One of the things I like about d20 systems is that doing math relating to a d20 is really easy. There’s a 5% chance to roll any given number, so probability calculations can be done quickly without having to get out a calculator. That said, D&D does have a fair bit of math for which a calculator can be helpful. Usually I resort to anydice for complicated math, because I believe in making informed decisions. The most obvious thing here is the Advantage/Disadvantage system 5e adds.
More Like “This Advantage”
Advantage and disadvantage were among the first new mechanics revealed in playtesting for what was once called D&D Next. If you’re unaware, having advantage (or disadvantage) on a d20 roll allows you to roll two d20s and take the highest (or lowest) result. Mathematically, how many pluses or minuses this works out to depends on what number you needed to hit; it’s exactly equal to +5 or -5 if you’re looking at a target number of 11, decreasing as you need rolls that are farther from “average”.
The nature of this bonus makes sense if you stop and think about it. If you only need a low number, then your already high chances of success aren’t increased much by rolling a second die. If you need an extremely high number, your chances of success still aren’t very large. The system math keeps things mostly in the middle, so estimating it as +/-5 works in most cases.
Let Justice Be Done
I looked at it when examining fighter features, but paladins also get to pick a fighting style (but from a reduced list consisting of Defense, Protection, Dueling, and Great Weapon Fighting). It turns out that Paladins don’t value these equally, as great weapon fighting would appear to apply to smite damage, making it way out of line.
Normally, GW Fighting is an average boost of 1.33 damage per hit normally, but if you start adding smite damage this changes, getting better and better as you roll more dice. Jury’s still out on whether or not this works, so check with your DM. (Speaking of checking with your DM, it turns out the dueling style is intended to apply to sword and board. Point them at this if they say otherwise, but remember rule 0.)