Why Attack Rates in AoE2 Are Often Wrong
ฝัง
- เผยแพร่เมื่อ 1 ต.ค. 2024
- Why do I keep saying in civ overviews that units with 20% faster attacking are actually 25% faster? This video will explain it in a bit more detail.
1:35 Why the tech tree numbers seem to make sense
2:03 If Legionaries are created in 8 seconds instead of 10, is that 20% faster?
2:48 Extending the incorrect method to 50%, 100%, and 200% faster
4:02 Reverse engineering the correct method
5:38 Back to the original question (+20% Legionary creation)
6:40 Car example
7:38 Common mistake
8:02 Team bonuses exception
8:20 Summary of attack rates (conversion chart)
Previous video on this topic (unlisted):
• Why the Japanese +25% ...
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Game: Age of Empires 2 HD with Forgotten Empires, African Kingdoms, and Rise the Rajas expansions
Now I understand it 25% better
Not 200%!?
That's my ignorance level, I am 200% less ignorant now :)
You mean you understood 80% of it before and now you understand it 100%? Ah SeemsGood Kappa
+burt591 Or in other words, you need 20% less time to get it.
Are you sure you don't misunderstand 33% less?
I'd like to quote SotL here,
"Say what you want about my mother, or me as a person, but how dare you say I'm not math-y."
-Is the Paladin Worth It Part 2
Jay Blodget just the video at the top of the sidebar.
I really would just change everything to:
*"Infantry training time reduced by 20%"*
instead of:
*"Infantry is trained 20% faster"...*
This is an easy solution
AoE 3 did that ;)
Would fix some, but there are also other cases like costs, speed, etc
@@mortache Speed has the same issues and should be fixed the same way. Think of the comparable car example.
This car is 1.2 times faster. Trips take 83.33...% of normal travel time. Trip time reduced by 16.66%. Trips completed 16.666% faster.
The first 3 of these are equivalent but the last one is grammatically ambiguous. In "Trips completed 16.666% faster." is the 16.66% referring to the trip time or the car. To put in aoe terms.
Infantry trains 1.2 times faster. Infantry takes 83.33% of normal train time. Infantry training time reduced by 16.66%. Infantry is trained 16.666% faster.
The problem is
No one ever says "Trips completed 16.666% faster." in our new airplane. They always say either the new airplane is 20% faster or trips take 16.66% less time in our new airplane. "Trips completed 16.666% faster." is not wrong mathematically(like Spirit of the law says). Its just grammatically ambiguous. Does the 16.66% percent refer to the planes speed or to the trip time.
This is such an easy mistake to fix. Really would help
Spirit of the Law is at it again, separating myth from math! (I still want that to be this channel's catchphrase...)
Spirit of the math
I would love a Video about healing, can't find anything about it on TH-cam. I hope he sees this :/
@ TeamTimeMr He talked some about it in the vikings overview video.
we don't play age of mythology bthough
Lllllllllllllll
This entire video summed up "The word faster actually should be in less time"
If anyone's wondering, the reason that the _team bonuses_ (like the Britons' Archery Ranges work 20% faster bonus) are actually correct is that they modify a different attribute to the other unit attack rate and creation time bonuses.
The team bonuses don't multiply anything by 0.8 or 0.8333 or anything like that. Instead, they multiply the _Work Rate_ attribute of the buildings by 120%. This affects the entire building; not only the units created from it, but the technologies researched at it too. It's also the same for Treadmill Crane; it doesn't _decrease the build time of buildings by 20%_ (which would mean it would actually be 25% faster), no, what it actually does is _increase the work rate of the Builder by 20%_ , which is the same effect as multiplying the build time of all buildings by 0.8333.
If you played CBA TTM, you must notice how 3x Conscription affects tech researches. It can also be noticed in 9tm or 81tm (it's a bit more obvious in the last mod). Sweet explanation bro!
Wrong.
Decent analysis. I have noticed that in AoE3 as well, if one enables the detailed Home City and Upgrade information tab thingy from Options, it actually gives a lot of the things as either a *build rate*, like with the building speed up card or infantry training, or a *build point count*, which is 'set to 500%' with the Chinese unique wall card.
The reason why the Build Rate ones work as intended and correctly labelled is that each unit or building has a specific number of Build Points to accumulate, before it can be 'fully' created. 12 Build Points per second creates a 120-pt unit in 10 seconds whereas it would take 12 without the boost - for the sake of argument, let's say 10 Build Points per second.
Unmodified/Modified = 12/10 = 20% faster.
