Overestimated/Underestimated Spells

[Frogreaver]

The fact that they can be freely converted to one another doesn't mean that they are used the same way though.

That’s what being able to be converted means...

[arnin77]

On the first, One cannot add unlike quantities together. That is basic math. One cannot simply add the numbers and ignore the ‘units’ for lack of a better word.

On the 2nd, I agree because that ‘of’ there is an indicator of multiplication. You’ll notice none of my examples used that same formation.

So are you saying 60 + 12.5% doesn’t equal 67.5 because they are unlike quantities? Do you think that’s true with 1-1/4 + .5 = 1-3/4?

I’m pretty sure you doing that is what set this whole thing off.

[Valmark]

That’s what being able to be converted means...

No, that depends on the context. Conversion can also mean changing something into something else that is completely different, for example.

[Frogreaver]

No, that depends on the context. Conversion can also mean changing something into something else that is completely different, for example.

Not in math.

[PhantomSoul]

Not in math.

Citation or elaboration?

Being able to convert shows there being a way to convert so maybe you're just playing on how different counts as completely different?

[cookieface]

Not in math.

Pure mathematics doesn't use units. And that is what is being discussed here.

[Segev]

Does anybody in this thread think that, even if we come up with a different nomenclature that is objectively better than any other nomenclature that has ever existed for this purpose, it will spread and become used outside of this thread?

[MaxWilson]

Well, there is value to knowing both numbers. The important part is just using them right and keeping straight what you're using them for and keeping both numbers separate with transparency to which you're using and why (this was my sticking point with Frogreaver's post: he claimed to be using one number but was actually using the other).

If you, again, wish to know how whether you'd be able to win a slugfest with three trolls (or how long you could tank them), you absolutely care about the percentual change. It's about 12,5% (not accounting for crits) of enemy's maximum damage. How much that is depends on the number the enemy hits on *snip* Get this: the same trolls average 3 damage against our 23 AC guy at Disadvantage with Bane. 3. They would go from needing 6,3 turns to kill him to needing 33 turns to kill him. Their damage drops to a fifth.

You're not wrong, it is valuable to know both number, but the final decision still should take the absolute HP savings into account, not just the relative, because resources are involved. Cutting the troll's damage to 1/5 is great if you're considering at-will abilities, like the tradeoff between grapple/proning a troll and beating it to death while it's prone vs. just attacking it normally. But in this case, we're talking about spending a spell slot, so the opportunity cost is other spell slots, e.g. Cure Wounds (which might heal more damage than the Trolls would inflict anyway), or a Command spell in another combat (which might prevent more damage than the trolls would have inflicted).

My math gives me results a little different than yours so I'll quote them: a troll attacking at disadvantage and +7 to hit against AC 23 does 1.89 damage per round, so roughly 3.78 damage if there's no Bane. (Computation method: plug "avg att 23 7d 5d6+12" into https://shiningsword.blob.core.windo...ex.html#battle.) Bane will give us an even split between +3/+4/+5/+6, so plug in

avg att 23 6d 5d6+12: 1.22
avg att 23 5d 5d6+12: 0.71
avg att 23 4d 5d6+12: 0.34
avg att 23 3d 5d6+12: 0.12

and average them all: (1.22+0.71+0.34+0.12)/4 = 0.59 per troll, 1.195 damage for two rolls if they're both affected by Bane. Rather than analyze the probability that they're both affected by Bane, at this point we should stop and ask: is saving 2.5 HP per round worth spending a spell slot on?

This is sort of like the above discussion on Shield. Shield is a great spell for emergencies and Deadly fights like the above-mentioned Chasme vs. wizard fight, but IMO it's usually a trap, in the sense that as long as you're going to win the combat anyway, it is often better NOT to shield, and to save those spell points/slots for later, e.g. on Extended Aura of Vitality if you're a paladorc. But IMO it's valid to Shield anyway for roleplaying reasons, even though it's tactically a bad idea, on the basis that getting hit with a giant club or monster tentacle hurts and that cold-bloodedly calculating the optimal value per spell point expended is not something your PC is likely to do when his life is on the line.

Oof..I was a bit harried yesterday and was unclear. The malus to attacks, I view as an additive bonus, and a secondary effect. The whole, point with the Corruptor of Cthulhu example, was not to model how best to use the the Bane spell.

