Stats

There are three primary stats, 16 secondary stats, and 2 pseudo-stats.

Primary stats
The primary stats are Strength (STR), Technique (TEC), and Intelligence (INT). These stats have no direct effect, but they provide the base value for the secondary Attack and Defense stats (STR for Physical, TEC for Skill, INT for Magic).

Each main class starts with different base values, as does each companion. Training, training ranks, evolution, titles, gems on gear, and aeons can all add on top of that.

The primary stats are shown in the main character screen, right above the Training button.

Training
There are 6 types of training:

The gold cost of Novice training goes up with your character's level. I think it's 500 every level and an additional jump every 10 levels. At level 91, it's 23000.

Each stat gets a random change within the appropriate range, except that those which have reached the training cap always get 0.

This is definitely not a linear random distribution. I think it's a triangular distribution, where the mean shifts based on your highest training. So, when you're starting out at +0/+0/+0 you almost always get max positives; when you're up at +500/+500/+500, normal training is much more likely to give you a negative number than a positive.

More expensive training also seems to shift the mean up, but not nearly enough to be worth the extra cost. For example, switch from Advanced to Expert at around 500 seems to increase the odds of getting a "keeper" roll by about 3x, but it costs 5x as much. It may be worth spending the money just to preserve your sanity (training is horribly tedious and frustrating…), but it is costing you money, not saving it.

Some people are pretty sure that the mean is also affected by time of day. While that might sound silly, there are other die rolls in the game that do vary with time, like forge success. Anecdotally, the most popular theories have either 03:00 or 03:30 as the best times to train.

Training caps
Each stat has a training cap, which goes up every level the character gains.

Although the cap is on the amount of training, what's shown on the interface is the maximum value you can reach—including your base value, training level bonus, evolution, etc. So, my level-89 Kelvin's training max is 742, and his STR is 934 + 500 training, it shows a max of 1676 (934 + 743).

Your main character's training cap is 40 + 6*level. For companions, it depends on the number of stars:

Training levels
Each character's training level is based on his highest training. So, if you're at +400/+505/+200, that's over 500.

If you achieve a training level, but then fall below the minimum, you lose the level (and its bonus) until you achieve the minimum again.

The levels are:

Secondary stats
You can see your secondary stats by clicking on the primary-stats panel right above the Training button, except for Crystal, which is on the primary-stats panel itself.

The six Attack and Defense stats are based on the primary stats. Some other stats have a fixed starting value, or a different starting value per class. Others start at 0.

To this base value, bonuses are added for crystals, gems, gear forge levels (Attack and Defense stats only), promotion bonuses (Attack and Defense stats only, main character only), Promotion level bonus (Health only, main character only), talents (Attack and Defense stats and Health only), title, and aeon stats.

Then multipliers are applied from aeon skills and talent specializations. (It's not clear which order.)

Secondary stats can all be modified in combat—Health by taking damage, Rage by hitting or being hit or using it, and anything by side-effects of normal or skill attacks. In a few places (tournament, CRPvP, Guild War and CRBG), Health carries over from one fight to the next; all other secondary stats are reset at the start of each fight.

Attack stats are your base damage, but these are opposed by the opponent's corresponding Defense, halved by successful block, modified by rage bonus and number of targets, increased by elemental damage, etc. See Combat for more details.

Health and Attack and Defense stats are just numbers of HP; Rage is a percent; everything else is a permil (like percent, but out of 1000 instead of 100… or like batting averages). So, for example, a Counter of 627 means a 62.7% chance of countering.

Many stats are opposed by other stats. Some people are sure this works by just subtracting one value from the other—a Dodge of 1777 vs. a Hit of 1210 means a 56.7% chance to hit. Others think it's an opposed roll or something more complicated.

The stats are:

Pseudo-stats
Overall (aka OA), shown in the secondary stats panel and in the Overall Power display, amalgamates a bunch of the secondary stats together using this formula: ???

This is not a great measure. For one thing, it completely ignores important stats like Rage; undervalues characters who are pure physical, skill, or magic instead of a hybrid; etc. This means that, given a hunter and a swordy with the same amount of resources put into their characters and roughly equivalent strength, the hunter will usually have a much lower OA. And, considering what types of companions are most helpful to the two, the hunter's team OA will often be even lower. For another thing, it's a linear measure, but power is not at all linear. An 800K OA team can't be taken down by two 400K teams; in fact, he probably won't take any damage at all.

Crystal, shown in the primary stats panel, shows how much of your OA comes from alchemy.

Tips
Rage values of 60, 80, and 100 are particularly valuable. Assuming you don't get tranquilized, 60 means you almost always skill in the second round, 80 means you skill in the first round if hit first or rage-boosted by another comp, and 100 means you skill in the first round no matter what. And once everyone is building their teams around tranq and skill blasts, having your tranquilizing skill-blaster go off first means that your opponent's doesn't get to go off at all.

When training, it's up to you what counts as a "keeper" roll. One extreme takes anything with positives on the main primary stat (at least for one-tricky ponies like Kelvin or Andre), but that will leave your defenses very weak. The other extreme accepts no negative values at all, not even a +4/+4/-1, but that will make it very expensive to train. Taking any net positive, and any net zero that shifts stats toward your main, is reasonable; the question is how often you're willing to take a net -1. (If you're at 499/391/355 and you get a +1/+0/-2, do you take the -1 to get the B+ bonus?)

When your primary stat is at the cap, that's a perfect time to raise your other stats, because you're guaranteed to get a zero on every roll for your primary. (This also means that if you spend enough to always be at the cap, you can afford to take more negatives on the way there and make up for them afterward.)

Every once in a while, there's an event to reach a certain training level. If you have a character who's just above that, you can easily drop down then climb back up to lose and regain the level, which will achieve the reward. (Ideally you can get a few points in your secondary stat while doing this, too.)