Level 3 Improved Critical: You get to crit on a 19 or 20. Let's look at the math with a Greatsword. Everyone already crits on a 20. You also crit on a 19. That is a 1/20 chance per roll that the ability will add to your damage (or 5% of the time) for an extra 2d6. 2d6 average roll = 7 damage.
Greatsword: 7 x 0.05 = 0.35 average extra damage per attack. Glaive = 0.275 extra damage. Longsword: 0.225
Here's another attempt to explain. Your example above assumes you roll 1 To-Hit die, which gives the champion an extra 5% chance on top of the base 5% any other class also gets for rolling a 20 (a crit).
The reason why this is wrong is because the % chance starts to diverge for the Champion when MORE To-Hit dice are rolled. If a non-Champion and a Champion both have advantage from some external source (ex: target is lit by faerie fire), then:
That 5% for the non-Champion becomes 9.75% with advantage. For a 2d6 weapon average damage: 7 x 0.0975 = 0.68 extra damage per attack.
that 10% for the Champion becomes 19% with advantage. For a 2d6 weapon average damage: 7 x 0.19 = 1.33 extra damage per attack.
That difference only grows when you build for crit fishing. By ALOT.
I was showing the increase in damage under specific parameter (Normal attack with a normal Greatsword). Same parameters with advantage: The Champion's chance to crit is increased by 9.25%. So with advantage, Improved Critical is giving you an extra 0.6825 damage per attack.
I've shown lots of numbers with lots of combinations of scenarios, but I can't possibly show them all in one post. In total, it's not terribly impressive. Yes, there are game mechanics that will make it better, but ALOS game mechanics that will make it worse (adding non-dice damage to attacks from things like GWM, ASI bonuses, and +1/2/3 weapons - and other factors can lower the percentage of your overall damage coming from Improved Critical.
Forgive me for not scrolling through nine pages of back & forths, but my understanding of the Champion subclass is that it is a mechanically simple subclass designed to be an introductory option for newer players. It isn't meant to be an amazing damage dealer. I do agree that calculations show the Champion is out-damaged by most other optimized builds.
The Champion specializes in being mechanically simple and (reasonably) effective. As said, it's meant to be a simple option for people to quickly pick up and have fun with. I see many people talking about taking feats and other build options to improve their damage for crit fishing, which is absolutely fair if you're going for straight optimization, but to me, the Champion is specifically catered to newer players, who likely have no knowledge / concept of optimizing builds. The Champion has little decision points at all compared to other subclasses / builds, and mechanically speaking, the Champion will perform well (not as well as well-built options, mind you) no matter what you do with it. A Champion will nearly always function, while a poorly-built Battlemaster might not be able to do so, not to mention the difficulty of choosing Battlemaster maneuvers for first-time new players.
TLDR, I believe Champions will often times serve newer players better than building around other options would. However, anything with a decent amount of thought / synergy behind it will outperform the Champion. Just my two cents.
NORMAL AVERAGE DAMAGE PER SWING FOR BOTH CHAMPION AND NON-CHAMPTION: (7 + 4) x 0.6 = 6.6 Damage
Non-Champion adds 0.35 for chance to crit: 6.6 + 0.35 = 6.95
Champion adds 0.70 for chance to crit: 6.6 = 0.7 = 7.3
With GWM the Non-Champion has a 2.5% chance to obtain another attack (per attack) (5% divided by 2 attacks per turn, because only one bonus attack): 6.95 + (6.95 x .025) = 7.12375
With GWM the Champion has a 5% chance to obtain another attack (per attack) (5% divided by 2 attacks per turn, because only one bonus attack): 7.3 + (7.3 x .05) = 7.665
7.665/7.12375 = 1.076
The Champion is doing 7.6% more damage if using GWM. This amounts to increasing damage form 20 to 21.52 on a hit.
