Extra damage from critical hits is VASTLY underestimated when looked at as a ratio of actual damage output.
Not really. It's vastly overestimated, as evidenced by the large number of people that think scoring crits on 19s is a good trade-off for other 3rd level subclass features. In the absence of crit damage bonuses a critical hit doesn't even manage to double your average damage for that hit. That means a 5 percentage point increase in your crit rate translates into a less than 5 percentage point increase in your overall damage.
Incorrect. It’s not a 5% increase in damage. It’s around 11%. See the following link:
It's neither. Everyone get's 5% chance to crit. Improved critical does gives you an additional 5% chance to crit. This mean the extra crit damage is only applied 5% of the time, making it whatever that damage is x .05.
Posting links to people in other threads who are wrong isn't an argument. They aren't here to defend their position. If you think my math is wrong, show me the math you think is right.
If we assume 2 3-round combats per short rest, a level 3 fighter can be expected to make 7 (counting Action Surge) Attack actions per short rest, and some unknown number of Opportunity Attacks -- call it 2. Thus, he's making 9 attacks per short rest. A two weapon fighter will be making 15
A level 3 Champion will on average get 0.45 more critical hits (0.75 for the two weapon fighter). A critical hit is worth between 3.5 (dual wielder using d6 weapons) and 8.3 (great weapon fighting with a two handed sword) bonus damage. Thus, the increased damage per short rest is a maximum of 3.75 (unless half-orc). This is roughly doubled by using Great Weapon Master, as a crit will be an extra attack.
A level 3 Battle Master will on average apply 18 bonus damage (4d8), or 21 with Great Weapon Fighting. Advantage: Battle Master. Also, non-damage maneuver effects.
At level 5, Extra Attack comes in, so the Champion increases to 16 attacks (0.8 crits) per short rest. Bonus damage is now up to about 6.5.
At level 11, the Champion is at 23 attacks (1.15 crits, worth about 9.5 for GWF), the Battle Master is at 5d10 (27.5, 31.5 w/GWF)
At level 15, the Champion is at 2.3 crits (worth 19), the Battle Master is at 6d10 (33, 37.8 w/GWF) and might get more depending on running out in early fights.
At level 20, the Champion is at 30 attacks (+3 crits, 25 damage), the Battle Master is at 6d12 (39, 44 w/GWF).
The Champion does get a second fighting style, which is nice, though not as relevant as it used to be since you can get one with a feat. Remarkable Athlete has the interesting quirk that it adds to Initiative (which is a Dexterity check) but isn't otherwise that exciting. Survivor isn't super relevant in combat, healing 5-10 per turn at level 18 barely affects anything, but does mean you can heal up to half health after any battle for free.
It's an ~11% relative increase if your hit rate starts at 45% (which is quite low) and there's no numerical bonuses in the damage roll. But weapon attacks do have numerical bonuses in the damage roll and focusing purely on the relative change doesn't tell you anything super useful. If you manage to get your attacks to only hit on 20s you can rightfully say expanding your crit rate to 19 doubles your damage, but if you're still doing way less damage than if you could hit on a 5 or more.
If you change the numbers to, say, 2d6 + 3 with a 70% hit chance you're back down to a 5% relative increase because you're not doubling that +3 and you're not starting at such an abysmally low hit rate. With a smaller damage die and bigger bonus (say, TWF or Dueling styles) you'd go below 5%.
Its not the strongest fighter subclass, and is probably competes with EK for weakest. But its still a fighter, one of the strongest, most versatile, and customizable martial classes in the game. And its abilities aren't bad.
I think the real downside of the Champion is that it is kind of mechanically boring compared to other fighters. There aren't really many buttons to push as far as abilities. The one thing you do get that is truly unique is chasing the high of crits a bit more, but there aren't even many ways to toy with that without multiclassing out of fighter.
It’s bad and boring. The “entry” subclass for a Fighter should be the Samurai, who is mechanically simple, but it’s quite effective. Champion shouldn’t exist at all.