I do realise I'm half a year late :p
There's a common mistake about percentage that 20% raise is the reverse of 20% reduction. Going from 8 to 10 is a 25% raise but going back from 10 to 8 is a 20% reduction, not 25%.
I guess that for the mongols, in the code the game reduces the reload time of cavalry archer to 20% so that actually makes cavalry archers fire 25% faster but not 20% because "25% raise" is the real opposite of "20% reduction". I hope my comment clarifies thing instead of adding confusion.
Top comment. I was thinking this all along.
I think it's more about the fact that rate is inverse of time. So from 10s to 8s (20% less time) will result in 1/10 to 1/8 attack rate(25% faster rate). If you calculate the ratio it's just like from 8 to 10, but the rationale is not the same.
The underlying problem is that people are thinking of things in terms of percentage increases or decreases, but that's useless. Just use factors, like 1.25 instead of 25% increase or 0.8 instead of 20% decrease and the problem never arises. Also don't mix up rates and other things.
Exactly
Remember, when we're talking about "faster" in this context, we're referring to speed. Speed is action/time, not time/action. That's why it's miles per hour and not the hours it takes to travel a mile. So when you start measuring attack rate the number they should be modifying is attacks per second, not seconds per attack. It matters! 2/1 is not equal to 1/2.
That's the perfect summary of this video.
Never have maths been more interesting! SOTL is awesome!!!
This stuff really interests me, I love looking at attack rates.
I've always found it funny how unintuitive rates and statistics can be. The human brain takes a lot of statistical shortcuts in day to day life that make finding the answer quicker, even if it's a less accurate answer. So when you try to define these operations explicitly (i.e. writing them as a formula), you naturally end up baking in all those shortcuts.
Hell, there's entire industries, such as casinos and game shows, that rely on these faulty shortcuts of ours to make money.
omg tocaraca you're everywhere...
Then you should learn math. This world is plagued with mathematically illiterate morons and their dumbass opinions, if this stuff is interesting to you, learn math and make the world just a little bit better place for everyone.
Are you the same Tocaraca from Reddit? Holy shit.
Essentially they should say it takes them 20% less time to reload, or 50% less time to make a unit.
Because a 20% reduction is equal to a 25% increase. 4/5 * 5/4 = 1 or with other words 0.8 * 1.25 = 1
And all this confusion is why we need proper public education!
He kinda said that exact thing at the end, but yes, you are right :)
Or Zerglings. 2 for 1.
TL;DR -- the AOE2 developers failed in using English to explain statistics.
As someone who works in the education technology industry, I thank you for this video ^^
or they failed at math
Day Y. They failed in math not English, since they knew what they were writing, as they thought it was 25% or whatever percent we're talking about, but the math failed out first
Romans in AOE2?? Since when?!
You should stop playing The Conquerors and try other parts :v
They fixed that now finally in DE. Had to rewatch this video for this glorious occasion!
Can we appreciate the fact that someone who works on this game probably saw these videos and fixed the numbers in the game?
was like a high school maths lesson as a break from med school revision. great video
Yo Spirit, Do you reckon in AoE:DE they'll add in the moon walking feature from AoE2:HD? Hahaha I like how you used Shelby Cobras as the cars :D
Is a unit is made in 8 seconds rather than 10 seconds, it’s 25% faster, or 80% the time. Similarly, a unit made in 5 seconds rather than 10 is made 100% faster, or 50% the original time. If you and your friend are each an identical model and your friend is putting it together twice as fast (100% faster) it’ll take him half the time (50%) to finish it compared to you. Wording is important if you want to make a sensible description.
Is just math... I remember that it got me confused when I learned all of that back in the day, even now I always double check when working with percentages
Basically, if 1.0 or 100% is the default rate and something is supposed to work 20% faster, then instead of multiplying it by (1-0.2) you should divide it by (1+0.2).
Just heated my leftovers after a long day at work. And this is the perfect thing to unwind to! Thanks!
What a noob you are! If you had a microwave which worked 200% faster your meal would have been ready 10 seconds before you came home.
Kalenz Now thats a dumbass joke right there lol
It's like in Planetside 2, where the Resist Shield 40% damage reduction actually grants 67% bonus health from full health when you calculate it out.
CleanSweepGaming Yep! Taking only 3/5 as much damage means it takes 5/3 as many attacks to kill you
If a tech let me build 4 Markets in 3 minutes, I have both:
"4/3 as fast construction"
AND
"it takes 3/4 as long to build each".
You easily get these inverse (aka reciprocal) values by flipping the fraction upside down.
