My feeling has always been that The Wizard is tricky because he doesn't have one single obvious advantage to say "that's the primary issue." When I look at the The Wizard what I see is a perfect storm of small overlapping advantages that just kind of add up to what I consider to be an over-effective mage:
A. Spell book construction- Before even looking at what the spells do, he has two important notes at this phase of the game:
1) He has no penalized school. This doesn't ALWAYS cause a major impact (Nature mages don't really suffer too hard from 3xfire. Necromancers non living forces don't mind his 3xholy), but it does come into play and particularly so at meta shifts. For example, whenever Frost comes out, there might suddenly be a very real need to have some burn spells on hand for that Defrost trait...suddenly the meta is a little harsher on those Nature mages than it currently is. Being the only mage who has no triple cost means he will always have a pretty good ability to evolve with future releases, he wont always be able to take maximum advantage but will never be the worst. When Necromancer came out, obviously the Warlock benefitted because of Dark training..Priestess benefitted the least from that due to Dark triple cost. Wizard stayed in the middle of the pack and always will at least be there because he doesn't have an unfavored school for a new set to put him in the "favored least" category.
2) that leads to his next spellbook advantage. He not only has a second full training (something some mages don't even get at all) but he gets to CHOOSE it. So, again, as the meta evolves and new cards come out the Wizard can evolve with it. If fire becomes the new thing, Warlocks benefit and Nature mages frown, but Wizards can opt in. If Earth suddenly sucks, Wizard can opt out of it and let Warlords bemoan it. Siren comes out.. Wizard can take a gander at her Water toys and see what hed like to borrow. Some mages have that ability (like Warlocks and Warlords) but its static, they cant swap it out for something more optimal at any point in the games life.
So, for all of the above he maintains 10 channel and while he doesn't have the highest health total he still has comparable health. Now, this is all just looking at a pure strength of spellbook design.. this isn't even factoring in that his core training is one of the most important schools, or the strength of his own restricted cards or even his own abilites. That's a totally different matter.
(Personally I have always felt Wizard should pay triple for Nature and War to offset his multi-faceted spellbook advantage. Nature because it seems thematically aproprate to put it opposite the Voltaric otherworldy flavored magic of Arcane school, and so that he has to pay more for things like creature buffs, tanglevines, grizzlies, wall of thorns, and so on. Then War because it makes him favor Arcane equipment like wands and elemental/supression cloak and discourages him from gearing up in heavy armor and morning stars and not favoring battlefield command style cards rather making him opt for more magical flavored schools like mind, dark and holy for support if not his chosen elemental. that's just my take on his training though)
B. Then there is his general action efficiency advantage. When preparing spells, you generally want to have as many options available to you as possible. You usually have 2 actions and 2 possible spells.. if your round is contengint on both, and one is botched sometimes it trainwrecks your entire round. Wizard has a pretty subtle and useful strength here:
1) Arcane Zap is easy to overlook, but the major advantage of it is that its effectively a third prepared spell every turn. If you think you "might" need to shoot something this round, you don't have to give up the Dispel or Teleport you wanted to prepare this turn just in case you need a hurl rock because you have Arcane Zap in your pocket. Did the opponent drop a Jinx on you or give himself a Block? You can just fire an Arcane Zap without wasting that prepared spell to open it up.
2) Voltaric Sheild is the same deal, if you want to cusion yourself defensivly there are good tools for it.. Block, Brace Yourself, etc. But those have to be prepared and cast, Voltaric Sheild lets you brace for damage without committing one of your prepared spells or spending actions to doing so. So the passive nature of these two abilities helps augment your options every turn while prepping spells that offer a broader options and more fluid strategies. This lets the Wizard be conservative with his spells, and always seem prepared for more options.
As mentioned before, this efficency exists on its own without factoring in his above spell building flexibility nor the strength of his tools and schools.