I was showing the increase in damage under specific parameter (Normal attack with a normal Greatsword). Same parameters with advantage: The Champion's chance to crit is increased by 9.25%. So with advantage, Improved Critical is giving you an extra 0.6825 damage per attack.
I've shown lots of numbers with lots of combinations of scenarios, but I can't possibly show them all in one post. In total, it's not terribly impressive. Yes, there are game mechanics that will make it better, but ALOS game mechanics that will make it worse (adding non-dice damage to attacks from things like GWM, ASI bonuses, and +1/2/3 weapons - and other factors can lower the percentage of your overall damage coming from Improved Critical.
OK, your 'specific parameter' completely ignores the fact that the increased To-Hit potential from Improved Critical causes a HUGE increase in % chance to crit in a round when you roll more To-Hit dice per attack. Hence, your math is custom picked, or oversimplified in favor of non-Champion classes to try to prove the point you want to make. That is no basis to make any conclusions about a sub-class.
I was showing the increase in damage under specific parameter (Normal attack with a normal Greatsword). Same parameters with advantage: The Champion's chance to crit is increased by 9.25%. So with advantage, Improved Critical is giving you an extra 0.6825 damage per attack.
I've shown lots of numbers with lots of combinations of scenarios, but I can't possibly show them all in one post. In total, it's not terribly impressive. Yes, there are game mechanics that will make it better, but ALOS game mechanics that will make it worse (adding non-dice damage to attacks from things like GWM, ASI bonuses, and +1/2/3 weapons - and other factors can lower the percentage of your overall damage coming from Improved Critical.
OK, your 'specific parameter' completely ignores the fact that the increased To-Hit potential from Improved Critical causes a HUGE increase in % chance to crit in a round when you roll more To-Hit dice per attack. Hence, your math is custom picked, or oversimplified in favor of non-Champion classes to try to prove the point you want to make. That is no basis to make any conclusions about a sub-class.
That would ONLY apply in cases that require a natural 20 to hit. That is so rare it's negligible.
I was showing the increase in damage under specific parameter (Normal attack with a normal Greatsword). Same parameters with advantage: The Champion's chance to crit is increased by 9.25%. So with advantage, Improved Critical is giving you an extra 0.6825 damage per attack.
I've shown lots of numbers with lots of combinations of scenarios, but I can't possibly show them all in one post. In total, it's not terribly impressive. Yes, there are game mechanics that will make it better, but ALOS game mechanics that will make it worse (adding non-dice damage to attacks from things like GWM, ASI bonuses, and +1/2/3 weapons - and other factors can lower the percentage of your overall damage coming from Improved Critical.
OK, your 'specific parameter' completely ignores the fact that the increased To-Hit potential from Improved Critical causes a HUGE increase in % chance to crit in a round when you roll more To-Hit dice per attack. Hence, your math is custom picked, or oversimplified in favor of non-Champion classes to try to prove the point you want to make. That is no basis to make any conclusions about a sub-class.
There is no increased to-hit potential. Any fighter who needs to beat an AC above 19 will beat it on a roll of 19.
The only enemies with higher ac's come in at higher levels when the figher's to hit bonus is already high enough to hit on a 19, like with the Terrasque's 25AC at CR 30.
It would take some theory craft home brew from the DM with ridiculous ac to make there be any increase in hit chance via improved critical.
That would ONLY apply in cases that require a natural 20 to hit. That is so rare it's negligible.
If you believe that, then you completely misunderstand the math.
The equation for % chance for ONE critical is:
% chance = 1 - (B/A)^C
Where:
A = Total posibilities for a die roll, ie: 20 on a d20
B = Total # of possibilities to not crit on a die roll, ie 19 ways to not crit for a crit on a 20. Or 18 ways to not crit for an Improved Critical Champion.
C = Times you make the attempt.
You are completely ignoring variable C.
Your math is cherry picking variables in such a way as to make the huge advantage of Improved Critical a non-starter.
If you believe that, then you completely misunderstand the math.
