Only a short article this week (at least in terms of word count) because there is easily five times as much work beneath the surface!

A few weeks ago, I read a really interesting analysis of the mathematics of the D&DNext advantage mechanic by the Online DM. And yet, there was a disconnect between that analysis and the actual situation in which that mechanic would be employed that meant that I still didn’t have a feel for the impact and implications that the new system would actually have in play.

So this week I wanted to go beyond the maths provided by the Online DM (and others) and think about the consequences.

Recapping The Results

The Online GM reduced his results to a single table, showing the % chance of success based on what you needed to roll in order to succeed, under three different conditions: a straight d20 roll, when you had Advantage, and when you were Disadvantaged.

The Mechanic

When you are adjudged to have the advantage, you roll two d20s instead of one and keep the best result. When you are adjudged to be at a disadvantage, you roll two d20s instead of one and keep the worst result. When neither side has the advantage, you roll a single d20.

The Table Of Results

The results from the Online GM were:

 Target   d20   With Advantage   With Disadvantage 
1 100% 100% 100%
2 95% 99.75% 90.25%
3 90% 99.00% 81.00%
4 85% 97.75% 72.25%
5 80% 96.00% 64.00%
6 75% 93.75% 56.25%
7 70% 91.00% 49.00%
8 65% 87.75% 42.25%
9 60% 84.00% 36.00%
10 55% 79.75% 30.25%
11 50% 75.00% 25.00%
12 45% 69.75% 20.25%
13 40% 64.00% 16.00%
14 35% 57.75% 12.25%
15 30% 51.00% 9.00%
16 25% 43.75% 6.25%
17 20% 36.00% 4.00%
18 15% 27.75% 2.25%
19 10% 19.00% 1.00%
20 5% 9.75% 0.25%
21 0% 0% 0%

The shortcomings of this result

This table of results is not as useful as it could have been, for the simple reason that the key variable by which they are indexed is not one that is immediately at-hand, but is the result of an earlier calculation – one that the system doesn’t actually require determining. The actual mechanic is to roll dice, add bonuses or penalties, and compare the result to the target number set by the DM.

Rather than the results of the analysis being instinctively understood and directly applicable by the GM to assess the impact, he has to interpret a theoretical situation, translate the result into the appropriate entry on the table, and then interpret the results. It’s no surprise that the significance of the mechanism is not readily accessible for most GMs.

Well, if that’s the problem, let’s fix it.

Relative Impact

As a first step, let’s rewrite that table of results so that instead of giving an absolute percentage of success, it displays the impact of the advantage/disadvantage mechanism relative to the base value of a straight d20 roll. For future reference, I’ll call this Table 2:

 Target   d20   With Advantage   With Disadvantage 
1 100% +0% -0%
2 95% +4.75% -4.75%
3 90% +9% -9%
4 85% +12.75% -12.75%
5 80% +16% -16%
6 75% +18.75% -18.75%
7 70% +21% -21%
8 65% +22.75% -22.75%
9 60% +24% -24%
10 55% +24.75% -24.75%
11 50% +25% -25%
12 45% +24.75% -24.75%
13 40% +24% -24%
14 35% +22.75% -22.75%
15 30% +21% -21%
16 25% +18.75% -18.75%
17 20% +16% -16%
18 15% +12.75% -12.75%
19 10% +9% -9%
20 5% +4.75% -4.75%
21 0% +0% -0%


Now, that’s a very interesting pattern. For targets of 9-13 there is very little difference – if you were to plot these on a graph, that range would be almost flat. 7 & 8 are also almost identical, as are 14 & 15, and the same can be said for 5 & 6 and 16 & 17. But we’re still not quite in a position to really look at what these results mean.

Bonuses & Targets

When you’re talking Advantage and Disadvantage, you’re generally talking about attack rolls. The target value – which is indexed to the results shown above – is the difference between the AC of the target and the combat bonuses or penalties of the attacker.

The example that the online GM mentions by way of proving that those bonuses are still around and part of the game system is prone, but really there are few other mechanisms for the implementation of magic weapons and the like. What’s more, an appropriate stat still contributes a bonus as well.