An Archer fires 20 shots in 40 seconds. His shots per second are 20/40 i.e. 0.5. His reload time is 40/20 i.e. 2s per shot.
Tripling his shots per second means 60/40 i.e. 1.5 per second. His reload time now is 40/60 i.e. 0.6666s.
There's no need to add or subtract anything. Just flip the fraction.
Btw this was explained in the "why the Japanese 25% bonus is actually 33%" to me it was good enough
You are awesome dood!
Hey SOTL! I have been wondering for quite some time now: How do blacksmith upgrades work?
For example, Do they only give +1 attack or do they also increase any bonus damage dealt?
I feel like, for example with halberdiers dealing an extra 32 against cavalry, that upgrading them would be incredibly insignificant then?
As always, keep up the great work!
Blacksmith upgrades do not increase bonus attack, so yes, getting forging or blast furnace for your halberdiers is near useless when they're solely fighting cavalry.
its funny, when i was a kid i used to hate fractions because they seemed so strange and unusable to me and i always used to change them to percentages or decimals to make it easier for myself. now, looking back at it as an adult, these sort of things make so much more sense when they are presented as fractions.
Woah what a beautiful opening design
It's pretty simple, 4/5 = 80% which means the first takes 80% less time to perform..
5/4 = 125% which means the first works 25% faster..
3/4 = 75% (25%), 4/3 = 133.33% (33%)
Seems legit.
Wow, everyone, including sol, is overcomplicating this so much ._.
One simply has to properly distinguish between _interval_ (time between attacks/recruits/whatever) and _frequency_ (attack/recruitment speed).
Devs said faster attack(frequency), they should have said less reload (interval). Why is this such a big deal ._.
Meanwhile over at Ensemble studios....Bob the programmer just smacked Ed the programmer upside the head and said, "TOLD YOU SO!"
Fishmonger !
^ LOL
how did spirit get the Gault and Roman's in aoe2?
mods
Romans? How does someone play as the Romans?? I want legionaries!
I think it's a MOD.
Probably true. I can't seem to find it though.
The Legions are a unit from the The Forgotten Expansion Goths/Alaric campaign, there is sadly no such thing as a Roman civ. They have pretty darn broken stats, so it's probably a good thing they aren't available in multiplayer...
Though I'd argue the Byzantines should be renamed the Romans, as it's what they called themselves (they still were the Senatus Populusque Romanus untill their fall in the 15th Century), and also technically what they were.
Jasper van Heycop they have the same stats as the elite jaguar warriors, except with 1 more pierce armor. So idk if that is really broken stats since jags aren't broken
pepperVenge What did the Romans ever do for us anyway?
What kind of education system confuses so many students on such a simple topic? It's horrible! I think schools throw as much stuff at their students until everything becomes a garbled mess after some years.
Stochastic and statistic is the same. People learn 10 different models at the same time in just a few weeks and can't remember ANY of those after a few months. Too much theoretical models, useless examples, not enough practical application and lack of long-term repetition.
And then you end up with rigorous studies, which get sensationalized by the press, abusing the common people's misunderstanding of statistics, which leads to an over abundance of "important studies" and a populous, which ignores health risks of e.g. asbestos, because "yeah, yeah, everything causes cancer nowadays".
The schools turn kids into memory zombies, which lack the skill to use their knowledge until it is forgotten.
nah...simple logic just doesn't work with every human in existence. try meeting more humans who have worse education
'' You can't fool me! Is 25% faster! ''
I hope this vid got you 20% more subs ! And why John Green ?
François Bergmans John Green often references the unusual and unorthodox ways of Mongols.
"Wait for it, the Mongols!"
~John Green
Are you gonna play aoe1 def ed??
Of course! Didn't it just get moved back to 2018 tho? :(
Spirit Of The Law i think so :'( im so sad... but they are working on aoe4 too so that kinda compensates
Me and my lack of using enough internet
will be here in 2019
dem hd graphics innit
1:31 why is that archer elwphant moving backwards?
Captain Nest4r moonwalk glitch
because moonwalking
Michaeljacksephant Archer
because you touch yourself at night
You but you are You. Does that mean that you, You, is the one that touches OP's self at night?
Romans and Gauls which mod is that?
Romans? Did I miss a DLC?
mods probably
The concept is basic mathematics but a very easy mistake to make if you're not careful. Initially I was a bit baffled by how people could doubt the numbers in your previous videos since it seemed so obvious but your final example in this video really showed me how easy it is to mix up the math depending on the wording used.
