This is going to be difficult to balance

Having advantage on a roll is roughly equal to having +5 to your roll, and having disadvantage is roughly equal to having -5 on your roll, as suggested by applying advantage and disadvantage to passive checks.

Your suggested change would require somebody to have 5 different sources of advantage to get the same bonus as they do now, which seems extremely difficult to get unless you start also house-ruling a lot of ways to get advantage.

And once you start houseruling a lot of ways to get advantage, to try and make up for advantage now being weaker, you're making special abilities that only work when you have advantage a lot stronger.

By changing just this one thing, you're very likely going to have to make a lot of extra changes that will break other parts of the balance.

Giving a +1 modifier is, under the vast majority of circumstances, weaker than giving Advantage

Below is a table with two sets of Columns:

• The possible results for a regular D20 roll, no other modifiers


• The possible results for a D20 roll made with advantage, no other modifiers

beginarraylcr
& & textNormal & & & textAdvantage & \
textOutcome & textOdds & text# of Trials & textOdds to Pass & textOdds & text# of Trials & textOdds to Pass
\ hline
text[1] & text5.000% & 1 & text100.000% & text0.250% & 1 & text100.000%\
text[2] & text5.000% & 1 & text95.000% & text0.750% & 3 & text99.750%\
text[3] & text5.000% & 1 & text90.000% & text1.250% & 5 & text99.000%\
text[4] & text5.000% & 1 & text85.000% & text1.750% & 7 & text97.750%\
text[5] & text5.000% & 1 & text80.000% & text2.250% & 9 & text96.000%\
text[6] & text5.000% & 1 & text75.000% & text2.750% & 11 & text93.750%\
text[7] & text5.000% & 1 & text70.000% & text3.250% & 13 & text91.000%\
text[8] & text5.000% & 1 & text65.000% & text3.750% & 15 & text87.750%\
text[9] & text5.000% & 1 & text60.000% & text4.250% & 17 & text84.000%\
text[10] & text5.000% & 1 & text55.000% & text4.750% & 19 & text79.750%\
text[11] & text5.000% & 1 & text50.000% & text5.250% & 21 & text75.000%\
text[12] & text5.000% & 1 & text45.000% & text5.750% & 23 & text69.750%\
text[13] & text5.000% & 1 & text40.000% & text6.250% & 25 & text64.000%\
text[14] & text5.000% & 1 & text35.000% & text6.750% & 27 & text57.750%\
text[15] & text5.000% & 1 & text30.000% & text7.250% & 29 & text51.000%\
text[16] & text5.000% & 1 & text25.000% & text7.750% & 31 & text43.750%\
text[17] & text5.000% & 1 & text20.000% & text8.250% & 33 & text36.000%\
text[18] & text5.000% & 1 & text15.000% & text8.750% & 35 & text27.750%\
text[19] & text5.000% & 1 & text10.000% & text9.250% & 37 & text19.000%\
text[20] & text5.000% & 1 & text5.000% & text9.750% & 39 & text9.750%\ hline
textAverage & 10.500 & & textAverage & 13.825
endarray

From these two tables, we can make a few casual observations:

• For a "coin-flip" roll, where a 10- fails and an 11+ succeeds, giving Advantage to someone is like giving them a +5 on their roll.
  
  
  • Sidebar: the Player's Handbook (Passive Checks, page 175) specifically says to just give +5 to Passive checks that would otherwise have Advantage (or -5 for checks with Disadvantage)
  
  


• There are a few times where your variant might be better, but they're limited.
  
  
  • The only time that giving someone +1 on their roll, which is what your system does, would be strictly better than having Advantage is if they would otherwise need to roll a natural 20 to succeed: in those circumstances, their odds improve from 5%→10%, whereas with normal Advantage, they'd go 5%→9.75%.
  