It’s bad and boring. The “entry” subclass for a Fighter should be the Samurai, who is mechanically simple, but it’s quite effective. Champion shouldn’t exist at all.
I'd probably change Born to the Saddle in Cavalier to something more generic and then make that the default. While "I want to hit people really hard" is a legitimate reason to want to play a fighter, "I want to protect the party" is also a pretty big one.
Firecat5, if using GWM bonus causes you to have to roll a natural 19/20 to hit, the math works out that you should not use it.
Use it on things that don’t have such a high AC. A sidenote, the more damage do you normally do without GWM, the lower the AC threshold is that you should not use it.
Higher normal (non-GWM) damage and higher AC both diminish the value of GWM.
I played a little bit of D&D a few years ago and then stopped. I started again this year. My character was a V. Human Barbarian, optimized to deal as much dmg as possible. I took GWM as the feat from V. Human. I died at lvl 2 without hitting my enemy even once because I kept using my GWM feat, even though I also used the reckless attack on every turn.
Tbf though, we were kinda stupid to fight a young green dragon as 3 lvl 2 characters, but still. With an avg of negative modifier in int, there wasn't much to do about it.
Firecat5, if using GWM bonus causes you to have to roll a natural 19/20 to hit, the math works out that you should not use it.
Use it on things that don’t have such a high AC. A sidenote, the more damage do you normally do without GWM, the lower the AC threshold is that you should not use it.
Higher normal (non-GWM) damage and higher AC both diminish the value of GWM.
I played a little bit of D&D a few years ago and then stopped. I started again this year. My character was a V. Human Barbarian, optimized to deal as much dmg as possible. I took GWM as the feat from V. Human. I died at lvl 2 without hitting my enemy even once because I kept using my GWM feat, even though I also used the reckless attack on every turn.
Tbf though, we were kinda stupid to fight a young green dragon as 3 lvl 2 characters, but still. With an avg of negative modifier in int, there wasn't much to do about it.
lol Yeah, but that one is on your DM. That's just... ridiculous. Especially if he knew you guys were new.
Kerrec, yes, the more times you attack the more often everything happens. You'll hit more times, crit more times, and miss more times.
Improved Critical still only amounts to 0.35 average extra damage per turn with a greatsword. But yeah, if you swing your toward 100 times, that does amount to 35 extra damage spread over all 100 of those swings. In contrast, if you have a 70/30 hit-miss ratio, just the level 1 Dueling Fighting Style that all Fighters get will amount to 140 extra damage over 100 attacks
Well, yeah. But I don't agree with your conclusion.
You chose a greatsword. Obviously because it rolls 2d6 which is nice damage. But your non-champion fighter is going to roll that thing once when a two weapon fighting champion is going to roll his piddly 1d6 shortsword twice. So here are some examples, with a caveat; I don't have the time or the patience to go through every fighter sub-class to find what would be an equivalent ability or feat to what I chose for the Champion for each of these examples:
Level 3 assuming 100% hit rate:
Non-Champion attacks once and does (2d6 + mod damage). He has a 5% chance to Crit on his turn (ignoring advantage).
TWF Champion attacks twice and does (1d6 +mod) + (1d6 + mod) damage. So Champion is 1xMod damage ahead so far. But, the champion has a 19% chance of landing ONE crit (ignoring advantage). And there's the potential for up to 2.
Level 4 assuming Elven Accuracy and 100% hit rate. (Again, no idea what would be equivalent or min/max feat for non-Champions):
Ignoring Advantage, we get the same result as above. However if both fighters have advantage...
Non-Champion attacks once with advantage and does (2d6 + mod) damage. He has a 9.75% chance to crit on his turn.
TWF Champion attacks twice, both times with advantage and does (1d6 + mod) + (1d6 + mod) damage. However, with Elven accuracy, he has a 46.9% chance of landing ONE crit. And there's the potential for up to 2.