(A) Rather, I wanted to demonstrate, that if one is caught flat footed at verge of an apocalypse, if the worst action one could take is to cast Bane, one still might be setting up one of their team mates. Yes, it is an extreme example, but the extreme does have a tinsy, bit of a tendency to happen at high level, from time to time.🃏

Now as a DM, I will admit, I do like that the penalty assessed by the Bane spell does apply to Death Saving Throws.☠️

(A) Okay, I agree with that. Bane is not a terrible spell for setting up someone else. It shines brightest in the same situations as Portent: high-stakes rolls, like influencing a Necromancer's one chance to Command Undead on a Mummy Lord. (Example drawn from current PbP game.) Interestingly, I believe that Bane would even stack with Portent, perhaps allowing you make use of a Portent roll which otherwise wouldn't be quite low enough for your purposes.

It's niche though, and I think the oft-cited advantage of targeting Cha rolls is overstated: Cha rolls and Wis rolls typically aren't all that far apart, no more than about +2. E.g. 10% of the time Bane will succeed on a Troll where Command would have failed, but Bane's effect is enough weaker (and requires concentration) that I think Command is still likely to be the better spell. (Or Phantasmal Force, if you want to spend a 2nd level slot to give the troll a phantom opponent like a fire elemental to distract it/drive it away.)

[Frogreaver]

Pure mathematics doesn't use units. And that is what is being discussed here.

I guess it depends on what you mean by ‘pure’.

Does anybody in this thread think that, even if we come up with a different nomenclature that is objectively better than any other nomenclature that has ever existed for this purpose, it will spread and become used outside of this thread?

Nope. But this isn’t just a nomenclature issue.

[PhantomSoul]

Does anybody in this thread think that, even if we come up with a different nomenclature that is objectively better than any other nomenclature that has ever existed for this purpose, it will spread and become used outside of this thread?

I didn't think anything on these forums is really expected to catch on, to be honest! (And that includes things that WotC definitely really really should listen to, of course.)

And really, people who deal with percentages already solved that problem with things like log odds (I'm partly just trying to make my prediction true, obviously).

EDIT:

I guess it depends on what you mean by ‘pure’.

So please elaborate! There's no wiki page for "Conversion (Mathematics)" to go on...

[arnin77]

Probability of hitting without Bless = .6
Probability of hitting due to Bless = .125
Probability of Missing = .275

Do you believe there's anything wrong with saying bless represents a +.125 increase in your chance to hit such that your new chance to hit is .725?

Now that we've established this is appropriate based on the increase example of 110 earlier. Let's convert the .125 to a percentage. It becomes 12.5% and not 12.5 percentage points.

Replacing .125 with it's percentage conversion in the above statement we get:
bless represents a +.125 increase in your chance to hit
bless represents a +12.5% increase in your chance to hit

One cannot simply change the units to percentage points in such a percentage conversion. Hopefully this highlights why it's not wrong to do it the way I did. At least think about it, instead of insisting that your convention is the only correct way.

You do it right here. You say probability of hitting without bless is 60%. Then you say bless adds +12.5%.

If your probably to hit without bless is 60% and bless adds 12.5% then your probability to hit with bless is now 67.5%, not 72.5%. That would be adding 20.8%.

If you mean that you have 60% to hit without bless and bless adds 12.5pp then you’d have 72.5% chance to hit with bless.

[Xetheral]

There's a bunch of misleading stuff being said by posters on both sides of the math debate. To clarify:

• A "percent" is not a unit of measurement. A percentage is a dimensional dimensionless number (specifically, a ratio with respect to 100).
  
• A "percentage point" is a unit of measurement. It is the unit of the arithmetical difference between two percentages.
  
• x% refers to x/100, and that ratio can be evaluated in decimal format. The reverse is not always true. A given decimal can be meaningfully expressed as a percentage only if that decimal is already being used as a ratio.

[Valmark]

Not in math.

You may have to prove that, since in this thread it has been showed the opposite.

Does anybody in this thread think that, even if we come up with a different nomenclature that is objectively better than any other nomenclature that has ever existed for this purpose, it will spread and become used outside of this thread?

Highly doubt it- mentioned so some posts ago. Wanting to come up with different names for the same things is pointless unless you can somehow convince the whole world to use them (or at least the relevant parts of it).

I didn't think anything on these forums is really expected to catch on, to be honest! (And that includes things that WotC definitely really really should listen to, of course.)

And really, people who deal with percentages already solved that problem with things like log odds (I'm partly just trying to make my prediction true, obviously).

EDIT:

So please elaborate! There's no wiki page for "Conversion (Mathematics)" to go on...