Most ACs in the game will fall in a range between 1 and 25. Let’s carry the results up to 30 to be on the safe side. Most often, bonuses will be zero-plus-stat bonus – when you’re talking PCs that’s anywhere from +1 to +5. Throw in the potential for a -2 (prone) and up to a +5 (magic) and possible bonuses totals run from -2 to +10. When you put all of these into a table of target numbers, we get:

Table 3:
Target
Numbers
Bonus
AC  -2   -1   +0   +1   +2   +3   +4   +5   +6   +7   +8   +9   +10
1 3 2 1 1 1 1 1 1 1 1 1 1 1
2 4 3 2 1 1 1 1 1 1 1 1 1 1
3 5 4 3 2 1 1 1 1 1 1 1 1 1
4 6 5 4 3 2 1 1 1 1 1 1 1 1
5 7 6 5 4 3 2 1 1 1 1 1 1 1
6 8 7 6 5 4 3 2 1 1 1 1 1 1
7 9 8 7 6 5 4 3 2 1 1 1 1 1
8 10 9 8 7 6 5 4 3 2 1 1 1 1
9 11 10 9 8 7 6 5 4 3 2 1 1 1
10 12 11 10 9 8 7 6 5 4 3 2 1 1
11 13 12 11 10 9 8 7 6 5 4 3 2 1
12 14 13 12 11 10 9 8 7 6 5 4 3 2
13 15 14 13 12 11 10 9 8 7 6 5 4 3
14 16 15 14 13 12 11 10 9 8 7 6 5 4
15 17 16 15 14 13 12 11 10 9 8 7 6 5
16 18 17 16 15 14 13 12 11 10 9 8 7 6
17 19 18 17 16 15 14 13 12 11 10 9 8 7
18 20 19 18 17 16 15 14 13 12 11 10 9 8
19 - 20 19 18 17 16 15 14 13 12 11 10 9
20 - - 20 19 18 17 16 15 14 13 12 11 10
21 - - - 20 19 18 17 16 15 14 13 12 11
22 - - - - 20 19 18 17 16 15 14 13 12
23 - - - - - 20 19 18 17 16 15 14 13
24 - - - - - - 20 19 18 17 16 15 14
25 - - - - - - - 20 19 18 17 16 15
26 - - - - - - - - 20 19 18 17 16
27 - - - - - - - - - 20 19 18 17
28 - - - - - - - - - - 20 19 18
29 - - - - - - - - - - - 20 19
30 - - - - - - - - - - - - 20

Once again, a very interesting – if fairly familiar – pattern. This sort of table should be fairly well-known and obvious to every GM who’s been around for a while.

It’s only when you make the mental connection between the two tables that the real significance of the fairly obvious pattern makes itself clear. An increasing bonus creates an upward trend in benefits (as shown in table 2) from a combat advantage AND a similar trend in penalties from a combat disadvantage.

This all becomes clearer when the appropriate values are transplanted from table 2 into table 3 to give tables 4 and 5:

Table 4:
With
Advantage
Bonus
AC -2 -1 +0 +1 +2 +3
1 +9%  +4.75%  +0 +0 +0 +0
2  +12.75%  +9% +4.75% +0 +0 +0
3 +16%  +12.75%  +9% +4.75% +0 +0
4 +18.75% +16%  +12.75%  +9% +4.75% +0
5 +21% +18.75% +16%  +12.75%  +9% +4.75%
6 +22.75% +21% +18.75% +16%  +12.75%  +9%
7 +24% +22.75% +21% +18.75% +16%  +12.75% 
8 +24.75% +24% +22.75% +21% +18.75% +16%
9 +25% +24.75% +24% +22.75% +21% +18.75%
10 +24.75% +25% +24.75% +24% +22.75% +21%
11 +24% +24.75% +25% +24.75% +24% +22.75%
12 +22.75% +24% +24.75% +25% +24.75% +24%
13 +21% +22.75% +24% +24.75% +25% +24.75%
14 +18.75% +21% +22.75% +24% +24.75% +25%
15 +16% +18.75% +21% +22.75% +24% +24.75%
16 +12.75% +16% +18.75% +21% +22.75% +24%
17 +9% +12.75% +16% +18.75% +21% +22.75%
18 +4.75% +9% +12.75% +16% +18.75% +21%
19 - +4.75% +9% +12.75% +16% +18.75%
20 - - +4.75% +9% +12.75% +16%
21 - - - +4.75% +9% +12.75%
22 - - - - +4.75% +9%
23 - - - - - +4.75%
24 - - - - - -
25 - - - - - -
26 - - - - - -
27 - - - - - -
28 - - - - - -
29 - - - - - -
30 - - - - - -

 