Level 5 assuming Elven Accuracy and 100% hit rate. (yada yada disclaimer same as above)
Ignoring Advantage:
Non-Champion attacks twice and hits twice for (2d6 + mod) + (2d6 + mod). He has a 9.75% chance to crit ONCE on his turn.
TWF Champion attacks three times and hits three times for (1d6 + mod) + (1d6 + mod) + (1d6 + mod). He has a 27.1% chance to crit once on his turn.
With Advantage:
Non-Champion attacks twice with advantage and hits twice for (2d6 + mod) + (2d6 + mod). He has a 18.55% chance to crit ONCE on his turn.
TWF Champion attacks three times with advantage and hits three times for (1d6 + mod) + (1d6 + mod) + (1d6 + mod). He has a 61.3% chance to crit once on his turn.
Level 15 assuming Elven Accuracy and 100% hit rate. (yada yada disclaimer same as above)
Ignoring Advantage:
Non-Champion attacks three times and hits three times for (2d6 + mod) + (2d6 + mod) + (2d6 + mod). He has a 14.3% chance to crit ONCE on his turn
TWF Champion attacks four times and hits four times for (1d6 + mod) + (1d6 + mod) + (1d6 + mod) + (1d6 + mod). He has a 38.6% chance to crit once on his turn.
With Advantage:
Non-Champion attacks three times with advantage and hits three times for (2d6 + mod) + (2d6 + mod) + (2d6 + mod). He has a 26.5% chance to crit ONCE on his turn.
TWF Champion attacks four times with advantage and hits four times for (1d6 + mod) + (1d6 + mod) + (1d6 + mod) + (1d6 + mod). He has a 85.8% chance to crit once on his turn.
Level 20 assuming Elven Accuracy and 100% hit rate. (yada yada disclaimer same as above)
Ignoring Advantage:
Non-Champion attacks four times and hits four times for (2d6 + mod) + (2d6 + mod) + (2d6 + mod) + (2d6 + mod). He has a 18.55% chance to crit ONCE on his turn
TWF Champion attacks five times and hits five times for (1d6 + mod) + (1d6 + mod) + (1d6 + mod) + (1d6 + mod) + (1d6 + mod). He has a 91.3% chance to crit once on his turn.
Now, I can tell you're all salivating (and probably stopped reading to reply) that 8d6 + (4*mod) ie: [28 + 20 = 48] is better than 5d6 + (5*mod) [17.5 + 25 = 42.5]. However, the % chance to hit above is calculated assuming there is ONE crit in a turn. That's comparing apples to oranges. If you want a proper apples to apples comparison, then you have to use a baseline 1 crit for the non-Champion and figure out how many equivalent crits per turn it would take for the Champion to have close to the same % chance. And this is where my math skills reach their limit. So I resorted to a little program I found online and:
The chances of rolling 18 or higher 4 times when rolling 15d20 is 17.73%. (3x is 39.6%. 5x is 6.2%). However, that doesn't factor in the fact that 3 of those rolls are per attack. Rolling 3 20's on the first attack and 1 20 on the 2nd attack doesn't give me more than 2 crits. However, if they happen to be spread out, it is possible to have 4 separate crits.
So, with an apples to apples comparison:
Level 20 assuming Advantage, Elven Accuracy, 100% hit rate and lands between 15-20% range for crit chance (yada yada disclaimer same as above):
IN THE LONG RUN, a TWF DEX Champion should be neck to neck with a non-Champion (that doesn't use any of their unique features or feats that would be exclusive to a non-TWF fighter) assuming worse case scenario of their 18-20's all happening on 2 of their 5 attacks. At the other extreme, assuming 4 of their 5 attacks are crits, they surpass the damage output.
A lot of the other sub-classes have resources they have to manage. Their potential is limited by this output, and that effect can vary greatly depending on what kind of game a DM runs. If those resources are easily replenished (lots of short or long rests), then the Champion probably lags behind. On the flip side, the Champion can do his thing all day, no resources to manage. Campaigns that are stingy on short/long rests are going to favor the Champion.
