An "opposed check" is a well-known kind of check in many games, when two opponents roll dice, add modifier and compare results. It differs from a convenient dice roll when you compare your result against a constant number (DC, target number or whatever).
There is also a concept of "passive check" in 5e when you just take 10 instead of rolling d20. An opposed check against a "passive" value effectively turns into a "simple" one, being made against a constant number.
Now, let's say there are two sides makes opposed rolls using modifiers A and B. First one rolls d20 and adds A, while second one always uses constant number 10 + B. In terms of statistics, should these checks have the same hit/miss rate? —
- d20 + A as opposed to d20 + B
- d20 + A as opposed to 10 + B
I'd say rolling d20 is a little better than 10, since the average of d20 is 10.5, but my probability intuition isn't very good.
In order to minimize number of dice rolls, if I change all opposed PCs vs. NPCs checks to "roll vs. passive" checks (players always roll, NPCs always use their passive values), how does it affect my games?