I think that tricks were pretty useless at first. People talked about that fact here, and it was written up on the wiki. Then, during the Christmas event, your opponent had stats with a slightly higher trick than her other two. I suspect there was a change in the code at the same time since it seemed to actually matter after that. How much it matters is still unclear. As Hornypony said, it looks like the outcome is determined immediately, and then some sequence plays out on the screen to justify that result. I haven't found an advantage that gives a "safe" fight yet. I've lost several attacks with more than a 20% average advantage over my opponent. I've also won from a slight disadvantage and have seen here that there is a non-zero chance to win any battle.
Enough people do well enough with very little in the tricks stat that it certainly isn't "critical" to your success. Sorry...