But as many have said, this is likely to be a very boring class to play. Get in melee range, attack. Rinse and repeat. No more depth than that.
Kerrec, you're overcomplicating this. What it all boils down to you is the more attacks you make, the more you will crit. That's for everyone. More attacks means more damage, again, that's for everyone.
All you have to do is calculate the average added damage per attack to gauge how effective an ability is (damage wise), setting aside abilities that give you additional attacks (you have to calculate those as well). Given the choice between:
1. Improved Critial (the level 3 Champion ability that many people rave about), and
2. Dueling Fighting Style (a level 1 ability for basic Fighters)
It doesn't matter how many swings you make. The Dueling Fighting Style (considered a modest ability by nearly everyone) destroys Improved Critical. With that said, if your point is the Duel-Weapon Fighting Style is superior (damage-wise) to the Dueling Fighting Style, I haven't crunched the numbers but at face value I find that very believable. In fact, I don't need to. If you're doing 50% more attacks then you're going to do 50% more damage (not factoring in using a less powerful weapon in your offhand, or a single attack from a bigger weapon).
Well, we were supposed to be 4 ppl and we were also supposed to clear a lot of minions around and get to lvl 3 first, but we (unknowingly) walked straight to the dragon. Also one of us gave up the element of surprise to try to speak to the dragon, hoping it would let him ride it (shrug). Actually, there were more problems that occurred before (like my team attacking me all the time because I managed to get a wolf (who died 2 sessions earlier) to be my sidekick), but we've learned our lesson.
Well, we were supposed to be 4 ppl and we were also supposed to clear a lot of minions around and get to lvl 3 first, but we (unknowingly) walked straight to the dragon. Also one of us gave up the element of surprise to try to speak to the dragon, hoping it would let him ride it (shrug). Actually, there were more problems that occurred before (like my team attacking me all the time because I managed to get a wolf (who died 2 sessions earlier) to be my sidekick), but we've learned our lesson.
That's ridiculous even at level 3. A young green dragon is a challenge rating 8!
To the OP, Have you actually played one? (full disclosure, I have not) Because there's people who say they have, and say it was good, if boring. They have actual in-game experience. I'm going to rate that over theory (not to mention reducing a subclass to its damage output and seemingly nothing else) any day.
Stop comparing numbers. If all of the classes and archetypes always outputted the same damage, then there'd be no point in choosing one. The chassis of the Fighter is fine. None of them get that much more from their archetypes.
Improved Critical.It's fine. It won't come up that often, but it comes up often enough. It gets better with weapons and features that increase the number of damage dice, like a flame tongue and the half-orc's Savage Attacks. And for a class that gets more attacks than anyone else, the odds of it happening are greater than with any other. It's also "always-on", unlike some other archetypes for other classes.
Remarkable Athlete.This is a skill and support-oriented feature; which is common for martial archetypes. It means your Fighter doesn't need proficiency with Acrobatics or Athletics as badly, freeing up their first-level skill choices. It also adds +2 to their Initiative; reaching +3 at 13th-level. Few classes or archetypes get any such bonus, so it's a welcome one.
Additional Fighting Style.No one else gets a second choice of one, and you can't go wrong with any of them. It's not flashy, but it's not supposed to be. Still, looking at just the PHB, some standout combinations include...
Archery & Defense
Defense & Great Weapon Fighting
Dueling & Protection
Superior Critical.The level 3 ability, but better. And they're making 3-4 attacks per round without turning to Action Surge. And at three attacks per turn, unless my math is wrong, that's a 39% chance that one of those hits will be a critical hit. Even just a single attack with advantage has a 27.75% chance of being a critical hit. Of course, the attack still has to hit. Any attack can still miss against a target with a sufficiently high AC. Only a Natural 20 is guaranteed to hit. And a vorpal sword will only decapitate on a Nat 20, as well.
Survivor. A free 9-10 hit points worth of healing per round, that technically stacks with temporary hit points, and they still have their Second Wind? Yes, please.
