What is WIT used for?

The WIT is used for calculating bonus resource gain when operating a major module with the Operate skill. To use this skill after you've learned it you have to stay in the same room as your selected major module for one turn, and after that, until you leave the room, you can enjoy bonus resources equal to half the character's WIT from the module.

For other modules it does different things:

Shop (with Merchant): One tenth of total wit rounded up is added to the Dust generation every turn.

Generator: Each point of wit adds 0.5% chance to find Dust on the level.

LAN: Each point of wit adds 1.2% percent defense to all modules (major and minor) on the level.

Tactical HUD: Each point of wit adds 1.2% percent attack power to heroes on the level. When upgraded to Tactical HUD IV, the bonus increases to 1.8% percent.

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Higher WIT will also allow you to repair modules faster with the Repair skill.

As to how it's calculated - as any other stat. Each character has his/her/it stat growth, and you can get bonus WIT from items or skills.