Doing the Math

A week or so ago, I became involved in one of those very fruitless internet discussions over on the D&D forums (a more joyless lot of players I’ll never meet) over what is referred to as “the Broken Math Fallacy.” The crux of the issue is that D&D4e math doesn’t work. Doesn’t work such that, at any given level it is possible to find yourself in a fight (and I’m going by what I saw from the forums, not my own experience here) where you need 16’s-18s to hit a monster. Check out the original thread on the forums if you want. Then come on back and we’ll talk… be warned, it’s long.

The Broken Math Fallacy Thread

This seemed strange to me, so I began to look into it. I didn’t have the sheer time to do a thorough job of it with the pressures of my grad workload. So, with the mighty influx of free time that is spring break, I’ve finally managed to get around to it. In case you didn’t have the time to check out the thread, a major 4e issue is the Expertise feats. These feats are basically, a “feat tax” used to do, (as one designer called it in his writing), “combat number maintenance.” This issue creates several problems. For some posters/players, the issue is that they don’t want to have a “must take” feat just to continue to be effective. On the other side of the coin, some optimizers are annoyed that such a fix isn’t accomplished by simply changing the “Level Up” chart to include these bonuses for all characters. The final subset of this issue is my group. The type of people who believe that the Expertise style feats aren’t necessary, and therefore ban them at their tables. We are generally sneered at by the forum dwellers for our stupidity, since clearly we’re wrong. If I seem overly critical of the conversation on the D&D forums, I apologize. A lot of posters there are decent, intelligent people, but I’ve been sneered at, talked at, and insulted one too many times not to see the overall demeanor of those boards in a negative light.

Well, let’s examine the issue shall we?

First off, let me set the stage for my little excursion into game math.

1. I start examining this issue at 11th level. Most players agree that heroic tier is “okay” and so the arguments don’t really start until paragon/epic.
2. I did all my math assuming two things: that a PC has an 18 in their prime attack stat, and that they use a +3 proficiency weapon. I did this because I was assuming some level of optimization, and because I have something further to say about implement users toward the end.
3. All the math below takes into account only: regular ability score increase, level increase and an appropriate magic item enhancement bonus.

***I based the magic item bonuses on the high side of the scale as well (favoring the monsters not the PCs). That is, I assume you won’t have a +1 item until Level 5, +2 until 10, +3 at 15, +4 at 20, +5 at 25 and +6 doesn’t arrive until 30. Obviously, most parties will have these items sooner than this, so, again, this actually favors the monsters, not the PCs.***

4. Even though I examined more than this, for this (already long) post, I am going to only write up numbers for 11th, 21st and 30th level.


Let’s do some Math!

11th Level
At the beginning of the paragon tier of play, a typical PC should have a +15 to attack. This is a +5 from level, an attribute bonus of +5 and a weapon bonus of +5 (+3 proficiency/+2 enhancement).

At this level, the average for Monster Armor Classes is:

Artillery: 24 (PC needs 9 to hit)
Brute: 23 (PC needs 8 to hit)
Controller: 25 (PC needs 10 to hit)
Lurker: 26 (PC needs 11 to hit)
Skirmisher: 25 (PC needs a 10 to hit)
Soldier: 27 (PC needs a 12 to hit)

*The outliers to these averages were a 29 AC at the highest end (only 2 monsters out of all those at this level), and 22 at the lowest end (also 2 monsters).

**One oddity which does raise an issue is with Lurkers. The overall AC for Lurkers at this level would have been lower (25) except for the inclusion of several Black Dragons in the monsters available. Since Wizards has come right out and said, “We messed up with original Monster Manual Solo monsters” this seems like they should also be considered outliers, but I’m going to use everything, to be fair.

Conclusion: Since the designers have made it pretty clear they shot for about a base of 50% for the normal PC “to-hit” rate, this seems pretty reasonable to me.

21st Level
Moving on to the beginning of the epic tier of play, a typical PC should have a +24 to attack. This is a +10 from level, an attribute bonus of +7 and a weapon bonus of +7 (+3 proficiency/+4 enhancement).

At this level, the average for Monster Armor Classes is:

Artillery: 34 (PC needs 10 to hit)
Brute: 33 (PC needs 9 to hit)
Controller: 34 (PC needs 10 to hit)
Lurker: 35 (PC needs 11 to hit)
Skirmisher: 35 (PC needs a 11 to hit)
Soldier: 37 (PC needs a 13 to hit)

*The outliers to these averages were a 39 AC at the highest end (only 2 monsters out of all those at this level), and 27 at the lowest end (1 monster).