  
  • For two sources of Advantage, they'd need to be facing a check that requires at least a natural 19 (10%→20% with your system, 10%→19% with normal Advantage)
  
  
  • For three sources of Advantage, they'd need to be facing a check that requires at least a natural 18 (15%→30% with your system, 15%→27.75% with normal Advantage)
  
  
  • On the other side of the spectrum, a +1 bonus is only better than normal Advantage if the roller must roll a natural 1 to fail(5%→0% for your rule, 5%→0.25% for Advantage), a +2 is only better on a roll requiring a natural 2 to fail (10%→0%, 10%→1%), a +3 is only better on a roll requiring a natural 3 to fail (15%→0%, 15%→2.25%)
  
  

Under normal gameplay circumstances, having more than 3 sources of Advantage is, strictly speaking, incredibly unlikely. So as a consequence, replacing Advantage with a strict +1 (stacking) bonus is going to reduce the power of Advantage by a considerable amount.

You'll need to come up with rules for how to handle features like Elven Accuracy

Elven Accuracy, a feat that can be taken by Elves and Half-Elves, has a specific effect that plays off the nature of how Advantage affects rolls:

• [...]


• Whenever you have advantage on an attack roll using Dexterity, Intelligence, Wisdom, or Charisma, you can reroll one of the dice once.

—Elven Accuracy, Xanathar's Guide to Everything, pg. 74

So if you allow characters in your campaign to take this feat, or any feat that has similar effects on an Advantage roll, you'll need to make a decision about how this feat should behave under these circumstances, bearing in mind that being given the option to reroll a single die is far less powerful than being able to do so when it is paired with another die in an Advantage roll.

Adding and subtracting values in the way that you have proposed is very much how 4th edition D&D worked. 5th edition has deliberately stepped away from that with the concept of "bounded accuracy".

The advantage/disadvantage system in 5e is designed to be simple and elegant. As someone who has played and DM'd both editions I really appreciate the simplicity of rolling two dice instead of doing a bunch of last-moment adding and subtracting. If your table really enjoys tactical combat and trying to finesse every angle then I suggest you try 4th edition out as it might appeal to you.

I don't think what you're proposing will work very well in 5th edition, as you can see in the graph in David's answer.

This makes one advantage significantly weaker and it becomes very difficult to reach enough advantages to compensate.

For demonstration purposes, let's take a standard d20 advantage roll minus a flat d20:

On average, this results in about +4 or higher as a benefit. This will require four stacked advantages before you get the approximate benefit of one advantage. You can read further on the effects of advantage in this Q&A.

Some Factors to Consider

The actual math is well covered by other posts, but I think there are a few further factors to keep in mind. It may be that balance-wise these factors make the proposed rule more in line with your goals, so this is not meant to be critical so much as simply point out instances where it makes a substantial difference.

What is Your Primary Goal

Your statement that "this way players can stack +1 for every clever thing they do" seems to indicate that you perhaps are focused on situations where the DM gives discretionary advantage to people for a clever plan, good roleplaying, etc. How often this applies depends entirely on the DM, and with a sufficiently generous DM may make this a very strong approach to advantage in many situations. It would essentially just make advantage a matter of the DM naming a modifier they will be give based on how many ways they think the player has been clever in their plan or what not. This seems like additional work on the part of the DM rather than just being able to say "you have advantage" if there is any advantage-worthy aspect, but it would give the DM more leeway to determine what is fair. Of course, they can already alter the DC to accommodate factors the players may initiate through their approach to the task, so this really makes little difference if the DM is comfortable making such adjustments.

If you are a DM for whom awarding people for clever approaches to skill checks is the primary goal with this house rule, then I would strongly recommend simply adjusting DCs based on their approach, and perhaps not even granting advantage in these situations if you don't like double rolls. It would then have no balance issues beyond this.

Multiple Advantage Would Be More or Less Plentiful and Important For Different Sorts of Circumstances

There are many situations where consistent advantage is dictated by the rules, namely various class and feat features, various spells, items, and the help action.

