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    Default D&D 5th Ed. - Let's untangle the Rogue math

    This is pure statistics, so I want a separate thread for it, not clogging up the 5th Edition thread.

    It's really only a very small rule that appears on the WotC website, so it's clear for discussion.

    Rogues have the special ability that on all their specialized skills, the dice roll is always treated to be at least a 10. It's like being able to both roll and take 10 at the same time and pick the better number. This compensates for the fact that there are no skill ranks and everyone can have the same skill modifier as a rogue, regardless of a class or level.
    What I want to know is, how much exactly does that improve the rogues chances?

    For the sake of this calculation, let's assume we have a rogue with a Stealth modifier of +0 and an orc with a Perception modifier of +0, just so we can clearly see what we are doing. There are no other effects that affect the rolls. It really is 1d20 vs 1d20, the one with the higher number wins. In case of a tie, the status quo remains in place, which in this case means the Rogue is still not detected.

    So how do we calculate the chances for the rogue staying hidden with just rolling 1d20 and compare that to rolling 1d20 with all numbers under 10 being treated as 10?
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    Doodling with a geometric solution without doing any math yet, I astimate the chance to increase from slightly above 50% to slightly below 62,5%.
    Last edited by Yora; 2012-05-28 at 07:20 AM.

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    Default Re: D&D 5th Ed. - Let's untangle the Rogue math

    Out of 400 possible results the Rogue can win 235 ways, draw 20 ways and lose 145. These all have equal weighting.

    Success: 58.75%
    Draw: 5.00%
    Failure: 36.25%

    Edit: When the rogue is the underdog in a contest the advantage is worth less than that, but when the rogue is the favourite the advatage is worth more than those numbers.
    Last edited by Totally Guy; 2012-05-28 at 07:28 AM.
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    Default Re: D&D 5th Ed. - Let's untangle the Rogue math

    Now I finally gor my 19x19 grid cleared up and figured out the draws on a 20x20 grid.

    Standard:
    190 Rogue win
    190 Orc win
    20 draw

    Skill Mastery
    235 Rogue win
    145 Orc win
    20 draw

    That means the rogues success rate rose from 52,5% to 63,75%.

    I did get the geometric solution right now, but I have to say I only did because I kept cross-checking with your method lots of time to find all the mistakes I made. But that's still close to my original estimate. Euclid be praised.

    But as a class feature that makes a rogue into a skill monkey, this is still quite a poor performance. Next step would be how much an impact a +3 bonus to a rogue with Skill Mastery has.

    Yeay! I solved that geometrically: 60 situations become impossible (all in which the rogue rolls 1 to 3), 60 new situations become possible (the rogue rolling 21 to 23). The new situations are all "Rogue wins". The impossible situations are Rogue: 3, Draw: 3, Orc: 54. That leaves 91 out of 400 for the orc to win, or 22,75%.

    So a rogue with Skill Specialization and Skill Mastery has a default success rate of 77,25% compared to 52,5% for other characters with the same ability scores.
    Last edited by Yora; 2012-05-28 at 08:31 AM.

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    Default Re: D&D 5th Ed. - Let's untangle the Rogue math

    What happens if the rogue has advantage or disadvantage? Or the person opposing rogue advantage or disadvantage!
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    Default Re: D&D 5th Ed. - Let's untangle the Rogue math

    You figure this out!

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    Default Re: D&D 5th Ed. - Let's untangle the Rogue math

    You're only comparing opposed checks, though, for which the Skill Mastery ability is a nice bonus but not game-changing.

    Where Skill Mastery becomes crazy useful is when you're rolling against a fixed DC with a success chance of 55% or better. If you have +3 to the relevant attribute and need a 12, then Skill Mastery bumps your success rate from 60% to 100%.

    On the other hand, if you have a +3 and need a 14, Skill Mastery is completely useless. Very sharp drop-off.
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    Default Re: D&D 5th Ed. - Let's untangle the Rogue math

    This is true. But unlike opposed rolls, DCs are set by the DM and unknown to the players. They will not be able to tell if Skill Mastery will make a difference in a given situation or not.
    Since the rogue can expect a +68% greater chance than other characters in the party who don't have Skill Mastery and Specialization in the skill, you will almost always want the rogue to give it a try.
    In addition, failing by 10 or more means that the rogue could only have made the roll on a 20 anyway, so letting the rogue do something makes any mishaps virtually impossible.
    Last edited by Yora; 2012-05-28 at 11:13 AM.

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    Default Re: D&D 5th Ed. - Let's untangle the Rogue math

    Hang on a second. This power interacts with static check DCs in an odd way.

