Percent Change Debunked

[@CyberDoedel]

80% of statistics on the internet are made up, but a new Crunch McDabbes video is 100% awesome to watch. And with all things math, context matters.

[@TheLocalDisasterTourGuide]

Oh no! Is Crunch's camera STILL running! This is bad... we need to send a rescue team!

[@LegendaryCMD]

Ha ha! hey buddy. I have like an hour of out takes I want to use up. I was surprised how hard TV is.

[@griztorc]

Percent change is useful because it relates to one of the most important stats: time to kill. Let's take your warpriest and fighter example. They do 10 damage on a hit, and they're up against a monster with 50 hit points. The fighter is doing 11 damage per swing while the warpriest is doing 6. So, it'll take the Fighter 4.54 turns to kill the monster, and the warpriest will need 8.33. Now, let's give them a +1 bonus: the fighter now needs 4.16 turns, and the warpriest needs 7.14 turns. As you can see, the fighter gained about .4 of a turn in their kill speed, but the warpriest gained a whopping 1.19 of a turn! So while this kind of thing won't show up if you're pooling all the damage together like in your original example, knowing the percent change is still important to consider. All that said, love your content! I link your stuff to my players all the time to help them grok the math.

[@DanAmurskiy]

What you are talking about is precisely the barbarian example. Both get +1 damage, but warpriest has a avg damage of 6 while fighter is 11. It does increase WP damage "more" in relation to the starting point, but it doesn't matter when both are in the group together and you have to choose which one to buff.

[@LegendaryCMD]

@@DanAmurskiy Yeah, I'm glad for this discussion. I'm trying to get my head around this. In some sense changing things into time to kill, it is pretty much the same thing as adding a bonus, or adding a percent of average damage, it's just another metric and the results will be the same. But...that comment has me thinking that there is something to this. The +1 bonus is more meaningful to the cleric because he has a lower starting attack bonus...so, yeah, that makes sense. But then, as you said, if they are in the same party they are going to be sharing that time to kill and it won't matter which character was buffed. Thanks you guys, still pondering this.

[@griztorc]

​@@LegendaryCMD One intuitive place where it makes sense is if instead of comparing a warpriest to the fighter, you're comparing a low AC monster to one with a high AC. In the case of a high AC, that +1 is going to be much more valuable because of the percent increase. With a low AC, you'll have better things to do with your action.

[@DanAmurskiy]

@@LegendaryCMD At the end of the day the actionable conclusion is that accuracy bonuses (Guidance, Heroism, Potency Runes) are more valuable for the highest hitting member of the party, while damage bonuses (Enlarge, Striking, Elemental runes) are more valuable to higher accuracy people. This information will actually buff the parties TTK, which is the main thing that matters. Pondering who gets the most personal benefit in relation to their starting value is ... of questionable use. This way you will get results that Enlarge gives the biggest increase to the parties Wizard, because his base is just d4 fist.

[@robinbernardinis]

Exactly. Though I think that the better way to conceptualize this is to consider the percentage change of the damage that each enemy receives, since that is the context in which time to kill makes sense. So if Fighter and Warpriest are fighting the same guy, +1 damage is always going to be the same percent change in damage received by the enemy, and that correctly reflects the fact that buffing either is the same. If they are not fighting the same enemy, then what you said about time to kill applies and thus it is better to buff the Warpriest. I know it is functionally the same as what you said, but I think concentrating on the damage received by the enemy rather than the damage dealt makes it easier to grasp.

[@Lucas-qp4ht]

In lots of situations, criting does more stuff than double the damage though. Crit specialisation, crit affects from traits (deadly/fatal) or from runes (persistent damage on crit from flaming rune)... In that case, you want to give +1 to the character with the most of those bonuses when criting.

