Guest Post: The Prosecution Rules

I did some math relating to the prosecution rules (AH page 80), and found that due to a quirk of those rules, a trained lawyer using his 50% Law skill to work the system has next to zero impact on average. More surprisingly, using his main professional skill for its intended purpose actually puts him at a slight disadvantage.

As written, a character's attempt to make the legal system work in his favor uses a Law roll to generate a modifier to a Luck roll. If the Law roll crits, the Luck roll is made at +40%, a success makes it at +20%, a failure at -20%, and a fumble at -40%. On it's face this sounds fair, but for reasons we'll get to later it is actually quite unusual for DG.

Here I calculate the expected value for the Luck roll modifier for a 50% Law skill [a character rolling Law at 50% has a 5% chance to crit, 45% chance to succeed, 44% to fail, and 6% to fumble)
    (.4 x 0.05) + (0.2 x 0.45) + (-0.2 x 0.44) + (-.4 x 0.06) = -0.002 = -0.2%

A reasonable player or Handler might expect a trained legal professional's skill to, on average, have a positive impact on the outcomes of criminal cases, rather than a negligible or negative one. The discrepancy is caused by the prosecution Luck roll modifier being negative on a Law skill failure rather than just on a fumble.

For the most part in DG, a failure on a skill roll produces a neutral result which does not change the situation (i.e. a failed attack roll does not change the target's hit points, a failed dodge roll does not change incoming damage, a failed first aid roll does not change the hit points of the patient) or a very slightly positive one (i.e. a failed therapy roll gives 1 SAN). Usually only a fumble has a directly negative outcome. This design means that in most of DG, taking action even with a low or medium skill value (i.e. 20%, 50%) has more favorable results than doing nothing. This is a good paradigm because it encourages players to act and engage with the situations they find themselves in, rather than passively waiting things out.

The Law roll to modify a prosecution Luck roll, however, breaks this paradigm by penalizing failure so severely that it can fully negate the effect of success. It means that trying with a low-to-medium Law skill value (any value below 51) is measurably worse than doing nothing because the probability-weighted penalties of failure outweigh the benefits of success.

If this rule is brought into line with the rest of the game's philosophy by simply removing the failure penalty (i.e. failure does not modify the prosecution Luck roll), while leaving in place the fumble penalty, the expected modifier moves closer to what a player or Handler might expect: an 8.6% expected improvement to the prosecution Luck roll on average.
    (.4 x 0.05) + (0.2 x 0.45) + (-.4 x 0.06) = 0.086 = 8.6%