    If the DC is impossible then there's no need for a roll, right? And also if it's certain to succeed there's no need for a roll either. That's in the text.

    If the player fails by at least 10 the GM may use a hazard to introduce a complication. But if the player fails by less than 10 then they can usually try again.

    Even if the rogue needs to roll a 19 to succeed then the GM will not be able to use the hazard at all. The rogue can effectively keep rolling until a 19 or 20 comes up or the GM narrates that enough time has passed that the situation has changed. (The exception being social stuff where the same RP can't be performed by the player multiple times.)

    The only way a rogue can fail hard is when a roll of 20 is neccessary.
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    Default Re: D&D 5th Ed. - Let's untangle the Rogue math

    The "take 10 or better" ability is very useful for opposed checks if the Rogue can be expected to have an advantage, and nearly useless if the Rogue is at a disadvantage.

    If the Rogue is at -5 points disadvantage, their base chance of winning is about 9/32. With the ability it improves to about 12/32. This cuts the chance of failure by <20%.

    If the rogue is equal with their opponent, their base chance of winning is about 16/32. With the ability, it improves to about 20/32. This cuts the chance of failure by 25%

    If the Rogue has +5 check advantage in the opposed roll, their base win chance is about 23/32. With the ability, it goes up to 28/32. This cuts the chance of failure by 50%.

    If the Rogue has +10 check advantage their base win chance is about 7/8, and the ability guarantees a win and cuts the chance of failure by 100%.
    Last edited by Kalirren; 2012-05-28 at 10:02 PM.
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    Default Re: D&D 5th Ed. - Let's untangle the Rogue math

    Essentially, this ability means that Rogues are more likely to reliably succeed on simple Rogue-ish tasks, and has no effect on their ability to do more complex tasks.

    For example, lets say that a Rogue has an ability modifier of +5. Thanks to his Rogue class ability to Take 10, he will always succeed on spotting a trap with a DC of 1-15, and never risks failure by having to roll to do so.

    If the trap had a DC of 16 and the Rogue did the "sensible" thing by taking 10, he would fail. Thus this elegant ability allows him to do both, and still have a chance to spot traps with a DC of 16-25, while traps with a lower DC are automatically detected.

    But keep in mind that the Rogue has the same probability of succeeding at such higher DC tasks as everyone else in the game. In this example, if everyone in the party had an ability modifier of +5, then everyone in the party has the same probability of spotting a trap with a DC of 16-25.

    It's also possible that Rogues might have other abilities, or that Traits or Feats might be limited to Rogues, etc. This just illustrates the impact of the Take 10 + roll ability.

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    Default Re: D&D 5th Ed. - Let's untangle the Rogue math

    Quote Originally Posted by Person_Man View Post
    Essentially, this ability means that Rogues are more likely to reliably succeed on simple Rogue-ish tasks, and has no effect on their ability to do more complex tasks.
    Yes. On static DCs.

    The idea is, that common tasks are not actually meant to be a serious obstacle and have no real impact on the parties progress, so you can simply skip rolling for them.

    On opposing (competing?) checks, this is different, since creatures can roll everything from 1 to 20, so if the creature rolls high, Skill Mastery can be a life-saver for the rogue.

    Static DCs are encountered mostly in Locks and Traps, which are thing nobody but rogues can do anyway, so they don't need and edge over other characters to be champs.
    Opposing checks are always against creatures, and stealth, negotiation, and deceptions are things everyone can do. Here Skill Mastery does make rogues the champs!

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    Default Re: D&D 5th Ed. - Let's untangle the Rogue math

    Quote Originally Posted by Yora View Post
    Now I finally gor my 19x19 grid cleared up and figured out the draws on a 20x20 grid.

    Standard:
    190 Rogue win
    190 Orc win
    20 draw

    Skill Mastery
    235 Rogue win
    145 Orc win
    20 draw

    That means the rogues success rate rose from 52,5% to 63,75%.
    I'm not sure where the 20 draw comes up.

    (Actually, upon making the chart, I am: you draw 10 times on the Orc's 10 roll and once for each higher roll the Orc could make. Silly me.)

    Here's my table, with the Orc rolls preceding the slash (the Y axis), and the Rogue rolls following the slash (the X axis).

