of the time you take 2/3 damage (non-critical hit). This averages out to 75% damage in the long run, even with critical hits factored in.
2. Double Team: 75% of the time, the attack hits. 25% of the time, the attack doesn't hit. 6.25% of the time when the attack hits (or 4.6875% of the time overall), it is a critical hit. This comes out to 75% * 1.0625 or the average amount of damage (including critical hits) * the chance of hit... or 79.6875% damage in the long run.
Clearly, Double Team takes more damage in the long run.
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Case 2: 2 Cosmic Powers and 2 Double Teams.
1. 2x Cosmic Power doubles your defense. You take 2x damage 6.25% of the time and 1/2 damage 93.75% of the time. This is 59.375% damage in the long run.
2. 2x Double Team gives you 40% evasion. Including critical hits (1.0625x damage in the long run), that is an average of 63.75% damage in the long run.
Again, double-team loses to Cosmic Power, even with Critical hit hax factored in.
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Case 3: 3x boosts
1. 3x Cosmic Power gives you reduces your damage by 60% (you take only 40% of the damage). So you take 2x damage 6.25% of the time, and .4 damage 93.75% of the time. Blah blah blah, 50% damage in the long run.
2. 3x Double team gives you 50% evasion. 1.0625x damage in the long run (including critical hits), you got 53.125% damage with 3x double team in the long run.
Double Team is still behind.
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Skipping to case 6: 6x boost
1. 6x Cosmic Power reduces your damage by 75%. Blah blah blah, 35.93% damage in the long run.
2. 6x Double Team gives 66.6% evasion. Blah blah, 35.42% damage in the long run.
So in the cases for 1x boost, 2x boost, and 3x boost, Double Team is worse in the long run, even after factoring in Critical Hits. At 6x boost, Double Team is only slightly better due to the chances of critical hit... and you still have to make up for being behind for 5 turns.
Or, your Porygon2 could spend 5 turns wasting Thunderbolt's PP.
Check the probabilities yo. The numbers are in favor of Porygon2 hitting on the first turn. And with an OHKO on T-Bolt vs Gyara... all you need is one turn.
Your opponent will have to play 1024 battles to get only a 63% chance of seeing 5 turns of misses from a single layer of Double Team. 37% of the time, it will take him more battles. In fact, it is very possible to go your whole life and never see 5 misses on a single layer of Double Team.
Of course... I think it is better if you didn't base your argument on something that has a 0.09765625% chance of happening. (Less than a tenth of 1 percent)