[Chris Byler]

The research formula:

Research = Sum of all mage levels + 2 + Experience bonus +/- Sage bonus/Witchdoctor penalty +/- Scale adjustment + Item bonuses

Mage levels are all magic paths except divine and unholy. Commanders without any mage levels can't research at all. Includes bonuses from path boosting items (e.g. Earth Boots).

Experience bonus is +1 rp per star.

Sage bonus - various units have this including sages, loremasters, the Great Sage pretender, adepts of the metal orders. I think it's +3 for most of those units, but I'm not sure of the exact value. There's also a heroic research bonus, I think - I assume this works like the sage bonus, I don't know if it's cumulative with a sage's natural bonus if a sage gets the heroic research ability.

Witchdoctor penalty - I've heard that they are bad at research now but haven't played Machaka recently.

Scale adjustment - +1 RP/magic scale, -1 RP/drain scale. Ulm Master Smiths ignore drain but do benefit from magic (but Ulm pretenders are affected normally).

Item bonuses - various items give RP bonuses of different sizes.

Research can't be reduced below 0 but can be reduced to 0 (non-experienced level 1 mage in drain-3).