    {table]O\R| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20
    1 | 1\10| 1\10| 1\10| 1\10| 1\10| 1\10| 1\10| 1\10| 1\10| 1\10| 1\11| 1\12| 1\13| 1\14| 1\15| 1\16| 1\17| 1\18| 1\19| 1\20
    2 | 2\10| 2\10| 2\10| 2\10| 2\10| 2\10| 2\10| 2\10| 2\10| 2\10| 2\11| 2\12| 2\13| 2\14| 2\15| 2\16| 2\17| 2\18| 2\19| 2\20
    3 | 3\10| 3\10| 3\10| 3\10| 3\10| 3\10| 3\10| 3\10| 3\10| 3\10| 3\11| 3\12| 3\13| 3\14| 3\15| 3\16| 3\17| 3\18| 3\19| 3\20
    4 | 4\10| 4\10| 4\10| 4\10| 4\10| 4\10| 4\10| 4\10| 4\10| 4\10| 4\11| 4\12| 4\13| 4\14| 4\15| 4\16| 4\17| 4\18| 4\19| 4\20
    5 | 5\10| 5\10| 5\10| 5\10| 5\10| 5\10| 5\10| 5\10| 5\10| 5\10| 5\11| 5\12| 5\13| 5\14| 5\15| 5\16| 5\17| 5\18| 5\19| 5\20
    6 | 6\10| 6\10| 6\10| 6\10| 6\10| 6\10| 6\10| 6\10| 6\10| 6\10| 6\11| 6\12| 6\13| 6\14| 6\15| 6\16| 6\17| 6\18| 6\19| 6\20
    7 | 7\10| 7\10| 7\10| 7\10| 7\10| 7\10| 7\10| 7\10| 7\10| 7\10| 7\11| 7\12| 7\13| 7\14| 7\15| 7\16| 7\17| 7\18| 7\19| 7\20
    8 | 8\10| 8\10| 8\10| 8\10| 8\10| 8\10| 8\10| 8\10| 8\10| 8\10| 8\11| 8\12| 8\13| 8\14| 8\15| 8\16| 8\17| 8\18| 8\19| 8\20
    9 | 9\10| 9\10| 9\10| 9\10| 9\10| 9\10| 9\10| 9\10| 9\10| 9\10| 9\11| 9\12| 9\13| 9\14| 9\15| 9\16| 9/17| 9\18| 9\19| 9\20
    10 |10\10|10\10|10\10|10\10|10\10|10\10|10\10|10\10|10\10|10\10|10\11|10\12|10\13|10\14|10\15|10\16|10\17|10\18|10\19|10\20
    11 |11\10|11\10|11\10|11\10|11\10|11\10|11\10|11\10|11\10|11\10|11\11|11\12|11\13|11\14|11\15|11\16|11\17|11\18|11\19|11\20
    12 |12\10|12\10|12\10|12\10|12\10|12\10|12\10|12\10|12\10|12\10|12\11|12\12|12\13|12\14|12\15|12\16|12\17|12\18|12\19|12\20
    13 |13\10|13\10|13\10|13\10|13\10|13\10|13\10|13\10|13\10|13\10|13\11|13\12|13\13|13\14|13\15|13\16|13\17|13\18|13\19|13\20
    14 |14\10|14\10|14\10|14\10|14\10|14\10|14\10|14\10|14\10|14\10|14\11|14\12|14\13|14\14|14\15|14\16|14\17|14\18|14\19|14\20
    15 |15\10|15\10|15\10|15\10|15\10|15\10|15\10|15\10|15\10|15\10|15\11|15\12|15\13|15\14|15\15|15\16|15\17|15\18|15\19|15\20
    16 |16\10|16\10|16\10|16\10|16\10|16\10|16\10|16\10|16\10|16\10|16\11|16\12|16\13|16\14|16\15|16\16|16\17|16\18|16\19|16\20
    17 |17\10|17\10|17\10|17\10|17\10|17\10|17\10|17\10|17\10|17\10|17\11|17\12|17\13|17\14|17\15|17\16|17\17|17\18|17\19|17\20
    18 |18\10|18\10|18\10|18\10|18\10|18\10|18\10|18\10|18\10|18\10|18\11|18\12|18\13|18\14|18\15|18\16|18\17|18\18|18\19|18\20
    19 |19\10|19\10|19\10|19\10|19\10|19\10|19\10|19\10|19\10|19\10|19\11|19\12|19\13|19\14|19\15|19\16|19\17|19\18|19\19|19\20
    20 |20\10|20\10|20\10|20\10|20\10|20\10|20\10|20\10|20\10|20\10|20\11|20\12|20\13|20\14|20\15|20\16|20\17|20\18|20\19|20\20
    [/table]

    Now, what I want to know is: how does the "luck reroll" mechanic from Complete Scoundrel affect this math? (Assuming that "luck reroll" is reintroduced into the mechanics in D&D Next.)
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