Mathfinder? Does Pathfinder 2e's Math Work at Later Levels?

Рет қаралды 1,810

3 ай бұрын

When you begin your adventure, the math in Pathfinder 2e's core mechanics is famously solid. It's easy for the GM to set and adjust encounters, players can reliably build characters built for adventuring, and every +1 matters. But at later levels, at least from what I've seen, the math can get a bit wild. Let's take a look at how adding dice as you level up can affect the reliability of your rolls and the outcomes of your sessions.

Пікірлер: 44

@RebelThenKing 3 ай бұрын

Since some of you asked about it, here are some additional numbers for the Standard Deviation from the Mean and the Standard Deviation divided by the spread to get a truer sense of how "average" dice rolls tend to me: 1d8 Standard Deviation 2.29 Standard Deviation / Spread 0.33 2d8 Standard Deviation 3.27 Standard Deviation / Spread 0.23 3d8 Standard Deviation 3.97 Standard Deviation / Spread 0.19

@magispitt 3 ай бұрын

I would advise calculating the standard deviation from the mean, this will give you a numerical representation of how much dice rolls vary from the “average”

@RebelThenKing 3 ай бұрын

I'm not sure how to account for this, but the variation is actually greater with more dice, but feels like less, in my opinion. Using www.calculatorsoup.com/calculators/statistics/standard-deviation-calculator.php I got a deviation of 3.968627 for the 3d8 scenario compared to 2.2912878 for the 1d8. But if I could include what "feels" average to me with d8, I would include 15,16,17,18, and 19 as all counting as average and that deviation for 3d8 would go WAY down. Not 100% sure if the numbers I got there are correct or if there's a way to adjust for what "feels" average versus what actually is, but if you know of anything, let me know.

@andrejbosiakov5726 3 ай бұрын

@@RebelThenKing The result show the deviation for 3d8 is only twice as big as 1d8. Since 3d8s average is three times the average of a 1d8, the deviation is tighter. For 1d8 3, 4, 5, 6 fall within standard deviation. For 3d8 its 10, 11, 12, 13, 14, 15, 16, 17. Edit: I didn't add the +4 that you did.

@RebelThenKing 3 ай бұрын

@@andrejbosiakov5726 Ha, literally just pinned a comment with this.

@emptyptr9401 3 ай бұрын

Yeah, I don't really think that this has anything to do with high level being more swing-y. If anything I believe the super-low levels should mathematically be the most swingy because player characters still have very low HP pools (And thus a lower margin for error) there and go down quickly. Mathematically speaking I would expect damage at higher levels to be a lot more consistent actually, because it is normally distributed. I mean, sure, the extremes are higher, but I think the extremes kind of don't matter when they statistically don't really come up in the first place. As a disclaimer, I have not played at high levels yet outside of simulation fights, I have only theorized a lot about playing at high levels. I have two theories however why high level combat could feel or even actually be more swingy: 1. While the extremes are statistically very unlikely, they might FEEL more prevalent, because they are far more noticable. So while mathematically I think this is not a very relevant factor, psychologically it is very relevant. 2. Abilities at higher level simply are stronger. That foes for both numerical effects and different effects. Numerically some high level boosts are absolutely ridiculous. Like Heroism giving a +3 on almost everything for example (That is a spell that I house-rule to be a little less ridiculous). A +1 is worth exactly as much at lv 1 as it is at lv 20, so if buffs/debuffs are more extreme it makes the round to round stat differentials a lot higher maybe leading to noticeably more swingy combat overall. Secondly, other abilities that are not just flat stat buffs also get stronger. LIke the Rangers Impossible Flurry for example or many former single target spells now being multi-target. Monsters also get more extreme abilities. This is kind of inherent to any level based system and pf2e is miles better than most other systems in that regard, but a bit of power-creep is unavoidable, necessary even. And this can also make combat more swingy as different combatants succeed or fail at using their powerful abilities.

@RebelThenKing 3 ай бұрын

I do agree that lower levels, really low levels like 1 and 2, are pretty swingy because your characters can go down in one hit. I think that starts to level off already at level 2, and by level 3 most characters feel like they can survive and combats don't feel too swingy. I've perceived more swing at later levels, like 7 and up though.

@emptyptr9401 3 ай бұрын

@@RebelThenKing Yeah, those were the ones I meant by "super low". In regards to higher level combat, I mean I guess I'll know for myself if I also notice it if when my players get there, but as I said, if it ends up being more swingy its probably not due to the fundamental math of the system, but due to higher level abilities being more impactful/extreme overall. I would expect the math itself to be more consistent higher on.

@eerosalonen Ай бұрын

One thing that creates perception of more swingy fights in high levels are classes that are able to make massive critical hits. Like example rogue with deadly weapon like rapier can go from normal hit without sneak attack 3d6+4 to critical hit with sneak attack (7d6+4)x2 + 3d8. In lower levels this swing does not feel that big 1d6+4 to (2d6+4)+d8

@richardmenz3257 3 ай бұрын

You should prob of added Weapon Specialization damage and stat increase damages that would have make things less swingy. Dice result in swingy combats so adding more would result in more swing chances of course but it also fun having randomnessso you don’t know the outcome. It is remarkable balanced from a random system that becomes more random over time.