[@StanNotSoSaint]

Percents are generally pretty confusing because they are masquarading multiplication as addition. Like if you go from 40 to 60, it's adding 20, as in 40+20=60. But if you do it via multiplication it's 40*1.5=60, right? So we can see that the ending result is 1.5 times bigger than starting point. Conversely 60/1.5=40 and 60-20=40, so both of these approaches are completely reversable and transparent. But when you decide to introduce percents, the room for mistakes grows. Because 60 is 1.5 bigger than 40 it means that it's 150% of 40. So the growth part would be presented as 40+50%=60. I used a plus sign there because it's like adding 50% to 100% and getting 150%, but in actuality it's a multiplication - I multiplied my base number 1.5 times. So if I decide to go back from 60 to 40 I couldn't just reverse my formula. 60-50%=/=40, because 50% of 60 is 30, not 20. Correct way would be to say 60-33.3%=40. Because it's still multiplication. In order to go from 60 to 40, you need to multiply a base number 0.667 times. But hey, where did this 0.667 even come from? In order to substruct 33.3% from something, you need to take 100%-33.3%=66.7%, and 66.7% of 60 is 60*0.667. That stuff can confuse people easily. But if you were to use multiplication, it would be much more transparent: 40*1.5=60 40*(3/2)=60 60/1.5=40 60/(3/2)=40 60*(2/3)=40 60*0.667=40 You can see where 0.667 comes from. But with percents you need to know what base number was for each of the percents. In the growth part 40+50%=60, it's 50% of 40. But in the reversed part 60-33.3%=40, it's 33.3% percent of 60. Base numbers are different but they are omitted from the formula. In this most basic of cases it's still not too confusing but when somebody starts throwing percentages around without saying what base numbers they were derived from, it can get really confusing really fast. Especially if used by bad faith artists. And it pisses me off, because as you can see, it's basically just fractions with omitted base number i.e. partially obscurred data.

[@PyroMancer2k]

Great break down. I've seen this percent change come up multiple times in forums and always just roll my eyes. Cause got people arguing that if you hit on a 2 then you are increasing your chance to hit by 50% so boosting it when you are extremely low is even more important. Which the correct math, as shown in this video, does not support that conclusion. The problem is people just taken numbers and do math on them without it actually being meaningful information. It's the old Correlation is not causation. People run the numbers and find a correlation then assume that implies some sort of cause that isn't really there. Like thinking the correlation of percent change has a causal relation to the average damage outcome.

[@SwingRipper]

Good video! Glad to see others also talk about what measurements are worthwile! I made a video on a similar topic a while ago and so I want to add one more bit of detail... % change is good *if* there is a clear correlation with respect to time (before vs after a feat, before or after a buff). Otherwise, percent difference or simple ratios are a better formula if you are comparing using a dagger vs a shortsword it is inaccurate to state either of them was "first". I agree that % difference does not make sense looking at accuracy in PF2e as each point more accuracy is just as valuable no matter the base. Dealing 1000 vs 1001 is nothing but 3 vs 4 is massive... Fighter accuracy being +38 vs a rangers +36 is not less valuable than the +9 and +7 much earlier in the game. Damage changes in value based on how much you have, bonus to hit does not. Of course the only measurement that really matters is Time to Kill as the purpose of damage is removing things from initiative and the purpose of accuracy is damage... % change in damage is just a far easier calc than TTK! An ability that deals 1000000 damage with a 1% activation chance spikes average damage per round, but isn't all that useful as it barely nudges TTK. Its best to remember that every measurement has flaws somewhere

[@zanderzingh]

+1

[@PaweMateuszBytner]