I realize I'm not sure what log odds are? I feel like I should have heard of it, but I think my brain is just confusing it because it knows the two words separately.

[5eNeedsDarksun]

3) You need to have a hand free to cast it. Even if you have a Pact Weapon as your focus. So if you're sword+boarding you're sol.

Yes, that's one that caught out a player of mine who tries to play fast and loose with the rules.

[Frogreaver]

You do it right here. You say probability of hitting without bless is 60%. Then you say bless adds +12.5%.

If your probably to hit without bless is 60% and bless adds 12.5% then your probability to hit with bless is now 67.5%, not 72.5%. That would be adding 20.8%.

If you mean that you have 60% to hit without bless and bless adds 12.5pp then you’d have 72.5% chance to hit with bless.

If I say bless adds +12.5% chance to hit - is that 12.5% a reference to the .125 probability that it’s adding or to a relative percentage increase. It’s still ambiguous. And adding in percentage points only makes things objectively worse - because now I can say things about the exact same quantity in percentage points terms that you are saying is incorrect for saying it in percent terms. That’s the problem. If percentage points and percent really are the same thing then you could use them interchangeably. If you cannot then They are not and combing them by addition is not possible.

[Segev]

Nope. But this isn’t just a nomenclature issue.

It is, though. You now know the terms of art. You feel they are bad, and want to make up new ones and try to get everyone in this thread, at least, to agree with you on using them. But for clarity of communication, the easiest and clearest thing to do is simply to adopt the terms of art.

[cookieface]

I guess it depends on what you mean by ‘pure’.

Again, we are discussing percentages and probabilities, not foreign exchange rates or distance conversions. That is a mathematical process, not economic or scientific. There are only "units" insofar as the abstract "percentage points" are units that have a direct conversion into probabilistic numbers.

Your last several posts are giving me the impression that you are no longer interested in learning why the difference between percentage points and percentages is important. Instead you are questioning everyone else's assertions with bad faith quips that take their words out of context.

Seriously, if you want to learn more about why these differences are important, use Google. Here are two immediate sources that help clarify why we need pp:
https://en.wikipedia.org/wiki/Percentage_point
https://www.macroption.com/percentage-point-vs-percent/

It took me all of two minutes to find (and read) those explanations. If you are still in disagreement about their uses, it is important you understand that you will be disagreeing with the entire mathematics community about it. It is not a half-dozen anonymous posters on one message board. You are going against decades (heck, maybe centuries, but so far I have been unable to find the first usage of the term percentage points) of consensus about how best to describe changes in probabilities and percentages.

Like Segev said, if you believe that we could actually change how the language works outside of this thread on this forum, then maybe this would be a useful conversation. As it is unlikely we will be able to do so, I will continue to use pp when it is necessary and I won't be responding any more here.

[MaxWilson]

3) You need to have a hand free to cast it. Even if you have a Pact Weapon as your focus. So if you're sword+boarding you're sol.

That's not that big a deal IMO, since you can't use your reaction for both Shield and opportunity attacks anyway. The requirement for a free hand simply forces you to decide up front whether you're going to end your turn with a weapon in hand (for opportunity attacks and/or Defensive Duelist) or with an empty hand, prepared to Shield.

I agree that it is a restriction and it is nice to get around it via Warcaster, I'm just saying it's not as big of a restriction as it looks on paper, because of reaction economy.

It is, though. You now know the terms of art. You feel they are bad, and want to make up new ones and try to get everyone in this thread, at least, to agree with you on using them. But for clarity of communication, the easiest and clearest thing to do is simply to adopt the terms of art.

I think the easiest thing to do would be to stop talking in abstract terms about %s (relative or absolute) and just talk about absolute numbers, like whether reducing the damage two trolls will inflict on an AC 23 character with a Cloak of Displacement from just under 4 HP per round to just over 1 HP is worth spending an action, your concentration and a 1st level spell slot to achieve. Whether you want to call that a N% reduction or a Y% reduction, making it a concrete example makes it easier to talk about.

[PhantomSoul]

I realize I'm not sure what log odds are? I feel like I should have heard of it, but I think my brain is just confusing it because it knows the two words separately.

