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The PHB mentions how it is possible to make ability checks based on different abilities, a variant "Skills with Different Abilities" rule.

In some situations, though, your proficiency might reasonably apply to a different kind of check. In such cases, the GM might ask for a check using an unusual combination of ability and skill, or you might ask your GM if you can apply a proficiency to a different check. For example, if you have to swim from an offshore island to the mainland, your GM might call for a Constitution check to see if you have the stamina to make it that far. In this case, your GM might allow you to apply your proficiency in Athletics and ask for a Constitution (Athletics) check.

Some answers here in RPG provide a similar solution, and even provide a custom sheet which decoupled those.

I usually ask my players for skill checks, but I'm okay with players saying "Can I deduce likely trap locations and use Investigation (Int) instead of Perception (Wis)?" or similar shenanigans.

I wonder how, in long-running games, implementing this variant rule for all skills (by using the aforementioned sheet, for example) affects the game and its pace. Does frequently decoupling the checks from their corresponding base abilities:

  • slow down the game considerably as all players try and suggest which ability they use for something?
  • end up with players trying to cheese EVERY check to use a specific ability "I climb the wall by leveraging my weight and the above counter-weight and choosing the simplest path, so I can use Intelligence (Athletics)"?
  • encourage players to RP more, which despite the slower game pace, makes the game enjoyable (for tables that like RP)?
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The way you phrase your question suggests that you have a bit of a misunderstanding of two fundamental pieces of the 5e rules. They are very frequently misunderstood because they differ from other games and previous editions of D&D in subtle ways. Having them clarified should alleviate the worries you have concerning this variant.

First is the roles of the DM and the players. The introduction of the Player's Handbook (which contains a surprising number of essential rules) explains "How to Play" D&D 5e as three steps.

  1. The DM describes the environment. This step is purely narrative and doesn't usually involve any mechanics of the game such as checks, classes, DCs, or anything else from the rulebooks. The DM relays what the characters see, hear, smell, feel, and taste.
  2. The players describe what they want to do. For the players, this step begins as purely narrative, which is where I think your worries are addressed. By the rules, players do not ask for checks. Players describe what they want their characters to accomplish. The DM then decides if any dice rolls are needed, and if so, what kind. A player might, after the DM calls for an ability check, suggest a modification to the check, such as adding proficiency or applying a class feature, but it is clear in the rules that the DM is the one that starts that process, not the player.
  3. The DM narrates the results of the adventurers’ actions. After dice are rolled, if rolls were even asked for by the DM, the DM describes what happens as a result of the narrative course of action described by the players. This is also a narrative step for the most part, describing what, as a result of step 2, has changed in what the characters see, hear, smell, feel, and taste.

So how these rules differ from what you described in your question is that players never ask for an ability check. They can try to narrate what their character does in such a way as to suggest a certain ability check or request a change to what the DM has asked for, but it is always the DM that asks for checks.

Second is the nature of Ability Checks. D&D 5e is ability driven. Almost every single roll of a d20 is tied to an ability. When a DM decides that an action described by a player for their character has a meaningful chance for failure and calls for a die roll to decide the action's success, the first and most important thing they decide is which of the 6 abilities are involved. Only after that is determined do things like the character's proficiencies in skills, tools, or weapons come into play. Now, there are plenty of times that the choice of ability and what proficiencies apply is either so obvious or is explicitly defined by the rules that the DM often glosses over this step. Attack rolls and saving throws rarely require decisions in this matter and the DM can assume that the players are on exactly the same page as them and skip thinking or talking about it. The variant rule that is the subject of this question, however, brings this decision process to the forefront. Thinking about skills first then attaching an ability to it will lead to the delays and cheese that you're worried about, while focusing on the ability, with proficiency with a relevant skill being a secondary add-on, will speed up decisions and encourage good role playing over cheese, especially when using this variant rule. A review of chapter 7 of the Player's Handbook might help here.

Now, this is what the rules say, but the rules also encourage you to change them to suit your group. Maybe your players like asking for checks. Maybe what you consider "good" roleplaying is better facilitated by a change. Great, change that rule for your game, but do it with the understanding that the variant rule assumes that you're following the rules exactly and you'll need to adjust accordingly.

In my experience, using the variant while strictly keeping the rules talked about here in mind has led to only positive changes to my games, and I strongly encourage its use.

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It changes almost nothing about the game.

This answer is largely adapted from my answer to this Q&A: Variant: Skills with Different Abilities confuses me.

The skill and attribute combinations printed on the character sheet are the most common applications of skills that turn up in the game. 99% of the checks you make will use those combinations. But the rules are the same for different combinations.

Here are the two relevant rules:

  • To make an ability check, roll a d20 and add the relevant ability modifier.
  • Sometimes, the DM might ask for an ability check using a specific skill — for example, “Make a Wisdom (Perception) check.” At other times, a player might ask the DM if proficiency in a particular skill applies to a check. In either case, proficiency in a skill means an individual can add his or her proficiency bonus to ability checks that involve that skill.

The formula is always the same. When you are proficient in the skill the DM calls for, the formula is:

1d20 + Ability + Proficency

This is exactly how Wisdom (Perception) checks are calculated, and it is exactly how Intelligence (Athletics) checks are calculated, should your DM call for such a thing. The only thing it changes is that there are more ability/skill combinations available than just the ones printed on the character sheet, but the rules for them are exactly the same.

The DM calls for checks, and players may ask if a skill applies.

Players asking if a skill applies is already part of the game without using this variant rule:

Sometimes, the DM might ask for an ability check using a specific skill — for example, “Make a Wisdom (Perception) check.” At other times, a player might ask the DM if proficiency in a particular skill applies to a check.

So when the variant rule says "you might ask your DM if you can apply a proficiency to a different check", this isn't "variant" in any sense, it's normal practice already.

This shouldn't change anything about the pace of your game, since the only thing it changes is that it adds more variety to the checks a DM might call for.

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  • \$\begingroup\$ You ninja'ed me by a full hour. \$\endgroup\$ Dec 15 '20 at 15:12
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    \$\begingroup\$ @DerekStucki Your answer approaches this from a different angle and provides some good information mine does not. Upvoted. \$\endgroup\$ Dec 15 '20 at 15:13

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