Table 4:
With
Advantage
(cont)
Bonus
AC +4 +5 +6 +7 +8 +9 +10
1 +0 +0 +0 +0 +0 +0 +0
2 +0 +0 +0 +0 +0 +0 +0
3 +0 +0 +0 +0 +0 +0 +0
4 +0 +0 +0 +0 +0 +0 +0
5 +0 +0 +0 +0 +0 +0 +0
6 +4.75% +0 +0 +0 +0 +0 +0
7 +9% +4.75% +0 +0 +0 +0 +0
8 +12.75% +9% +4.75% +0 +0 +0 +0
9 +16% +12.75% +9% +4.75% +0 +0 +0
10  +18.75%  +16%  +12.75%  +9% +4.75% +0 +0
11 +21%  +18.75%  +16%  +12.75%  +9% +4.75% +0
12 +22.75% +21% +18.75% +16%  +12.75%  +9% +4.75%
13 +24% +22.75% +21% +18.75% +16%  +12.75%  +9%
14 +24.75% +24% +22.75% +21% +18.75% +16%  +12.75% 
15 +25% +24.75% +24% +22.75% +21% +18.75% +16%
16 +24.75% +25% +24.75% +24% +22.75% +21% +18.75%
17 +24% +24.75% +25% +24.75% +24% +22.75% +21%
18 +22.75% +24% +24.75% +25% +24.75% +24% +22.75%
19 +21% +22.75% +24% +24.75% +25% +24.75% +24%
20 +18.75% +21% +22.75% +24% +24.75% +25% +24.75%
21 +16% +18.75% +21% +22.75% +24% +24.75% +25%
22 +12.75% +16% +18.75% +21% +22.75% +24% +24.75%
23 +9% +12.75% +16% +18.75% +21% +22.75% +24%
24 +4.75% +9% +12.75% +16% +18.75% +21% +22.75%
25 - +4.75% +9% +12.75% +16% +18.75% +21%
26 - - +4.75% +9% +12.75% +16% +18.75%
27 - - - +4.75% +9% +12.75% +16%
28 - - - - +4.75% +9% +12.75%
29 - - - - - +4.75% +9%
30 - - - - - - +4.75%

 

Table 5:
With
Disadvantage
Bonus
AC -2 -1 +0 +1 +2 +3
1 -9% -4.75% -0 -0 -0 -0
2  -12.75%  -9% -4.75% -0 -0 -0
3 -16%  -12.75%  -9% -4.75% -0 -0
4 -18.75% -16%  -12.75%  -9% -4.75% -0
5 -21% -18.75% -16%  -12.75%  -9% -4.75%
6 -22.75% -21% -18.75% -16%  -12.75%  -9%
7 -24% -22.75% -21% -18.75% -16%  -12.75% 
8 -24.75% -24% -22.75% -21% -18.75% -16%
9 -25% -24.75% -24% -22.75% -21% -18.75%
10 -24.75% -25% -24.75% -24% -22.75% -21%
11 -24% -24.75% -25% -24.75% -24% -22.75%
12 -22.75% -24% -24.75% -25% -24.75% -24%
13 -21% -22.75% -24% -24.75% -25% -24.75%
14 -18.75% -21% -22.75% -24% -24.75% -25%
15 -16% -18.75% -21% -22.75% -24% -24.75%
16 -12.75% -16% -18.75% -21% -22.75% -24%
17 -9% -12.75% -16% -18.75% -21% -22.75%
18 -4.75% -9% -12.75% -16% -18.75% -21%
19 - -4.75% -9% -12.75% -16% -18.75%
20 - - -4.75% -9% -12.75% -16%
21 - - - -4.75% -9% -12.75%
22 - - - - -4.75% -9%
23 - - - - - -4.75%
24 - - - - - -
25 - - - - - -
26 - - - - - -
27 - - - - - -
28 - - - - - -
29 - - - - - -
30 - - - - - -

 