Since your proposed form of advantage is weaker under most circumstances and the class features (barbarian reckless attack for example) and feat features (shield master for example) are mostly major mechanical aspects of the given class, subclass, feat, etc. this can radically weaken these character build options. These are mostly combat oriented sources of advantage, and opportunities to stack advantage in combat will be generally less frequent because there are simply too many other uses for peoples actions, bonus actions, etc. in combat. Perhaps the barbarian suffers most on this front since reckless attack is a major class feature and brutal criticals are also a major class feature which is twice as easy to trigger when granted advantage (criticals are explained below).

Spells, such as fairy fire, are one of the other major sources of automatic advantage (and disadvantage), particularly in combat. This radically changes the value of these spells. Particularly for low level casters for whom advantage granting spells are one of their strongest potential contributions to combat this is a substantial change, and further so if applied to disadvantage as well. The bard in particular comes to mind, as her primary damage dealing cantrip is vicious mockery, which is weak on damage but causes disadvantage, and for whom direct damage dealing spells are fairly rare until she gets to raid other class's spell lists at higher levels (not until level ten for non-Lore Bards).

Some items, such as the Boots of Elvenkind also grant advantage on something. You would have to consider whether you, effectively want to make them just +1 items on some sort of roll or not.

Finally we have the help action. Being able to grant this as a bonus action is one of the key features of the Mastermind Rogue (I would argue that it is the only really strong feature they get in the first two tiers), so we have another class who is now balanced much differently. Being able to grant it through a familiar is a major aspect of being a wizard as well.

Beyond this taking the help action in combat is something most players do but rarely, and certainly many party members spending combat actions on help seems unlikely so heavily stacked advantage from this is going to be fairly rare. Meanwhile in the case of many ability checks there is no reason the whole party would not each help the one player make the roll if the DM allows. The significance of this will depend heavily on how amenable the DM is to letting multiple people try the same skill check and to letting players use help in these circumstances.

There is also the aspect of the help action that it often involves one player giving up there roll so another player gets two rolls. Whatever the mechanical strengths this both makes it a more straight-forward choice for the player and for some players a source of camaraderie.

Natural Ones and Twenties

If you are only rolling one die than in combat Crits are half as likely, which is a further reason that this is substantially less powerful. This is a particularly important thing to keep in mind in terms of the balance of classes or subclasses for whom a substantial benefit revolves around the crit, such as a barbarian or a champion fighter. A critical failure would be more likely, since you have half the chance to avoid one, but these are far less important since usually one is just part of a range of numbers that will obviously not hit, however this is also tied to the a few mechanics such as the halfling "luck" and would effect the balance.

Also consider that at many tables the principle that a natural twenty or one leads to a dramatic critical failure or success on ability checks regardless of modifiers (this is quite possibly the most common house rule). For advantage this halves the chance of such a critical success and doubles the chance of critical failure.

Applying the comparable rule to disadvantage, if you adopted that as well, would of course have the inverse effect for all of this.

Advantage AND Disadvantage?

One aspect of advantage and disadvantage not stacking is that the cancel each other out completely no matter how many more sources you have on one side or the other. You would also have to take into account how you would handle this rule.

Final Note

I am presuming that you intended this rule to apply to all advantage rather than just your houserule additional advantage. If that is not the case than the significance of this rule is quite different and much, much lower for the very reasons that have been explained in this and several other answers. It would simply be a (usually) modest buff (or if you apply it to disadvantage debuff) to rolls, and, unless you let whole party take help actionS on an out of combat skill check, doesn't seem like it could really break any aspect of the game.

Most things that give advantage or disadvantage in 5E previously gave a +2 bonus or -2 penalty to one participant or the other. They also had typed bonuses so you could stack several but not infinitely. The 5E system is more streamlined and requires less bookkeeping, though as you note it reduces the ability of players (or enemies) to benefit from strategic planning. If you want to reverse that move, going back to providing +2 bonuses for advantage is fairer than +1.

However, that's not what I would do. I would instead just not cap advantage at one bonus die; the second source of advantage gives a third die, the third source grants a 4th die, etc. Each successive die grants a smaller benefit, but it would still let you reward good planning, and it would be very good at letting a detailed plan be more likely to go off without a hitch; if they can stack 4-5 sources of advantage, they're basically taking 20.