@SquidasaurusRex 3 ай бұрын

Property runes adding smaller (d4 or d6) damage bonuses too! For spells, being a casting class with a dedicated flat damage boost (like Sorcerer or Psychic) really help raise that damage floor as well. Same for strikes and boosts like bard's Inspire Courage or the Marshal's scaling damage boost on the Dread aura. At later levels, class features or spells that apply persistent damage or ongoing debuffs also help make bad rolls more palatable. I've had some pretty 'unlucky' fights where the persistent damage from a Wounding Rune did more damage across the whole fight than the total of just the strike-damage.

@RebelThenKing 3 ай бұрын

I think what you're both getting at here is there is A LOT of potential variation based on the way you build your character and party. So much so that there are almost infinite possibilities! When you get into stuff like persistent damage you have to start taking into consideration not only the damage rolls, but the enemy saves, the number of rounds left in an encounter, and then maybe even things like stacking poison exposures or dealing with resistances or weaknesses to the persistent damage. 😵‍💫

@kadmii Ай бұрын

a more experienced PC finding an opening and striking an exceptionally deadly foe is exactly how I'd roleplay it

@jonathanbennison9220 3 ай бұрын

8:30 Flavoring the narrative, to explain the outcomes the dice are giving us. Is brilliant. Just a great use of the storytelling opportunity. I had a friend who once said that it's almost, more fun to write for the failures than the Crits.... But. Who doesn't love exploding the monster with a timely Mortal Finisher?

@BlueSapphyre 3 ай бұрын

The variance is definitely higher and can make for swingier combats. In a campaign I'm running, the group wizard dropped a 6d6 fireball and only dealt 8 damage. It drastically changed how the party could handle the horde of insects coming at them. Made the encounter feel like it went from trivial to moderate-severe.

@DGenHero 3 ай бұрын

That's... Holy shit that's one of the worst feels bad moments ever.

@BillErak 3 ай бұрын

now that's impressive, I'd definitely use it to get some good roleplaying about _why_ the fireball came out so small and useless.

@harrythefish4593 3 ай бұрын

With more dice the dice end up being average more often. This actually tend to make crits more important I feel at later levels. Having played in multiple adventure paths to 20 I find at higher levels debuff/buffs were more important than raw damage. A caster throwing a fireball and getting 2-3 people in it was nowhere as useful as removing reaction or causing bad guys to lose actions.

@philippedaigneault366 3 ай бұрын

I'd be interested in seeing a similar chart with the "to hit" because you need to be able to hit the thing before damaging it. I'm just saying that because the fighter with their extra +2 to hit and thus to crit tends to be a lot more successful.

@BlueSapphyre 3 ай бұрын

FIghters have spikier damage because of the crits, whereas Barbs with their flat damage is more consistently high. So fighters have a higher mean, but barbs have a higher median.

@pavfeira 3 ай бұрын

Also since Aid is a static DC15, it's way easier at high levels for Aid to Critically Succeed. Can make a big difference if the party is feeding their Magus or their Fatal weapon user.

@sethb3090 2 ай бұрын

I'd rather argue that the math in Pathfinder breaks down at low levels. The difference between level 1 and 3 is way bigger than the difference between level 16 and 18, which combined with the fewer options players have means above-level bosses are much scarier at the start.

@TheLibGamer 3 ай бұрын

Is there a reason you didn't look at the numbers for 4d8? I know if wouldn't change too much, but might be interesting.

@RebelThenKing 3 ай бұрын

Mostly because I've never actually played nor listened to any gameplay at Level19-20, which is, in theory, when you first would access a +3 rune to roll 4 total dice.

@philopharynx7910 3 ай бұрын

It seems odd to see this as a pie chart. I'm much more used to seeing a line graph. Stacking these graphs on the same chart would show the progression. With the huge variety of options, it makes sense for things to get swingy. Having completed several 20th level campaigns, i still think PF2 works better than any D&D-like game at high levels.

@jonathanbennison9220 3 ай бұрын

7:18 And, imagine the next step. All this, dramatic differences, But now consider a critical. Then Deadly (1/2/3) Then, consider Fatal d12s, instead of these d8s. ... Party also has damage bonuses. Thauma has implements empowerment,but is also buffing out 2 points bonus Regalia damage to all damage rolls within 15 ft. The party is now using some Crit Spec Picks, among others. They have the early weapon specialization bonus damage. And the pick adds bonus damage on a Crit. It is also Fatal. (bigger base dice, plus bonus Crit dice) Some of The party also has +5 for their Str Score now. So, it's a much larger low end, the minimum rolls have really increased. That said, with striking, fatal, and infused vitality (+1d4 vitality dmg) The party is rolling 2 weapon dice. (4+1 on a critical) . + the vitality bonus, (double on a Crit) Its a lot of dice. They are hoping to Uograde property runes soon, And add some. Damage. Frost. Flame. Astral. Something. Its definitely a lot of damage from the bottom end up.

