Constitution (CON) increases the maximum amount of AP you can have. I think it's a base of 7 AP + 1 AP per point of CON you have. Your maximum AP only really matters when it comes to saving AP for a turn or using the Glass Cannon Talent (doubles your turn AP). If you spend enough AP each turn to never reach the cap, the cap doesn't matter much. If

Your AP on the first turn only is determined by a combination of your Speed (SPD) and Perception (PER). But that's only for one turn, so don't worry much about getting PER high unless you are a Ranger or trap-finder.

Your AP on all subsequent turns is determined by your SPD. You gain one additional Turn AP for every 2 points into SPD (on odd-numbered levels). I don't quite remember the forumla.

Points into SPD also increase how far you can move per point of AP. Higher speed lets you move much farther for fewer AP. Essentially, Speed is the main thing to consider when you want more AP and better use out of it.

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The staff is just another magic weapon.