The equation for % chance for ONE critical is:
% chance = 1 - (B/A)^C
Where:
A = Total posibilities for a die roll, ie: 20 on a d20
B = Total # of possibilities to not crit on a die roll, ie 19 ways to not crit for a crit on a 20. Or 18 ways to not crit for an Improved Critical Champion.
C = Times you make the attempt.
You are completely ignoring variable C.
Your math is cherry picking in such a way as to make the huge advantage of Improved Critical a non-starter.
I understand the math perfectly. I might not understand the point you are making. The math on your chance to crit is quite simple. On a normal roll you have a 5% chance to crit, and a 9.75% chance to crit with advantage. With Improved Critical, you have a 10% chance to crit, and 19% chance to crit with advantage.
There is no increased to-hit potential. Any fighter who needs to beat an AC above 19 will beat it on a roll of 19.
The only enemies with higher ac's come in at higher levels when the figher's to hit bonus is already high enough to hit on a 19, like with the Terrasque's 25AC at CR 30.
It would take some theory craft home brew from the DM with ridiculous ac to make there be any increase in hit chance via improved critical.
There is no increased to-hit potential. Any fighter who needs to beat an AC above 19 will beat it on a roll of 19.
The only enemies with higher ac's come in at higher levels when the figher's to hit bonus is already high enough to hit on a 19, like with the Terrasque's 25AC at CR 30.
It would take some theory craft home brew from the DM with ridiculous ac to make there be any increase in hit chance via improved critical.
Not at all what I'm talking about.
Then you are using "to-hit potential" where you actually mean something like "crit-potential"
If you believe that, then you completely misunderstand the math.
The equation for % chance for ONE critical is:
% chance = 1 - (B/A)^C
Where:
A = Total posibilities for a die roll, ie: 20 on a d20
B = Total # of possibilities to not crit on a die roll, ie 19 ways to not crit for a crit on a 20. Or 18 ways to not crit for an Improved Critical Champion.
C = Times you make the attempt.
You are completely ignoring variable C.
Your math is cherry picking in such a way as to make the huge advantage of Improved Critical a non-starter.
I understand the math perfectly. I might not understand the point you are making. The math on your chance to crit is quite simple. On a normal roll you have a 5% chance to crit, and a 9.75% chance to crit with advantage. With Improved Critical, you have a 10% chance to crit, and 19% chance to crit with advantage.
What point are you making here?
When you calculate your average damage, you just say the Champion gets an extra 5% to average damage. Or as you write it, p = 0.05.
But to be fair to the Champion sub-class, you would also have to show calculations where both have advantage. So adding the average of an extra 5% is wrong when calculating average damage output for situations with advantage. It should be 19% - 9.75%? At the very least this would show how a Champion performs played by a player that isn't min-maxing and doesn't know enough about feats and such to take advantage of the class that much.
But to show where the Champion would shine, you'd have to add feats make it stand out from just a plain Champion. That delta would grow significantly. For example, a TWF DEX fighter with Elven Accuracy using a bonus action to attack with the offhand attacks 5 times at level 20 with Superior Critical. Ignoring situations with advantage, that Champion would have an 80% chance to crit ONCE during his turn. A non-champion attacks 4 times with only a 20 to crit, gets a 18.55% chance to crit ONCE on his turn. That's a delta of 61.45%!!! Where is that factored into your math? Or another way to look at it: A Champion would crit 3-4 times each time a non-champion crits.
You'd also have to show how teamwork helps. Haste with improved/superior critical just increases that delta even more. And with the introduction of Tasha's, some feats produce benefits on crits which benefits everyone, not just the Champion. So crit-fishing becomes more than a selfish self indulgence.
My point: Your math is unfair because of your limited parameters.
When you calculate your average damage, you just say the Champion gets an extra 5% to average damage. Or as you write it, p = 0.05.
No. You don't. A 5% better chance to crit does NOT de facto mean 5% more damage. It depends on the crit damage in relationship to the base damage. To give an extreme example to illustrate the point: Imagine you have a dagger that grants +100 damage, and you have a 16 Dex.
