Rerolls vs. Flat bonuses, which is better?

[Elricaltovilla]

Specifically as a math fix which is the more powerful option: the ability to reroll a d20 or other die with the same bonuses or having overall higher bonuses to begin with?

What might be a good balance point between them? I.e. how many +1s to a roll are equal to 1 or more rerolls per day?

[Snowbluff]

Like, 3. IIRC, the math of 5th edition says that a reroll changes the average from 10.5 to about 13-14. So 3. When you add in a target, the value of the reroll varies with your static bonus.
EDIT:
Here's a link. (http://onlinedungeonmaster.com/2012/05/24/advantage-and-disadvantage-in-dd-next-the-math/) It says about +5/-5.

[Piggy Knowles]

By raw numerical advantage, Snowbluff's right from what I recall, but on rolls with automatic success or failure (such as attack rolls or saves), re-rolls have an added bonus of significantly decreasing your chances of auto-failure and increasing your chances of auto-success/crits. Depending on the build or roll, that can be even more valuable than, say, a +5 (despite the latter giving a more significant numerical advantage).

[OldTrees1]

1d20 take best ~= 10.5
2d20 take best ~= 13.825
3d20 take best ~= 15.4875
4d20 take best ~= 16.48334


Obviously a 1/day ability is much weaker than a passive ability.

[Elricaltovilla]

Like, 3. IIRC, the math of 5th edition says that a reroll changes the average from 10.5 to about 13-14. So 3. When you add in a target, the value of the reroll varies with your static bonus.
EDIT:
Here's a link. (http://onlinedungeonmaster.com/2012/05/24/advantage-and-disadvantage-in-dd-next-the-math/) It says about +5/-5.

Thank you, that was very informative and pretty much exactly what I needed! Have a cookie:

(::)

[Snowbluff]

Thank you, that was very informative and pretty much exactly what I needed! Have a cookie:

(::)

Oh, dark orange. That means it's a crunchy one! Thanks! *nom nom nom*

Good thing I played the 5e playtest. :smallsmile:

[Chronos]

And on rolls without auto-success or auto-failure, a bonus or penalty can take it into the realm where the die is completely irrelevant, something that a re-roll can never do. For instance, if I can succeed on a skill check on a roll of 3 or better (i.e., 90% chance of success), then a single re-roll will improve my chances to 99%, two re-rolls to 99.9%, etc., but an additional +2 to my check will improve my chances to 100%.

[hymer]

On the other hand, you're going to be using your reroll at the most critical time you can. As you calculate it right now, 1/day reroll is worse than a +1 bonus. Using those simplified maths it may be. In practice it may be entirely different. A reroll on a saving throw, e.g., is very useful.

[ericgrau]

A reroll worth about a +4. +1 to +5 and closer to the +5 side. It works best in the more common middle cases but worse in the extreme cases.

{table] Chance of success/20 | With Reroll | Equivalent +
1 | 1.95 | 0.95
2 | 3.8 | 1.80
3 | 5.55 | 2.55
4 | 7.2 | 3.20
5 | 8.75 | 3.75
6 | 10.2 | 4.20
7 | 11.55 | 4.55
8 | 12.8 | 4.80
9 | 13.95 | 4.95
10 | 15 | 5.00
11 | 15.95 | 4.95
12 | 16.8 | 4.80
13 | 17.55 | 4.55
14 | 18.2 | 4.20
15 | 18.75 | 3.75
16 | 19.2 | 3.20
17 | 19.55 | 2.55
18 | 19.8 | 1.80
19 | 19.95 | 0.95
Average | | 3.50
5-15 Average (more common) | | 4.50
[/table]

The first (and unfortunately for the practicality of most gaming groups, only) fight of the day is the most important, the first 3 rounds of that fight tend to decide the fight, and the first round matters the most. So I'd say a 1/day reroll on an attack roll is worth about a +2 to hit, or half as much as unlimited rerolls once per round. But you might have multiple attacks so it's worth more like +1 to hit. Usually anyway; I'm sure you could point to long game days where unlimited rerolls once per round would get nuts. But generally I'd say 1/day is about half as good as unlimited because days are so brief.

For saving throws you often only roll one save so a reroll on any save 1/day is worth almost as much as a +4 on all 3 saves. Well actually it's more like zero saves part of the time when you can't use it and 2-3 saves other times when you can only use it on the first save. So maybe a 1/day save reroll is worth more like a +3 to all saves. And if you use it to shore up an especially low or high save it's more like a +2.

When creating abilities you should expect players to exploit them and so use the worst case scenario as the balance point. So a 1/day save reroll should apply to only 1 save if you want it to match the Player's Handbook feats, though splatbooks are stronger. Likewise a 1/day reroll on an attack is about right for a PHB feat (but weak for a splatbook feat).