Anyone noticed John Green from crash course
Param Rajguru Don't forget...wait for it...the Mongols.
they mean less time when they say faster. you mean dps or units/time when you say faster. you are just looking at the reciprocal because time is the denominator. faster is generally related to speed which is some unit divided by time. so they arent wrong they are just saying 'faster' when they should say 'less time' to make things clear. even then though knowing how much less time is not as useful as knowing how much more units/time, so they should be giving your values
just used this video to proof my argument of correct attack speed calculations in WoW Classic :)
The formula for rate of change is (New - Old)/New. That's it. Nothing to argue
Been waiting for this all day
and by all day I mean all week, this is the only thing I look forward to in life
there are other things in life
like civ overviews and AoE 1: DE :D
advancing and deepening my understanding of aoe2 IS life, Silly Billy. To say 'there are other things in life' just means 'there are other topics for SotL to cover yet'
I actually think that it is sad that SotL has to do another video about the same subject just because some people did not get basic maths in school.
Hey mate just wanted to know if you will do statistics videos for AoE4?
after learning about rate of reaction in chemistry, It make sense now.
I was hopping he said, "unless you are the mongols"
I learned three things here:
- Spirit Of The Law is good at maths and explaining it
- AoE2's programmers are neither
- this channel's comment section is seemingly a nesting ground for math nerds (which I still prefer over the troll infested swamp some other channels cultivate)
Only because some of us here like math and are good at it doesn't mean none of us are trolls, you racist!
My brain hurts now, but it was worth it
how you create a legionaryon barrack? '-'
Where's the new intro??
As a eve player, I have never got confused with these "xxx% faster" shenanigans.
Aleverette S want a cookie?
MultiGK8 your complement is enough for my ego.
MultiGK8 I'll take the cookie. Thanks.
So how that ads up to gathering bonuses like the slavs, celts, franks, Mongols, turks and British?
Those ones are actually correct. What they do is increase the "Work Rate" attribute of the vills by a certain number, like for the Celts it would increase the Work Rate by 15%, or multiply it by 1.15, which is in fact 15% and is totally correct.
Spontaneus video ideas:
01) The behaviour of deer and how to lure it.
02) The pronounciation of the numerous special units, with evidence and source. (Condotierro etc.)
Just found out I wasn't subscribed to SOTL yet
so what you do about it?
You think some modding could add some clarity to these *mAtH nUmBeRs* n stuff?
spirit of the law = math teacher
1:20 & 1:29 was epic loss tho 😜
CAN U BE MY MATH TEACHER pls
So AoE Devs couldn't do math.
StealthVice7 or English, either one :)
Or teamwork, maybe.
It's much easier when you quantify the speed to create as "work" to create, rather than seconds to create.
Say it takes 200 "work" to create a Knight, and a Stable does 10 "work" per second. A 100% increase in speed would then increase it to 20 "work" per second.
That's *exactly* what is going on, I believe. In AoE 3, which I am sure uses the same sort of principles as AoE 2 except when it comes to the unit train rates, every unit and building, for example, requires a certain number of Build Points in order to be created - or the so-called 'work' here.
About the Working Speeds,I always uses this
"If the Tech tree says the Building Works 20% Faster,it's means every second of that building working,it works in 1.2 Seconds"
So if you're producing a Crossbowman that took 20 Seconds,a Normal Archery Range will create a Crossbowman in 20 Seconds,while the 20% Faster would create it in 20/1.2 = 16.6 Seconds.
From this it's concluded that the "Faster Building Work Rate",and "Reduced Unit Train Time" isn't the same.
SO MANY GOOD AOE2 VIDS COMING OUT RIGHT NOW
This video made me wonder: is there is a x10 scenario or mod for Age of Empires 2 yet like with EU4? All civilization stat bonuses multiplied by ten? Techs too maybe?
Or in short: Just divide 1/time for creation.
For example: Unit created in 10 sec, that means in 1 sec we are creating 0.1 of unit.
Now let's add the added bonus to play.
20% faster, so that means: 0.1+0.1*0.2 = 0.12 unit per sec.
Now take 1/0.12, we got 8.333333, which is the 20% faster creation time.
It's really good to have this maths stuff.Even if I like gameplay or ideas to improve my skills,I found this truly interesting cause it's part of the game and it's (again) interesting to see.Good job ;)
A different way to think about it is: Don't work with the time, work with speed (x per time, e.g. attacks per time, units built per time). In the first example you have 1 unit per 10 seconds, to increase your rate to 150% speed, you would be making 1.5 units per 10 seconds. Now you divide 10s by 1.5 to get a build time of 6.67s per unit. So yeah, don't work with the seconds, they aren't a unit of speed, think "miles per hour", speed is in "units per time." not just time.
