In this Unearthed Arcana, they give rules so that players can make all the rolls, rather than the DM sometimes rolling for enemies. In one section, there are specifically rules for converting saving throw bonuses into an equivalent DC, which the players roll against, rather than the DM. However, after doing some math, I think they've made a mistake.
They say that you convert a Saving Throw into a Saving Throw Check by adding 11 to the defender's saving throw modifiers, and using that as the DC for the check. The player then rolls against this DC, adding their spellcasing ability modifier and proficiency bonus. However, according to the following math, this conversion does not produce the same results.
In this math, I compare the chances of a player succeeding on a saving throw check, using the rules in the UA article, and of a monster failing its saving throw using the standard PHB rules. If the math is correct, both of these results should have the same chance.
These are the formulas I used.
Chance to succeed Saving Throw Check = (20 - DC + 1 + proficiency + casting mod) / 20
Chance to FAIL a Saving Throw = (DC - 1 - save proficiency - save mod) / 20
Assuming a proficiency bonus of +2, +0 for all ability mods, and no save proficiency:
Monster's Saving throw Check DC = 11 + save mod = 11
Chance to succeed a saving throw check DC11: (20 - 11 + 1 + proficiency + casting mod) / 20 = 12/20 = 60%
Player's Saving throw DC = 8 + proficiency + spellcasting ability mod = 10
Chance for monster to fail saving throw DC10: (10 - 1 - save proficiency - save mod) / 20 = 9/20 = 45%
If this were a valid conversion, both formulas would result in the same chance of success for the player, and failure for the monster respectively, however, they are off by 15%. This suggests that the unearthed Arcana's rules are not a valid conversion.
Are the Unearthed Arcana rules wrong, or is my math wrong?