Conclusion: Since the designers have made it pretty clear they shot for about a base of 50% for the normal PC “to-hit” rate, this seems pretty reasonable to me. PCs may have lost about one point overall, when compared to 11th level but I’m not accounting for several things here:
1. Any bonuses gained from paragon paths
2. The fact many epic destinies will boost attributes at this level (good for another +1)
3. Finally, the fact that I am low-balling the magic items. Many PCs will have a +5 item at this level. (good for another +1)

30th Level
Finally, at the capstone of a career, the typical PC should have a +32 to attack. This is a +15 from level, an attribute bonus of +8 and a weapon bonus of +9 (+3 proficiency/+6 enhancement).

At this level, the average for Monster Armor Classes is:

Artillery: 42 (PC needs 10 to hit)
Brute: 43 (PC needs 11 to hit)
Controller: 44 (PC needs 12 to hit)
Lurker: NA (Not a single example of a 30th level lurker exists in the Encounter Builder)
Skirmisher: 44 (PC needs a 12 to hit)
Soldier: 46 (PC needs a 14 to hit)

*The outliers to these averages were a 48 AC at the highest end and 42 at the lowest end.

**As mentioned above at 11th level, this level’s worth of monsters may have been skewed a little high by the inclusion of a lot of Monster Manual solos/elites, which Wizards has already changed, going forward, how these monsters will have their ACs assigned. After all, the original MM had the Ancient Red Dragon at 48 AC. This means a PC needs a 16 to hit, which is, clearly, too high.

Conclusion: As my note above mentions, this level is a little skewed by the majority of its monsters being solos/elites, with many being pre-MM2-changes. Overall, the PCs have lost a little ground here, but consider that if they had Expertise in the mix, they would be hitting on a range of 7-11 instead (lower than the intended curve).

Final Thoughts (for now)
Because this post is running long, I’ll post a few final thoughts and move on.

1. The highest AC a PC can expect to face at most tables, ever, is going to be 48.
2. These calculations do not include any other modifiers, such as Combat Advantage, Aid Another (happens all the time in fantasy literature), the +1 fighter weapon talent, +1 rogue weapon talent, dragonborn +1 when bloodied, tiefling +1 vs bloodied opponents, elven re-roll on an attack, twin strike, avenger double-rolling, situational bonuses like nimble blade, or any sort of bonus granted by another party member such as Warlords/Battle Captains. Ultimately, with a typical party trying to get CA (which a lot of posters over at the forums already figure in) every number needed above could be effectively lowered by 2. 4e is supposed to be a party based game, that’s why the roles matter so much in this edition. You will have other bonuses from your companions.
3. Some people are saying, but what about those +2 proficiency weapons? To that I say, this is one area of 4e design that I feel the designers really messed up. If the only two choices were +2 or +3, why even bother with weapon proficiency numbers at all? Couldn’t you have individualized weapons some other way? Also, in the case of hammers and scimitars, they have accounted for this some with “damage on a miss” effects, and with axes, well, axes are overall the worst weapons in 4e, so… whatever. But if you want a +2 proficiency weapon, raise the numbers by one, and you are still in a pretty good range.

!!One final note about Implement Users!!
This is the one area where I feel the designers let us down, in terms of the math. Quite often (not always, but most of the time), a monster will have at least one-NAD lower than its AC, by 3 to 5 points. This means that they are still on the same par as weapon using PCs. And most implement users will have options to hit multiple non-AC defenses. That said, enough monsters have defenses which are all equal, or only drop by 1 point, to make life much harder for implement using PCs. Why? I vote designers not paying attention to how that decision will impact characters. This is easy for DMs to errata, “on the fly” at their tables though, so it’s not really worth sweating over. The one glaring failure is Fortitude defense, which for a large number of monsters is actually higher than or equal to AC. This needs looking into, but that’s another post.

Thanks for reading. Now, let me know what you think.


7 responses

  1. I really like 4e. I may or may not have mentioned this. I haven’t really gotten to play it enough, but I’ve run it a few times – I’ve experienced enough games, I feel, to give some opinion on it. As much as I like it, I don’t feel that it’s a perfect system. Some stuff bugs me, though not enough to be a deal breaker. One thing in particular really sticks in my craw:

    I did all my math assuming two things: that a PC has an 18 in their prime attack stat, and that they use a +3 proficiency weapon. I did this because I was assuming some level of optimization, and because I have something further to say about implement users toward the end.