@americannerdinnz 3 ай бұрын

I've watched most of your videos. This is the first one I've thought was bad. Others have commented on things you left out. Standard deviation is vital in this kind of discussion. It frustrated me that you first said how nearly impossible the max and min are and then every measure of "swingy-ness" was comparing these to each other and the mean. Maybe high level play feels swingy because you don't go down after being crit twice in a row and have time to come back, whereas one crit at level 1 can see you at dying 2.

@RebelThenKing 3 ай бұрын

I'm actually finding Standard Deviation a bit tough to use here but am open for suggestions. I think this is because Standard Deviation measures against the true mean, so in cases like 3d8 where you never actually can roll the true mean, the deviation is actually a lot larger than the single dice example. Is there way to broaden what you consider the "mean" in these calculations so that you could consider a range within 1 or 2 plus or minus of the true mean to be "average". I think that would be an interesting number. Disclaimer: I've never taken a stats course in my life 😅

@RebelThenKing 3 ай бұрын

For reference, here's a link to a standard deviation calculation for 3d8, which is 3.9686269665969. You can use the same tool to punch in the 1d8 numbers to see the lesser deviation of 2.2912878. www.calculator.net/standard-deviation-calculator.html?numberinputs=3%2C4%2C4%2C4%2C5%2C5%2C5%2C5%2C5%2C5%2C6%2C6%2C6%2C6%2C6%2C6%2C6%2C6%2C6%2C6%2C7%2C7%2C7%2C7%2C7%2C7%2C7%2C7%2C7%2C7%2C7%2C7%2C7%2C7%2C7%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C8%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C9%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C10%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C11%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C12%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C13%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C14%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C15%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C16%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C17%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C18%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C19%2C20%2C20%2C20%2C20%2C20%2C20%2C20%2C20%2C20%2C20%2C20%2C20%2C20%2C20%2C20%2C21%2C21%2C21%2C21%2C21%2C21%2C21%2C21%2C21%2C21%2C22%2C22%2C22%2C22%2C22%2C22%2C23%2C23%2C23%2C24&ctype=p&x=Calculate

@RebelThenKing 3 ай бұрын

If you see any errors in those calculated deviations, let me know. Also if you know of a way to adjust the deviation calculation for a broader definition of "average", that could help out too. Much appreciated!

@americannerdinnz 3 ай бұрын

@@RebelThenKing Okay, I've put together a spreadsheet to do what you've asked. I didn't add in any strength modifiers, but that doesn't have any effect on the variance of the numbers. Let me know if you want changes or take it to your favorite geek. docs.google.com/spreadsheets/d/1rXrI-fo5QgDW2RkBnkbM-IbZvVJLDmJ7Ad2cHr4zU68/edit?usp=sharing

@americannerdinnz 3 ай бұрын

I added a (Standard Deviation)/(Spread) to look at how much the numbers tend to vary as a fraction of the possible swing. This goes down as you add more dice. I'm not saying that high level play isn't swingy-er, but I don't think it's the dice that does it. It may be other factors (like buffs and debuffs making crits more common).

@SheenaTigerspielt 2 ай бұрын

I see a bell curve more than a pie chart.

@jonathanbennison9220 3 ай бұрын

Love. Math.

@mikehe4778 3 ай бұрын

I've really liked your videos overall, but this one is so far off that I had to comment. This is misusing math to a significant degree, and to come to the *opposite* conclusion of what the math actually says, this video misinforms your followers and does them a disservice. Adding a higher number of dice *reduces* volatility and swinginess. This can be seen in metrics such as standard deviation, which is an actual mathematically rigorous way to analyze a statistical distribution. The metrics used in this video such as "ratio of maximum to minimum" are not conceptually useful or rigorous for this problem. For one thing, imagine if one rolled 100 random numbers from 0..10, vs a single dice from 1d1000. The "ratio" in the former case is... *infinite*, but clearly less "swingy". There's also the problems in applying this to the actual game of PF2e, where flat bonuses become more and more prominent as well, and reduce swinginess further. The conclusion hinted at the beginning that high level combat may be swingier is just incorrect on both practical and theoretical merits. Really disappointed in this video.

@RebelThenKing 3 ай бұрын

Sorry to hear that. Three things that might help out - (1) See the pinned comment. What we used here was (Standard Deviation)/(Spread), which tells a pretty good story about how the numbers add up. (2) Despite what the math says, things can still "feel" different. Some other commenters have mentioned how surprisingly terrible rolls, the kind the numbers tell you won't happen often, have completely changed encounters. (3) The summary section around 7:20 mentions a greater ranger of outcomes, but concludes that you have a much better chance of rolling near average, in contrast to the opening hypothesis.