Roughly a different way to present percentages that allow you to add or subtract them meaningfully (because log laws make addition equivalent to multiplication and subtraction equivalent to division [in the converted outputs]), so it's what regression uses for instance. Instead of going from 0 to 1 (like decimal representations of percentages) or from 0 to 100 (like... uh... per 100ths-y representations of percentages), you go fom negative infinity to positive infinity in values, but the conversion to the other representations gives an s-shaped curve so that you tend towards the asymptote on each end. If you know of the logistic function, it's just the inverse of that.

I'm a convert (haha) from using them for things like regression (as a tool; I'm neither a mathematician nor a statistitian): https://en.wikipedia.org/wiki/Logit

EDIT: It's probably worth adding that thinking log odds is useful is, uh, not an indication that it's not a joke for this thread. Logit values (without converting them) tend to be a lot less easily interpreted for what people tend to want to know (things like hit rates).

[arnin77]

If I say bless adds +12.5% chance to hit - is that 12.5% a reference to the .125 probability that it’s adding or to a relative percentage increase. It’s still ambiguous. And adding in percentage points only makes things objectively worse - because now I can say things about the exact same quantity in percentage points terms that you are saying is incorrect for saying it in percent terms. That’s the problem. If percentage points and percent really are the same thing then you could use them interchangeably. If you cannot then They are not and combing them by addition is not possible.

It’s not ambiguous - you saying bless adds 12.5% to hit is a reference to a percentage increase. It only adds .125 probability to hit depending on what you need to hit. Unless you don’t know what you mean of course.

[Xetheral]

If I say bless adds +12.5% chance to hit - is that 12.5% a reference to the .125 probability that it’s adding or to a relative percentage increase. It’s still ambiguous. And adding in percentage points only makes things objectively worse - because now I can say things about the exact same quantity in percentage points terms that you are saying is incorrect for saying it in percent terms. That’s the problem. If percentage points and percent really are the same thing then you could use them interchangeably. If you cannot then They are not and combing them by addition is not possible.

Percentage points and percent are not the same thing. A percentage is a dimensionless quantity with no units of measurement.

A percentage point is the unit of measurement for an arithmetic difference of two percentages.

Because a percentage point is a unit of measurement for a difference between two percentages, percentages and percentage points can (actually, must) be combined. So: x% - y% = (x-y) percentage points. Equivalently, y% + (x-y) percentage points = x%.

[arnin77]

Also just wondering if this is still a DnD5e post or has it turned into Math5e

[PhantomSoul]

Also just wondering if this is still a DnD5e post or has it turned into Math5e

Speaking of which, it still surprises me that there's no dedicated PF(1/2) section on this site. (Unless I'm just blind, which wouldn't be surprising. It just seems like a spot to creep despite not playing PF haha)

[Frogreaver]

There's a bunch of misleading stuff being said by posters on both sides of the math debate. To clarify:

• A "percent" is not a unit of measurement. A percentage is a dimensional number (specifically, a ratio with respect to 100).
  
• A "percentage point" is a unit of measurement. It is the unit of the arithmetical difference between two percentages.
  
• x% refers to x/100, and that ratio can be evaluated in decimal format. The reverse is not always true. A given decimal can be meaningfully expressed as a percentage only if that decimal is already being used as a ratio.

On the first, Percent is similar to an expression of of something in hundredths. It’s closer to the metric prefixes in meaning. Say centimeter. So I agree it’s not an actual unit, but similar in many respects and I don’t have a better word to express those similarities. Maybe that word is dimensional number as you referenced but I’ve never heard that term before.

On the second, We don’t need a unit for arithmetic difference though. I think that’s a big part of the issue. If I ask you the difference in 5 and 11 you don’t respond 6 number points. It’s just 6. And just think how confusing an expression like (11-5)+7 would become if we used number points to express those differences - you would evaluate the parenthesis to (6 number points)+7 = ???. Would the final answer be 13, 13 number points, something else?

On the third, I agree.

[PhantomSoul]

On the first, Percent is just an expression of of something in hundredths. It’s closer to the metric prefixes in meaning. Say centimeter. So I agree it’s not an actual unit, but similar in many respects and I don’t have a better word to express those similarities. Maybe that word is dimensional number as you referenced but I’ve never heard that term before.

On the second, We don’t need a unit for arithmetic difference though. I think that’s a big part of the issue. If I ask you the difference in 5 and 11 you don’t respond 6 number points. It’s just 6. And just think how confusing an expression like (11-5)+7 would become if we used number points to express those differences - you would evaluate the parenthesis to (6 number points)+7 = ???. Would the final answer be 13, 13 number points, something else?

On the third, I agree.