Total damage on a regular hit would be 1d4 + 4 + 100 for an average of 106.5 damage.
If you crit, you're going to add 1d4 to the damage total, to make: 109 average damage.
If your normal average damage to per hit is 106.5, and you're doing an extra 2.5 damage on a critical, being able to crit and extra 5% of the time is not adding 5% to your damage per attack.
But to be fair to the Champion sub-class, you would also have to show calculations where both have advantage. So adding the average of an extra 5% is wrong when calculating average damage output for situations with advantage. It should be 19% - 9.75%? At the very least this would show how a Champion performs played by a player that isn't min-maxing and doesn't know enough about feats and such to take advantage of the class that much.
You mean you would need to show the numbers for parameters that include advantage, as well as not having advantage? Cool. I've done that. And I've also included numbers with feats.
Feats can definitely improve the numbers with Improved Critical, but they still don't amount to great numbers. And a subclass ability should not have rely on very specific builds to be effective.
When you calculate your average damage, you just say the Champion gets an extra 5% to average damage. Or as you write it, p = 0.05.
No. You don't. A 5% better chance to crit does NOT de facto mean 5% more damage. It depends on the crit damage in relationship to the base damage. To give an extreme example to illustrate the point: Imagine you have a dagger that grants +100 damage, and you have a 16 Dex.
Total damage on a regular hit would be 1d4 + 4 + 100 for an average of 106.5 damage.
If you crit, you're going to add 1d4 to the damage total, to make: 109 average damage.
If your normal average damage to per hit is 106.5, and you're doing an extra 2.5 damage on a critical, being able to crit and extra 5% of the time is not adding 5% to your damage per attack.
I don't see the point of adding MOD damage (or whatever other non dice bonus) damage to your math, UNLESS one class is attacking more often in a round.
I am just talking about rolled damage for the weapon. Don't care about MOD because in an apples to apples comparison, they should be the same.
Battlemaster will be using precision attack with GWM instead of adding the damage die.
This will increase chance to hit across all ACs and generally pull them ahead of champion in most calculations. Champ does more if you have a LOT of encounters in a day which may be a thing for some groups.
Also its value comes from stuff like Half-Orcs and MC with barbarian IMO vs battlemaster is the superior single class build.
When you calculate your average damage, you just say the Champion gets an extra 5% to average damage. Or as you write it, p = 0.05.
No. You don't. A 5% better chance to crit does NOT de facto mean 5% more damage. It depends on the crit damage in relationship to the base damage. To give an extreme example to illustrate the point: Imagine you have a dagger that grants +100 damage, and you have a 16 Dex.
Total damage on a regular hit would be 1d4 + 4 + 100 for an average of 106.5 damage.
If you crit, you're going to add 1d4 to the damage total, to make: 109 average damage.
If your normal average damage to per hit is 106.5, and you're doing an extra 2.5 damage on a critical, being able to crit and extra 5% of the time is not adding 5% to your damage per attack.
I don't see the point of adding MOD damage (or whatever other non dice bonus) damage to your math, UNLESS one class is attacking more often in a round.
I am just talking about rolled damage for the weapon. Don't care about MOD because in an apples to apples comparison, they should be the same.
How can you possibly think you can calculate the percent increase in damage per attack, without factoring in mod damage?
But to be fair to the Champion sub-class, you would also have to show calculations where both have advantage. So adding the average of an extra 5% is wrong when calculating average damage output for situations with advantage. It should be 19% - 9.75%? At the very least this would show how a Champion performs played by a player that isn't min-maxing and doesn't know enough about feats and such to take advantage of the class that much.
You mean you would need to show the numbers for parameters that include advantage, as well as not having advantage? Cool. I've done that. And I've also included numbers with feats.
Feats can definitely improve the numbers with Improved Critical, but they still don't amount to great numbers. And a subclass ability should not have rely on very specific builds to be effective.