To the OP, Have you actually played one? (full disclosure, I have not) Because there's people who say they have, and say it was good, if boring. They have actual in-game experience. I'm going to rate that over theory (not to mention reducing a subclass to its damage output and seemingly nothing else) any day.
You're going to rate anecdotal impressions over mathematical proof? Okay.
You chose a greatsword. Obviously because it rolls 2d6 which is nice damage. But your non-champion fighter is going to roll that thing once when a two weapon fighting champion is going to roll his piddly 1d6 shortsword twice.
TWF is a losing choice for any high level fighter, Champion or not. Four greatsword swings beat 5 short sword swings, and while the greatsword has 20% fewer opportunities to crit, it's doing ~40% more damage per crit.
A lot of the other sub-classes have resources they have to manage. Their potential is limited by this output, and that effect can vary greatly depending on what kind of game a DM runs. If those resources are easily replenished (lots of short or long rests), then the Champion probably lags behind. On the flip side, the Champion can do his thing all day, no resources to manage. Campaigns that are stingy on short/long rests are going to favor the Champion.
In practice the Champion's potential is also limited by the fact that no party can go on fighting forever, and the fact that they're starting at a deficit compared to subclasses that can spend their resources at will on extra damage.
Putting it simply, if we're comparing a Champion and a Battle Master and there's very little fighting, the Battle Master wins by default because they're guaranteed at least 4d8 extra damage no matter what. For every 19 you assume the Champion scores, the Battle Master is equally likely to have scored a 20 in which they could've chosen to use a maneuver for an extra 2d8 until they're out of dice. So the Champion has to accumulate enough extra crits to exceed 8d8 extra damage before the party takes a rest, at which point the Battle Master has all of their dice back.
With a greatsword dealing an extra 2d6 per crit, that's 2.57 extra crits, which is about 51d20 rolls. That's a lot of d20s to roll in probably only 3 or 4 fights at best before the party likely has to rest unless the DM absolutely forces them not to. And remember that target is going to get bigger as the Battle Master gets more and larger dice. By 7th level they need extra 3.21 crits or ~64d20 rolls. By 10th level they need 3.92 extra crits or ~79d20. And this is ignoring any side benefits of the maneuvers like the potential to give other melee characters advantage too, or synergies like Commander's Strike giving rogues another Sneak Attack.
To the OP, Have you actually played one? (full disclosure, I have not) Because there's people who say they have, and say it was good, if boring.
A fighter is a perfectly solid class, and being a champion doesn't make you not a fighter. It's just that Champion is adding very little to the base class. At level 3, it's adding 0.225 dpr to a dueling fighter, 0.35 dpr to a 2WF fighter, 0.416 to a GWF fighter. By comparison, Battle Master is adding 18 damage (21 damage with GWF) so BM is better over fewer than 80 rounds combat for dueling, 52 for 2WF, 51 for 2WF. I've certainly never had that many rounds of combat per short rest. And that's ignoring the fact that battle master dice can crit.
It's plausible to think that the issue is battle master overperforming rather than champion underperforming, but in the end, every fighter subclass except champion meaningfully changes how you play. Champion just makes you very slightly better at what a fighter does anyway.
To the OP, Have you actually played one? (full disclosure, I have not) Because there's people who say they have, and say it was good, if boring. They have actual in-game experience. I'm going to rate that over theory (not to mention reducing a subclass to its damage output and seemingly nothing else) any day.
You're going to rate anecdotal impressions over mathematical proof? Okay.
Yeah, because those anecdotal impressions consider what it was like to play an actual character over, presumably, a number of session including combat and non-combat challenges. The other way is looking only at damage output, which is reductive and doesn't really capture the experience.
To the OP, Have you actually played one? (full disclosure, I have not) Because there's people who say they have, and say it was good, if boring. They have actual in-game experience. I'm going to rate that over theory (not to mention reducing a subclass to its damage output and seemingly nothing else) any day.
You're going to rate anecdotal impressions over mathematical proof? Okay.