Table 5:
With
Disadvantage
(cont)
Bonus
AC +4 +5 +6 +7 +8 +9 +10
1 -0 -0 -0 -0 -0 -0 -0
2 -0 -0 -0 -0 -0 -0 -0
3 -0 -0 -0 -0 -0 -0 -0
4 -0 -0 -0 -0 -0 -0 -0
5 -0 -0 -0 -0 -0 -0 -0
6 -4.75% -0 -0 -0 -0 -0 -0
7 -9% -4.75% -0 -0 -0 -0 -0
8  -12.75%  -9% -4.75% -0 -0 -0 -0
9 -16%  -12.75%  -9% -4.75% -0 -0 -0
10 -18.75% -16%  -12.75%  -9% -4.75% -0 -0
11 -21% -18.75% -16%  -12.75%  -9% -4.75% -0
12 -22.75% -21% -18.75% -16%  -12.75%  -9% -4.75%
13 -24% -22.75% -21% -18.75% -16%  -12.75%  -9%
14 -24.75% -24% -22.75% -21% -18.75% -16%  -12.75% 
15 -25% -24.75% -24% -22.75% -21% -18.75% -16%
16 -24.75% -25% -24.75% -24% -22.75% -21% -18.75%
17 -24% -24.75% -25% -24.75% -24% -22.75% -21%
18 -22.75% -24% -24.75% -25% -24.75% -24% -22.75%
19 -21% -22.75% -24% -24.75% -25% -24.75% -24%
20 -18.75% -21% -22.75% -24% -24.75% -25% -24.75%
21 -16% -18.75% -21% -22.75% -24% -24.75% -25%
22 -12.75% -16% -18.75% -21% -22.75% -24% -24.75%
23 -9% -12.75% -16% -18.75% -21% -22.75% -24%
24 -4.75% -9% -12.75% -16% -18.75% -21% -22.75%
25 - -4.75% -9% -12.75% -16% -18.75% -21%
26 - - -4.75% -9% -12.75% -16% -18.75%
27 - - - -4.75% -9% -12.75% -16%
28 - - - - -4.75% -9% -12.75%
29 - - - - - -4.75% -9%
30 - - - - - - -4.75%

 

Some interpretation

Viewing the results in this way makes a number of implications clear.

  • For any given combat bonus, there is an optimum AC which maximizes the benefits of Combat Advantage which is equal to 11 plus the bonus.
  • That same optimum AC also maximizes the penalties that result from Combat Disadvantage.
  • At ACs lower than the optimum, Combat Advantage makes a likely outcome (a success) even more likely.
  • ACs lower than the optimum are divided into two bands: those that are 6 or more less than the optimum, where combat disadvantage has a relatively small effect, and those that are between that value and the optimum, where combat disadvantage is significant.
  • At an AC greater than about 16 more than the total combat bonus, chances of success begin to decline rapidly despite combat advantage.
  • At an AC greater than about 7 more than the total combat bonus, chances of success decline rapidly with combat disadvantage.
  • The greater the combat bonuses, the less significant (in general) combat advantage is except for a small band of low ACs.
  • The 50% success mark is at (approximately) target=11 (straight d20), target=15 (with advantage), and target=7 (with disadvantage).
  • The 25% success mark is at (approximately) target=16 (straight d20), target=18 (with advantage), and target=11 (with disadvantage).
  • These can be used by the GM to select opponents posing different standards of tactical challenge.
  • The relative tactical importance of achieving advantage over your opponents is variable depending on your combat bonuses and the AC of the opponent.
  • The relative tactical importance of denying an opponent advantage over you is variable depending on your AC and your opponent’s combat bonuses.
  • The two will rarely be the same. The optimum tactics to employ in any given situation are hence highly variable.
  • The higher your combat bonuses, the less important tactical advantage and disadvantage are. It follows that min-maxing a character construction will often be less effective than being average and using smart tactics.
  • It also follows that the optimum target value for min-maxing is different in every encounter. Past a certain point, the player is expending a great deal of effort to replace part of one benefit with an increase in another. As a result, it is both more difficult and less rewarding to min-max a character.

Conclusions

For my money, that last point is the greatest possible justification for this mechanic. All the other benefits – a more complex set of tactical considerations, the ability of a smart GM to work the system to provide a greater challenge to the players, and so on – are simply icing on the cake. In fact, there will be circumstances in which it is better overall for a min-maxed character to make themselves secondary to the battle and permit a character with good but not perfectly-tweaked ability totals to assume a better tactical position.

This will be especially true if the DM makes the precision of his adjudications with respect to combat advantage and disadvantage proportionate to the attack bonus of the min-maxed PC while being a little more generous (either way) on the part of non-min-maxed characters.

Will this end min-maxing and an elitist approach to character construction? I doubt it. Will it make these things less of a concern to DMs? Quite probably.

And that’s a very good thing.

P.S.

Anyone interested in the subject might also like to read Advantage vs Flat Bonuses at Critical Hits.

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