I'm sorry if you did and I missed it. I want to see those posts of yours, but there are so many pages and I wasn't able to keep up with the thread over the weekend. I just skimmed this morning. Please link the post so I can see this math of yours.
TWF Champion (4 attacks + bonus action offhand), with 18-20 Crit threat range, all 1d6 weapons, with Elven Accuracy:
VS a 2d6 weapon with 4 attacks, with a 20 crit threat range:
Seems pretty telling to me.
EDIT: Note, I don't know where on that sheet to add mod damage to the bonus off hand attack that you get for picking the 2 weapon fighting style. So I think the Champion damage should increase slightly.
I was showing the increase in damage under specific parameter (Normal attack with a normal Greatsword). Same parameters with advantage: The Champion's chance to crit is increased by 9.25%. So with advantage, Improved Critical is giving you an extra 0.6825 damage per attack.
I've shown lots of numbers with lots of combinations of scenarios, but I can't possibly show them all in one post. In total, it's not terribly impressive. Yes, there are game mechanics that will make it better, but ALOS game mechanics that will make it worse (adding non-dice damage to attacks from things like GWM, ASI bonuses, and +1/2/3 weapons - and other factors can lower the percentage of your overall damage coming from Improved Critical.
Forgive me for not scrolling through nine pages of back & forths, but my understanding of the Champion subclass is that it is a mechanically simple subclass designed to be an introductory option for newer players. It isn't meant to be an amazing damage dealer. I do agree that calculations show the Champion is out-damaged by most other optimized builds.
The Champion specializes in being mechanically simple and (reasonably) effective. As said, it's meant to be a simple option for people to quickly pick up and have fun with. I see many people talking about taking feats and other build options to improve their damage for crit fishing, which is absolutely fair if you're going for straight optimization, but to me, the Champion is specifically catered to newer players, who likely have no knowledge / concept of optimizing builds. The Champion has little decision points at all compared to other subclasses / builds, and mechanically speaking, the Champion will perform well (not as well as well-built options, mind you) no matter what you do with it. A Champion will nearly always function, while a poorly-built Battlemaster might not be able to do so, not to mention the difficulty of choosing Battlemaster maneuvers for first-time new players.
TLDR, I believe Champions will often times serve newer players better than building around other options would. However, anything with a decent amount of thought / synergy behind it will outperform the Champion. Just my two cents.
Brewsky, I'm not using your spreadsheet because I prefer to check the numbers myself to make sure they're right.
Agree or disagree?
OK, your 'specific parameter' completely ignores the fact that the increased To-Hit potential from Improved Critical causes a HUGE increase in % chance to crit in a round when you roll more To-Hit dice per attack. Hence, your math is custom picked, or oversimplified in favor of non-Champion classes to try to prove the point you want to make. That is no basis to make any conclusions about a sub-class.
That would ONLY apply in cases that require a natural 20 to hit. That is so rare it's negligible.
There is no increased to-hit potential. Any fighter who needs to beat an AC above 19 will beat it on a roll of 19.
The only enemies with higher ac's come in at higher levels when the figher's to hit bonus is already high enough to hit on a 19, like with the Terrasque's 25AC at CR 30.
It would take some theory craft home brew from the DM with ridiculous ac to make there be any increase in hit chance via improved critical.
If you believe that, then you completely misunderstand the math.
The equation for % chance for ONE critical is:
% chance = 1 - (B/A)^C
Where:
You are completely ignoring variable C.
Your math is cherry picking variables in such a way as to make the huge advantage of Improved Critical a non-starter.
I understand the math perfectly. I might not understand the point you are making. The math on your chance to crit is quite simple. On a normal roll you have a 5% chance to crit, and a 9.75% chance to crit with advantage. With Improved Critical, you have a 10% chance to crit, and 19% chance to crit with advantage.
What point are you making here?
Not at all what I'm talking about.