Yeah, because those anecdotal impressions consider what it was like to play an actual character over, presumably, a number of session including combat and non-combat challenges. The other way is looking only at damage output, which is reductive and doesn't really capture the experience.
And how is this, in any way, refuting my OP? The very first sentence: "First, the caveat, "Bad" is referring specifically to mechanical effectiveness."
I was intentionally as clear as I could possibly be to articulate that I'm exclusively referring to mechanical combat effectiveness.
It's neither. Everyone get's 5% chance to crit. Improved critical does gives you an additional 5% chance to crit. This mean the extra crit damage is only applied 5% of the time, making it whatever that damage is x .05.
Posting links to people in other threads who are wrong isn't an argument. They aren't here to defend their position. If you think my math is wrong, show me the math you think is right.
If we assume 2 3-round combats per short rest, a level 3 fighter can be expected to make 7 (counting Action Surge) Attack actions per short rest, and some unknown number of Opportunity Attacks -- call it 2. Thus, he's making 9 attacks per short rest. A two weapon fighter will be making 15
The Champion does get a second fighting style, which is nice, though not as relevant as it used to be since you can get one with a feat. Remarkable Athlete has the interesting quirk that it adds to Initiative (which is a Dexterity check) but isn't otherwise that exciting. Survivor isn't super relevant in combat, healing 5-10 per turn at level 18 barely affects anything, but does mean you can heal up to half health after any battle for free.
Overall, Champion is just pretty bad.
It's an ~11% relative increase if your hit rate starts at 45% (which is quite low) and there's no numerical bonuses in the damage roll. But weapon attacks do have numerical bonuses in the damage roll and focusing purely on the relative change doesn't tell you anything super useful. If you manage to get your attacks to only hit on 20s you can rightfully say expanding your crit rate to 19 doubles your damage, but if you're still doing way less damage than if you could hit on a 5 or more.
If you change the numbers to, say, 2d6 + 3 with a 70% hit chance you're back down to a 5% relative increase because you're not doubling that +3 and you're not starting at such an abysmally low hit rate. With a smaller damage die and bigger bonus (say, TWF or Dueling styles) you'd go below 5%.
The Forum Infestation (TM)
Its not the strongest fighter subclass, and is probably competes with EK for weakest. But its still a fighter, one of the strongest, most versatile, and customizable martial classes in the game. And its abilities aren't bad.
I think the real downside of the Champion is that it is kind of mechanically boring compared to other fighters. There aren't really many buttons to push as far as abilities. The one thing you do get that is truly unique is chasing the high of crits a bit more, but there aren't even many ways to toy with that without multiclassing out of fighter.
It’s bad and boring. The “entry” subclass for a Fighter should be the Samurai, who is mechanically simple, but it’s quite effective. Champion shouldn’t exist at all.
I'd probably change Born to the Saddle in Cavalier to something more generic and then make that the default. While "I want to hit people really hard" is a legitimate reason to want to play a fighter, "I want to protect the party" is also a pretty big one.
I played a little bit of D&D a few years ago and then stopped. I started again this year. My character was a V. Human Barbarian, optimized to deal as much dmg as possible. I took GWM as the feat from V. Human. I died at lvl 2 without hitting my enemy even once because I kept using my GWM feat, even though I also used the reckless attack on every turn.
Tbf though, we were kinda stupid to fight a young green dragon as 3 lvl 2 characters, but still. With an avg of negative modifier in int, there wasn't much to do about it.
Varielky
lol Yeah, but that one is on your DM. That's just... ridiculous. Especially if he knew you guys were new.
Well, yeah. But I don't agree with your conclusion.