C) Then, there is the advantage any mage has simply by having access to the Arcane school. Setting aside the Wizard-only aspects or his secondary training, its a big deal to have premium access to all the core functions of this school. You save spell points from obvious things like Dispel, Nullify, and Jinx to other staples like Mana Crystals, Elemental Cloak, and Spell Wands. While most major schools have "must haves" Arcane seems to have the most important, and the ones that are most important to have in multiples. Not only that, the cards for combating the Arcane school are primarily contained... in the Arcane school. Denying/Draining mana, and sources of boosting/protecting mana are both arcane. Magic utility and Metamagic counters are both Arcane. So, when these core elements are used by all other mages an Arcane trained mage is in the best position to counter his opponent out without as much spellbook compromise. As previously stated.. regardless of the mage abilities and spellbook design perks.. this training is strong on its own. A mage with weak abilities would still have a good spellbook situation by having Arcane training.
D) The Wizard uniquely has some potent cards that are restricted just to him. Ignoring his mage card, ignoring his trainings, for example I think Gate to Voltari is the best spawnpoint in the game. Its durable, it triggers mana without requiring a gameable gimmick...you get mana by the opponent playing the game, and it summons creatures from a wide spread of strong options. Wizard Tower is one of the most flexible support cards a mage can run, even Huugin is a strong familiar. (Though other familiars like Gurmaash, Fellelia and Serseryx are also strong in their own contexts) So on top of being trained in a good school, the Wizard has some strong tools that would be potent regardless of his spellbook constraints.
That's all a pretty basic and general overview without going too hard in depth. Taken individually, none of those advantages are a smoking gun to say "this makes him broken!" nor are they individually without some degree of tit-for-tat against other mages. But they compile in a way that is hard to pinpoint the cleanest way to prescribe a clear picture of why the Wizard is so strong and how to easily tailor him down or to tailor other mages mages/schools up to close that gap.
That's just my general overview on why he seems stands out among other mages anyway.
Okay, that was the simplest and most intuitive way that anyone's explained it to me so far. You've got me convinced. It's been pointed out to me that I was setting up my standard of evidence too high. I was underconfident and should not have dismissed all the evidence because it wasn't a controlled experimental trial. While such a method would help settle the argument more definitively, it isn't necessary for me to make up my mind. The Wizard is overpowered.
The question that I'm wondering now is this:
Has the wizard always been overpowered? The Frugal Fire Wizard seems to hold its own just fine without being OP in the current global meta or at least before Domination/Academy as far as I can tell, but then so do the other Core set x1 only mages I've made (although I'm not entirely sure how viable the beastmaster build is yet). So how much of the problem is the wizard's abilities and how much is the arcane school?
Paying triple for nature and war...hmm. I think part of the thematic dillemma here is that the wizard is presented as the "science/research mage", but science includes things like biology (study of life), neuroscience/psychology (study of the brain/mind), chemistry (the study of the elements)...
Ideally magical zoologists would tend to be beastmasters and magical botanists would tend to be druids. Ideally magical medical doctors would tend to be priestesses and magical pathologists would tend to be necromancers.
Of course, in this hypothetical scenario, the people who diagnose a disease (necromancers) are not the same as the people who treat the disease (priestesses). This probably makes sense in Etheria because this way no one has to be cut open in order to treat whatever is ailing someone. How does the priestess know where to direct her healing magics in a patient's body if she can't sense the disease or the internal wound? If it's an open external wound she has no problem, but if it's anything that you can't see without cutting someone open, you would need a necromancer.
And of course, the magical equivalent of neuroscientists and psychologists would tend to be forcemasters or other mages from the mind school.
Having arcane school be the "science" school doesn't really work, and only serves to justify imbalances like what we're seeing now.
A wizard is the magical equivalent of a physicist/chemist. He shouldn't pay triple for war, physics and chemistyr is very useful for making weapons--just look at Goblin Alchemist!
He shouldn't pay triple for nature. There is no reason someone who is a physicist can't also be good with animals or grow a pretty good garden of his own.
So what are physicists and chemists bad at?
Well, stereotypically, physicists and chemists tend to have trouble communicating their findings to regular people, and they're so engrossed in their studies of the deeper more fundamental nature of reality that they sometimes are a bit out of touch with everyday surface phenomenon (or maybe they just forget sometimes that most people don't know anywhere near as much as they do about the fundamental nature of reality, and that they're operating from a completely different frame of reference.)
Furthermore, being smart, sensible, methodical and curious is not the same thing as having a good understanding of one's own mind or of minds in general. And a person can be good at the former things and still be bad at the latter things.
Maybe wizards should pay triple for mind.