Then you are using "to-hit potential" where you actually mean something like "crit-potential"
Exactly, I'm interpreting what he said the same way you are.
When you calculate your average damage, you just say the Champion gets an extra 5% to average damage. Or as you write it, p = 0.05.
But to be fair to the Champion sub-class, you would also have to show calculations where both have advantage. So adding the average of an extra 5% is wrong when calculating average damage output for situations with advantage. It should be 19% - 9.75%? At the very least this would show how a Champion performs played by a player that isn't min-maxing and doesn't know enough about feats and such to take advantage of the class that much.
But to show where the Champion would shine, you'd have to add feats make it stand out from just a plain Champion. That delta would grow significantly. For example, a TWF DEX fighter with Elven Accuracy using a bonus action to attack with the offhand attacks 5 times at level 20 with Superior Critical. Ignoring situations with advantage, that Champion would have an 80% chance to crit ONCE during his turn. A non-champion attacks 4 times with only a 20 to crit, gets a 18.55% chance to crit ONCE on his turn. That's a delta of 61.45%!!! Where is that factored into your math? Or another way to look at it: A Champion would crit 3-4 times each time a non-champion crits.
You'd also have to show how teamwork helps. Haste with improved/superior critical just increases that delta even more. And with the introduction of Tasha's, some feats produce benefits on crits which benefits everyone, not just the Champion. So crit-fishing becomes more than a selfish self indulgence.
My point: Your math is unfair because of your limited parameters.
No. You don't. A 5% better chance to crit does NOT de facto mean 5% more damage. It depends on the crit damage in relationship to the base damage. To give an extreme example to illustrate the point: Imagine you have a dagger that grants +100 damage, and you have a 16 Dex.
Total damage on a regular hit would be 1d4 + 4 + 100 for an average of 106.5 damage.
If you crit, you're going to add 1d4 to the damage total, to make: 109 average damage.
If your normal average damage to per hit is 106.5, and you're doing an extra 2.5 damage on a critical, being able to crit and extra 5% of the time is not adding 5% to your damage per attack.
You mean you would need to show the numbers for parameters that include advantage, as well as not having advantage? Cool. I've done that. And I've also included numbers with feats.
Feats can definitely improve the numbers with Improved Critical, but they still don't amount to great numbers. And a subclass ability should not have rely on very specific builds to be effective.
I don't see the point of adding MOD damage (or whatever other non dice bonus) damage to your math, UNLESS one class is attacking more often in a round.
I am just talking about rolled damage for the weapon. Don't care about MOD because in an apples to apples comparison, they should be the same.
Battlemaster will be using precision attack with GWM instead of adding the damage die.
This will increase chance to hit across all ACs and generally pull them ahead of champion in most calculations. Champ does more if you have a LOT of encounters in a day which may be a thing for some groups.
Also its value comes from stuff like Half-Orcs and MC with barbarian IMO vs battlemaster is the superior single class build.
How can you possibly think you can calculate the percent increase in damage per attack, without factoring in mod damage?
I'm sorry if you did and I missed it. I want to see those posts of yours, but there are so many pages and I wasn't able to keep up with the thread over the weekend. I just skimmed this morning. Please link the post so I can see this math of yours.
Here is the calculator I use for DPR:
https://docs.google.com/spreadsheets/d/14WlZE_UKwn3Vhv4i8ewVOc-f2-A7tMW_VRum_p3YNHQ/edit#gid=151780215
It allows you to add things like BA attacks from Crossbow expert and precision die.
Using the calculator linked HERE:
TWF Champion (4 attacks + bonus action offhand), with 18-20 Crit threat range, all 1d6 weapons, with Elven Accuracy:
VS a 2d6 weapon with 4 attacks, with a 20 crit threat range:
Seems pretty telling to me.
EDIT: Note, I don't know where on that sheet to add mod damage to the bonus off hand attack that you get for picking the 2 weapon fighting style. So I think the Champion damage should increase slightly.