Short story: PF2's DCs and roll bonuses don't act multiplicatively, but additively, and we don't mix up those measures. Percents are a weird cursed construct liked by nobody. By definition it is simply a unit of 0,01, but that is not the end of the story, because it is not used to just move the decimal, but to indicate the context that we are talking about relative difference. The few problems we have with it are: -relative difference is not always a useful measure -relative to what. The Attack Bonus situation is particularly crazy, because on ist own it doesn't mean anything, we need the target's AC for the full picture. After we get one, we deduct AB from AC, we normalise it against the D20 and only now we can do any comparisons beside "more is good". And another funny thing is... neither additive nor multiplicative analysis approach seems sufficient. Let's start with the even situation when we get AC-AB = 11, so 50:50 chances of hitting, or more precisely 1:9:9:1 chances for crit-miss : miss : hit : crit-hit. Getting a +1 to AB makes this 1:8:9:2. It is (obviously) 5 percentage points decrease in chance for (any) miss, or 10% decrease. If we consider full mechanics of critting, and assume that there is no meaningful difference between miss and crit-miss, we have ~18% increase in average dmg: 9*regular dmg + 1*double dmg / 20 = 11/20 regular dmg, vs 9*regular dmg + 2*double dmg / 20 = 13/20 regular dmg on average. When AC-AB = 5 we have 1:3:9:7, +1 makes it 1:2:9:8 - still 5 percentage points decrease for miss, but it is whopping 25% decrease. For full mechanics: 9*regular+7*double/20 = 23/20 regular, vs 9*regular+8*double/20 = 25/20 regular. It is below 9% increase in average dmg. Finally, the other side of the spectrum, AC-AB = 17, so 7:9:3:1, becoming 6:9:4:1 after a +1. Still 5p.p. decrease in chance for miss, and mere 6,25% decrease. Avg dmg goes from 3*regular+1*double/20 = 5/20, to 4*regular+1*double/20 = 6/20, so whopping 20% increase. We are turning crit-misses into only regular hits now, but since we are starting low we are getting more in relative terms. So, is it better to get a +1 when you already have high chances, or worse, or same? One number is equal, one is not, yet another shows completely opposite relation. Well, everything depends, we are only normalising chances to hit and calculating expected dmg in most simple terms. What exactly we are hitting, anyway? Is it a bag of meat at full health that needs to be reduced over time? Is it a bag that is already reduced to 1HP but will wreck havoc if missed? Are we even targeting the same bag of meat in each case?

[@HiImLerazzo]

I believe that this issue becomes further complicated than "it does not really matter who to buff" if you consider different scenarios. If you are in a two man party with one buffer and one dpr character, it is obvious that if the dpr character is the warpriest +1 buffs are worth more than for the Fighter, since they account for all the damage. It is also worth thinking about the crit threshold where buffs matter more, as well as when fighting extreme AC enemies, where going from hitting on a 19 to hitting on a 18 is way more valuable than with lower numbers. In that sense it is correct that the percentage increase is lying when the question is "who should I buff", but it is actually a helpful tool to know which situations your buffs are making the biggest impact in order to compare whether or not buffing is even worthwhile at all compared to other actions. Generally +1 buffs are at their most worthless when you hit on a 11, since that doesn't increase your critical chance

[@schemage2210]

And this makes perfect sense, as long as you're talking about percent chance to hit. Or percent increase to damage. Where you loose me is when you try to conflate percentage chance to hit, with "damage dealt". You don't deal damage on a miss (at least in terms of weapon attacks), so it really doesn't matter if you have an 80% chance to hit or a 5% chance to hit. If you miss, you deal no damage. And even if you try saying, its the average damage dealt over time, there are so many assumptions (more maths) that aren't being qualified there.

[@Ultra_DuDu]

Statistics are great tools but you have to know how to use them. And very useful to tell "technically the truth".

[@linus4d1]

"I'm not a math guy" Ok, that's a lie. Lol

[@mizark3]

I think the context also matters for the percent increase. Some people would refer to the same +1 of 60-70% in additive percent (+10%) or multiplicative percent (+16%). For example the consistency of hitting the enemy across the team to prevent a regeneration mechanic might be better for the Warpriest to get the buff. At the same time accounting for multiple attacks would likely be better for the Fighter, especially if they had a critical specialization the party wanted to make use of. Specifically if the first hit with the greatsword Crit from the extra +1 and Flat-Footed/Off Guarded the enemy in a corner, enabling everyone to hit/crit them more easily.

[@andrewstewartbunker9966]

I always go for an increasing chance to crit. During Boss fights, the cleric may not be able to crit on a 19 even with a +1.

[@undrhil]

Wouldn't you also need to take into account the attack bonus? Because if you give the plus one bonus to the fighter, the fighter has a better chance to critical and therefore make that plus one bonus into a + 2 bonus

[@juho1069]

He did do that. That's why the +1 resulted in expected damage increasing by 10% of average damage, even though the hit probability only increased from 70% to 75%.

[@SigurdBraathen]

I advice reading up on Percentage point on e.g. wikipedia and learn the difference between pp and percentage. I don't think I can link to wikipedia (KZbin will suppress it), but I'll try as a comment to this comment.

[@SigurdBraathen]

en.wikipedia.org/wiki/Percentage_point Maybe this works? :)

[@russischerzar]

There was someone doing some elaborate math on the power of +1 quite a while ago, maybe it'll also be helpful for comparison: kzbin.info/www/bejne/Z3vLmHaGhp6Afck