    Your math works out. You’ve got in most cases about a 50% chance to hit, and the worst case scenario against a non-solo/non-elite is a 30% chance to hit, assuming the player has taken part in some optimization. But what if they haven’t? Let me tell you a story…

    My second game of 4e was at our local gaming store, one of their monthly rotating GM one-shot days. I was very excited to be playing, and rolled up and brought a fun character – Teagan Featherfoot, Halfling Cleric.

    I was assigned to a table with people I had never met before, including a guy named Albert. Before the game even started, I knew the deal with this guy – nobody liked him, and nobody liked playing with him. One other player told me in confidence that he was always placed at a table with Albert because he was one of the few players who could reign the guy in. I wasn’t worried. I’ve dealt with some annoying gamers in my day.

    Albert, as it turns out, was a colossal douche, and he gave me shit the entire game. He criticized my decisions in combat (partially character-motivated – I did what I thought my character would do, as I refuse to play D&D as a board game). He gave me shit for not taking his direction in combat (not my character refusing to take direction from his character, but ME refusing to do what HE, the player, said). He criticized my spell/power choices. And then he criticized my choice of class/race combo.

    That last one really pissed me off. One of the things I loved most about the transition from 2nd to 3rd ed was that there were no more class/race restrictions. If you wanted to be a Dwarven wizard, you could. Elven paladin? Fine, your call. I love this. I embrace it. And no pushy, smelly, unlikeable asshole is going to tell me what kind of character I should or shouldn’t play, as long as it’s allowed in the rules.

    So what’s the point of that story? It is that I realized, some time later, that it wasn’t just Albert telling me that I shouldn’t play a Halfling Cleric. It was the game as well. 4e has done a great job of making every class feel like they have a role in combat, like they can get in on the action. At the same time, though, every class has become a slave to hit rolls. And the creators figured on a 50% hit rate with optimization. 18 in your primary class, modified to 20 with your racial bonus for a +5 to hit. But if your class has a primary stat that isn’t boosted by your race, that 50% standard has now gone to 40%. At 30th level my halfling cleric, at his best, is looking at a 20% chance to hit that soldier. A 16, which you’ve called too high above. And Gods help him if he’s using an implement, as you’ve pointed out.

    It isn’t just a matter of race/class combos, though. I really like the point buy system, but it forces you to make some tough choices with regards to sacrificing any level of diversity to get that 18 – and as you’ve pointed out with your math, those choices aren’t really choices at all. A 16 strength (modified up to 18 with whatever race bonus you have) for a warrior may not seem like such a raw deal when you’re rolling the character up, but 20 levels later enemies are filing past you like you’re a Wal-Mart greeter and stomping on your friends because you can’t hit those essential opportunity attacks. Not every warrior has to be Mr. Olympia – just the ones who don’t want to see their mates die a gruesome, stabby death.

    “But CC,” you say, “It has always been thus. A character who maxes out his score in his primary stat has always and will always outperform one who takes a lower score, whether that’s because they chose to mix up their ability scores a little or because they chose a race and class mixture that wasn’t optimal.” To that I say, “Seriously? ‘It has always been thus?’ Who talks like that?” I also say that, as I mentioned above, hitting your opponent is now more important than ever. We’ve got all these cool new powers, and the vast majority of them require you to roll above that magic number if they’re going to work, or at least work the way they’re supposed to. The change from a 50% hit chance to a 40% or even to a 35% on normal opponents doesn’t just make you switch up your strategy – it makes you pretty much useless.

    I see where it comes from. They want to have a little something for everyone. If someone wants to min/max, why not reward them? The problem is that with the scenario as it stands, the min/maxers aren’t rewarded – everyone else is punished.

    I’ll draw this very very long response to a close by admitting that Teagan Featherfoot, ineffectual Halfling Cleric Extraordinaire, was heroic tier, and fairly low on it at that. Would he have been more effective once I started piling on cool bonuses from higher levels? Would I find his role in a higher-level party one that didn’t actually place such high emphasis on his hit chance? I don’t know the answer to those questions.

    I know one thing, though.