You chose a greatsword. Obviously because it rolls 2d6 which is nice damage. But your non-champion fighter is going to roll that thing once when a two weapon fighting champion is going to roll his piddly 1d6 shortsword twice. So here are some examples, with a caveat; I don't have the time or the patience to go through every fighter sub-class to find what would be an equivalent ability or feat to what I chose for the Champion for each of these examples:
Now, I can tell you're all salivating (and probably stopped reading to reply) that 8d6 + (4*mod) ie: [28 + 20 = 48] is better than 5d6 + (5*mod) [17.5 + 25 = 42.5]. However, the % chance to hit above is calculated assuming there is ONE crit in a turn. That's comparing apples to oranges. If you want a proper apples to apples comparison, then you have to use a baseline 1 crit for the non-Champion and figure out how many equivalent crits per turn it would take for the Champion to have close to the same % chance. And this is where my math skills reach their limit. So I resorted to a little program I found online and:
The chances of rolling 18 or higher 4 times when rolling 15d20 is 17.73%. (3x is 39.6%. 5x is 6.2%). However, that doesn't factor in the fact that 3 of those rolls are per attack. Rolling 3 20's on the first attack and 1 20 on the 2nd attack doesn't give me more than 2 crits. However, if they happen to be spread out, it is possible to have 4 separate crits.
So, with an apples to apples comparison:
IN THE LONG RUN, a TWF DEX Champion should be neck to neck with a non-Champion (that doesn't use any of their unique features or feats that would be exclusive to a non-TWF fighter) assuming worse case scenario of their 18-20's all happening on 2 of their 5 attacks. At the other extreme, assuming 4 of their 5 attacks are crits, they surpass the damage output.
A lot of the other sub-classes have resources they have to manage. Their potential is limited by this output, and that effect can vary greatly depending on what kind of game a DM runs. If those resources are easily replenished (lots of short or long rests), then the Champion probably lags behind. On the flip side, the Champion can do his thing all day, no resources to manage. Campaigns that are stingy on short/long rests are going to favor the Champion.
But as many have said, this is likely to be a very boring class to play. Get in melee range, attack. Rinse and repeat. No more depth than that.
Kerrec, you're overcomplicating this. What it all boils down to you is the more attacks you make, the more you will crit. That's for everyone. More attacks means more damage, again, that's for everyone.
All you have to do is calculate the average added damage per attack to gauge how effective an ability is (damage wise), setting aside abilities that give you additional attacks (you have to calculate those as well). Given the choice between:
1. Improved Critial (the level 3 Champion ability that many people rave about), and
2. Dueling Fighting Style (a level 1 ability for basic Fighters)
It doesn't matter how many swings you make. The Dueling Fighting Style (considered a modest ability by nearly everyone) destroys Improved Critical. With that said, if your point is the Duel-Weapon Fighting Style is superior (damage-wise) to the Dueling Fighting Style, I haven't crunched the numbers but at face value I find that very believable. In fact, I don't need to. If you're doing 50% more attacks then you're going to do 50% more damage (not factoring in using a less powerful weapon in your offhand, or a single attack from a bigger weapon).
Well, we were supposed to be 4 ppl and we were also supposed to clear a lot of minions around and get to lvl 3 first, but we (unknowingly) walked straight to the dragon. Also one of us gave up the element of surprise to try to speak to the dragon, hoping it would let him ride it (shrug). Actually, there were more problems that occurred before (like my team attacking me all the time because I managed to get a wolf (who died 2 sessions earlier) to be my sidekick), but we've learned our lesson.
Varielky
That's ridiculous even at level 3. A young green dragon is a challenge rating 8!
To the OP, Have you actually played one? (full disclosure, I have not) Because there's people who say they have, and say it was good, if boring. They have actual in-game experience. I'm going to rate that over theory (not to mention reducing a subclass to its damage output and seemingly nothing else) any day.
That’s conceivably doable. A fresh party of 3 2nd level characters can conceivably kill CR 8 creature.
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Stop comparing numbers. If all of the classes and archetypes always outputted the same damage, then there'd be no point in choosing one. The chassis of the Fighter is fine. None of them get that much more from their archetypes.
Improved Critical. It's fine. It won't come up that often, but it comes up often enough. It gets better with weapons and features that increase the number of damage dice, like a flame tongue and the half-orc's Savage Attacks. And for a class that gets more attacks than anyone else, the odds of it happening are greater than with any other. It's also "always-on", unlike some other archetypes for other classes.