Maybe thinking of it like bases (in math) or like denominators (in math) would help? Not that something being confusing is a good argument that it's wrong or unhelpful, of course!

[Frogreaver]

Maybe thinking of it like bases (in math) or like denominators (in math) would help? Not that something being confusing is a good argument that it's wrong or unhelpful, of course!

None of those things have this same issue. X base 10 + Y base 2 can be computed, but whatever we say about the result is going to be true for any base.

That’s not true with percentage points as I’m told. It’s really about the same as being told I must only use base 2 to answer or be incorrect.

[Xetheral]

On the first, Percent is just an expression of of something in hundredths. It’s closer to the metric prefixes in meaning. Say centimeter. So I agree it’s not an actual unit, but similar in many respects and I don’t have a better word to express those similarities. Maybe that word is dimensional number as you referenced but I’ve never heard that term before.

On the second, We don’t need a unit for arithmetic difference though. I think that’s a big part of the issue. If I ask you the difference in 5 and 11 you don’t respond 6 number points. It’s just 6. And just think how confusing an expression like (11-5)+7 would become if we used number points to express those differences - you would evaluate the parenthesis to (6 number points)+7 = ???. Would the final answer be 13, 13 number points, something else?

On the third, I agree.

I misspoke, the word for a value without a unit of measure is "dimensionless", not dimensional. (Corrected in original post.)

We have a unit for the arithmetic difference between two percentages precisely to avoid the type of confusion as seen in this thread. :) Yes, as a unit for a non-physical dimension it's a little on the unusual side, but it's useful, and has been in use since at least 1600 according to Google N-Grams, although it only started seeing widespread use in the 20th century. (It's possible the really old uses were in a different context, misspellings, bad OCR, or misdated texts. Google N-Grams isn't always the best source. But it does show that the convention has been around for at least a century.)

[Frogreaver]

I misspoke, the word for a value without a unit of measure is "dimensionless", not dimensional. (Corrected in original post.)

We have a unit for the arithmetic difference between two percentages precisely to avoid the type of confusion as seen in this thread. :) Yes, as a unit for a non-physical dimension it's a little on the unusual side, but it's useful, and has been in use since at least 1600 according to Google N-Grams, although it only started seeing widespread use in the 20th century. (It's possible the really old uses were in a different context, misspellings, bad OCR, or misdated texts. Google N-Grams isn't always the best source. But it does show that the convention has been around for at least a century.)

Thanks that’s Interesting on the history.

The thing is - there was no confusion at the start of this thread. The poster knew exactly what I meant and decided to inform me i was incorrect due to not aligning with that terminology.

I understand it’s intent is to remove ambiguity and it does to some degree but it mucks with other more important mathematical concepts IMO. I mentioned before - mathematically speaking what is 60% + 12.5 percentage points and the answer without fail was 72.5%. Making 12.5 pp equivalent to 12.5%. But only when we aren’t talking about the increase from 60% to 72.5%. Essentially if that convention is actually examined it breaks virtually every other mathematical rule and convention out there.

[PhantomSoul]

I mentioned before - mathematically speaking what is 60% + 12.5 percentage points and the answer without fail was 72.5%. Making 12.5 pp equivalent to 12.5%. But only when we aren’t talking about the increase from 60% to 72.5%. Essentially if that convention is actually examined it breaks virtually every other mathematical rule and convention out there.

Except it seems fine for all of math (the system of which it's already part)...? The fact that a proportion changes value based on what it's a proportion of it just expected by virtue of it being a proportion. It's not "only when not talking about an increase from 60% to 72.5%", it's "whenever it's out of 100, since that's what a percentage is a proportion of by default". Exactly why that 1/5 is more when it's 1/5 of a bigger pizza compared to a smaller pizza. Or that value of 25 cents changes when the value of the dollar changes. It's not breaking rules and conventions; it's part of them.

[JNAProductions]

Thanks that’s Interesting on the history.

The thing is - there was no confusion at the start of this thread. The poster knew exactly what I meant and decided to inform me i was incorrect due to not aligning with that terminology.

I understand it’s intent is to remove ambiguity and it does to some degree but it mucks with other more important mathematical concepts IMO. I mentioned before - mathematically speaking what is 60% + 12.5 percentage points and the answer without fail was 72.5%. Making 12.5 pp equivalent to 12.5%. But only when we aren’t talking about the increase from 60% to 72.5%. Essentially if that convention is actually examined it breaks virtually every other mathematical rule and convention out there.

What rule does it break?