    If I ever have to game with that prick Albert again, I’m going to punch him in his fucking throat.

  2. When I said, “some optimization” I meant taking an 18 in their prime attack stat after all modifiers, not taking an 18 then modifying it to 20 with racial bonuses.

    I chose an 18 prime as the base for this experiment because it seems most likely for the largest range of characters. I might have chosen a +2 proficiency weapon instead to show off the system, but again, I wanted to pick one thing and stick with it. And I believe I addressed some of the issues with +2 proficiency weapons near the end (not enough, I know, but some.)

    And remember, that roughly 50% hit chance is actually closer to 60% assuming the party takes part in any attempts to get combat advantage, use aid another, or pass out bonuses from the leader types/lower defenses with their controller types.

    I’ve played several characters, so far, who were not optimized between race/class (dwarven rogue anyone), and it’s possible to get that 18 and still have a lot of options with your other stats. I was a little off with my rider stat (only 14 instead of 16) but since I had bonuses to both CON and WIS, that made up for it some by evening out my defenses well.

    (I had a 12 CON and a 13 WIS, which, not all that useful for my ‘class’ was still useful for skills such as perception and insight, and allowed me to take the cleric multiclass, which fit my background and gave me one more chance to heal as a minor action/day.)

    I guess the point of this long response is, I’ll avoid the D&D forums, you avoid Albert, and we’ll both be able to go on enjoying 4e.

    1. As an added aside (in addition to my previous response), I would like to point out that I have messed around with generating hybrid characters, and I like it a lot more than using the multiclass feats if you want to set up a character concept that is multiclassed from the beginning. The multiclass feats work well enough for characters who pick up a new path along the way, but for those spellswords out there, the hybrid class seems to do a pretty good job…at least, the Knight (fighter/warlord) that I created looked good. I don’t enough chances to play to actually test all my characters out.

  3. And I see where my misunderstanding came in – I looked at your numbers for paragon level, saw the +5 to hit and thought “So that’s a 20 in that stat. Which means that he put an 18 in there and modified it by race.” I wasn’t considering the +2 bonus you get from your ability increases as you level. Even if you’re diversifying, you’re still likely to increase your primary stat every chance you get. After all, a strong guy gets stronger as he continues to swing that sword.

    I still contend that the emphasis on being able to hit in order to use the majority of abilities makes optimization more necessary than it has been in the past…but the numbers aren’t as bad, then, as I had originally thought.

    It wasn’t enough of a complaint to make me not appreciate the game anyway 😉

  4. I have been very satisfied with the ability to create a viable character with just about any race/class combination. My only disappointing character I’ve ever played was an Eladrin two-weapon Ranger: it was the first character I created in 4e and I was forced to spread my points so thin that I had to have a 16/14 in my primary/secondary stats. I was jealous of the other characters that seemed to hit more often than I could.

    I’m very baffled at the ‘Alberts’ of the D&D 4e world: yes, there are combinations of classes and races that work better together; but, so what? Even the most optimized character can miss, and if the party works well together, the character with 16’s in his primary stat can be a real asset. The power gamer mindset is totally lost on me.

    I will admit that it’s disappointing to miss with your daily power – but that’s the point! If there wasn’t a chance of failure, there would be no challenge. The point of D&D is not to always hit or always survive; it’s to create heroic situations and to have fun.

    1. Yeah, I know I’m way behind on replying to this, but I somehow missed these last two comments.

      Missing a daily power sucks, but that’s one of the (many) reasons to play a fighter – they’ve got a lot of “Reliable” powers.

      Whatever else they’ve done right or wrong with 4e, they took a class that was pretty boring before (run up, stand and slash, rinse and repeat) and made it one of the best in the game to play. Fighters are fun and they’re badass. And even though they keep on adding Defender classes, the fighter still remains near or at the top of the list for Defender effectiveness.

  5. I haven’t tinkered with the hybrid rules much yet. I am looking forward to giving them a try. Without those rules it is difficult to do a real ‘spellsword’ type of character. The swordmage is great, but is very firmly a Defender. I’d like to make a more striker capable arcane melee character.

    I also know at least one of my players eager to try out Artificer/Shielding Swordmage hybrid, if we start up again.

    Powergamer/Albert types will exist in any group of players, anywhere, for almost any game. Whenever you reduce storytelling to a numeric system, someone will always be looking for the “leg up” on the competition (which strangely enough, often means his fellow players.)

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