Remarkable Athlete. This is a skill and support-oriented feature; which is common for martial archetypes. It means your Fighter doesn't need proficiency with Acrobatics or Athletics as badly, freeing up their first-level skill choices. It also adds +2 to their Initiative; reaching +3 at 13th-level. Few classes or archetypes get any such bonus, so it's a welcome one.
Additional Fighting Style. No one else gets a second choice of one, and you can't go wrong with any of them. It's not flashy, but it's not supposed to be. Still, looking at just the PHB, some standout combinations include...
Superior Critical. The level 3 ability, but better. And they're making 3-4 attacks per round without turning to Action Surge. And at three attacks per turn, unless my math is wrong, that's a 39% chance that one of those hits will be a critical hit. Even just a single attack with advantage has a 27.75% chance of being a critical hit. Of course, the attack still has to hit. Any attack can still miss against a target with a sufficiently high AC. Only a Natural 20 is guaranteed to hit. And a vorpal sword will only decapitate on a Nat 20, as well.
Survivor. A free 9-10 hit points worth of healing per round, that technically stacks with temporary hit points, and they still have their Second Wind? Yes, please.
You're going to rate anecdotal impressions over mathematical proof? Okay.
TWF is a losing choice for any high level fighter, Champion or not. Four greatsword swings beat 5 short sword swings, and while the greatsword has 20% fewer opportunities to crit, it's doing ~40% more damage per crit.
In practice the Champion's potential is also limited by the fact that no party can go on fighting forever, and the fact that they're starting at a deficit compared to subclasses that can spend their resources at will on extra damage.
Putting it simply, if we're comparing a Champion and a Battle Master and there's very little fighting, the Battle Master wins by default because they're guaranteed at least 4d8 extra damage no matter what. For every 19 you assume the Champion scores, the Battle Master is equally likely to have scored a 20 in which they could've chosen to use a maneuver for an extra 2d8 until they're out of dice. So the Champion has to accumulate enough extra crits to exceed 8d8 extra damage before the party takes a rest, at which point the Battle Master has all of their dice back.
With a greatsword dealing an extra 2d6 per crit, that's 2.57 extra crits, which is about 51d20 rolls. That's a lot of d20s to roll in probably only 3 or 4 fights at best before the party likely has to rest unless the DM absolutely forces them not to. And remember that target is going to get bigger as the Battle Master gets more and larger dice. By 7th level they need extra 3.21 crits or ~64d20 rolls. By 10th level they need 3.92 extra crits or ~79d20. And this is ignoring any side benefits of the maneuvers like the potential to give other melee characters advantage too, or synergies like Commander's Strike giving rogues another Sneak Attack.
The Forum Infestation (TM)
A fighter is a perfectly solid class, and being a champion doesn't make you not a fighter. It's just that Champion is adding very little to the base class. At level 3, it's adding 0.225 dpr to a dueling fighter, 0.35 dpr to a 2WF fighter, 0.416 to a GWF fighter. By comparison, Battle Master is adding 18 damage (21 damage with GWF) so BM is better over fewer than 80 rounds combat for dueling, 52 for 2WF, 51 for 2WF. I've certainly never had that many rounds of combat per short rest. And that's ignoring the fact that battle master dice can crit.
It's plausible to think that the issue is battle master overperforming rather than champion underperforming, but in the end, every fighter subclass except champion meaningfully changes how you play. Champion just makes you very slightly better at what a fighter does anyway.
Yeah, because those anecdotal impressions consider what it was like to play an actual character over, presumably, a number of session including combat and non-combat challenges. The other way is looking only at damage output, which is reductive and doesn't really capture the experience.
And how is this, in any way, refuting my OP? The very first sentence: "First, the caveat, "Bad" is referring specifically to mechanical effectiveness."
I was intentionally as clear as I could possibly be to articulate that I'm exclusively referring to mechanical combat effectiveness.