I am really like your channel , cause it has math and mechanics of this game...specially for designers, programmers and devs too, what's your source to this article? thx
Yo Spirit! Please I beg of you to do an impression video of Star Wars: Galactic Battlegrounds! Just one video please! Your video about the "All Techs" reminded me of that masterpiece!
am the like n°365
good video Spirit of the Cow
after AoE 2 would you start with 3 or would u wait for definitive or 4?
i also want videos about Battle Realms+Winter of the Wolf if you can
long story short: the game takes the difference percentage from the result resulting in a whacky number
tl;dw: the devs don't know how to math.
Instead of using the obvious "x per second" formular, they used some wonky made-up bullshit.
Well, the average people might be more stupid that i thought, because your previous explanation was perfectly clear!
Its "average PERSON" and "more stupid THAN I thought". My work here is done.
Hey Spirit if you are out of civilization to overview I sugest to make civilization Overview about the Mod of AoE 2 (the original) called age of chivalary hegemony
From a Canadian to another Canadian...
RIP Gord Downie.
how did you train Legionarys or are you just using a spawn trigger
Triggers :)
Vindication!
Let's find the formula of time that take of number of vills that build a building. It'll be very interesting SOTL
ok how about this: 8/10=0.8, 1-0.8=0.2 but 10= 8 x 1.25
Basically 80%(100%-20%) of 10 is 8 BUT 120%(100%+20%) of 8 is not 10. And 125%(100%+25%) of 8 is 10 in fact. Is that the principle that most ppl have hard time understanding?
Great! I liked how you completely debunked how developers increase rate with "increase by 100%". A simple and intuitive counterexample. Especially since rates can be very unintuitive. A lot of people are tricked by "X per Y", and think that a decrease of Y increases X linearly. But this "per" is important as it defines an inverse relation, not a linear one.
To add to what was said in the video, in this case, rate should be an inverse, so instead of:
10s ~> 100%
8s ~> 80%
we should have that we generate (one unit) per (Y seconds). So:
1/10s ~> 100%
1/8s ~> 125%
e.g. Decreasing reload time by 20% results in rate of fire increase of 25%.
Why 25%? You can calculate it, but the intuitive idea is that 1/10 => 1/5 and 1/8 => 1/4, and to make 4 pieces out of 5 pieces, the 5th piece needs to be divided into 4 equal parts, and added onto the remaining 4, meaning that each piece is 25% larger than before.
you could have saved a lot of time, by showing, that
1.25 * 0.8 = 1
1.33 * 0.75 = 1
(etc.)
... and work from there to unravel, that there's a difference between
"time" and "work-unit"
... and throw in the -real life- in game examples afterwards...
So polite and cordial... as he SHUTS ALL YOU FAKE ASS COMMUNITY COLLEGE KIDS DOWN! OOOOOOHHHHHH!!!!
All those crazy numbers... Make my head spin! :P
Spirit of the Law @Spirit of the Law 10% less time ~11.11% faster, 15% less time ~17.65% faster, 20% less time = 25% faster, 25% less time ~33.33% faster, 33.33...% less time = 50% faster. 50% less time = 100% faster.
Hi Spirit, I'm Marco, an Italian writer and big fan of "Age ofe Empires". I've seen all your videos and you're awesome, for analysis and reflection. I wanted to ask you if you could upgrade the first civilizations (Teutons - Huns ...) and also post video about new civilizations (Malaysian - Vietnamese ...). I would also be curious to see your tutorials on the various types of rush, faced step-by-step.
ps: only your video on Aztecki has subtitles in Italian: how come? : D
Thanks for all
The trick is looking at the 50% not as time, but output.
If you get a soldier if you reach value 300x and your output is 100x/s you get one every 3 seconds. If you add 50% to the "speed" ("faster") you add output, not speed. Aka. you have 150x/s and you fill the 300x requirements and get a soldier every 2 seconds. So, the car analogy is the best.
I believe the devs had a brainfart at the time. Simple wording revision or the number fix would remedy all this confusion.
Nice! I see this confusion come up somewhat often as people tend not to think of things as being greater than 100%, so they instinctively use the lower percentage in the math and get the wrong result. I occasionally still make the same mistake when I'm in a rush despite knowing the correct way, lol
It seems that when the makers of AoE say "Barracks work 50% faster", the true meaning of this is that the "Barracks produces 50% more units." Therefore, only 2 possibilities:
1. They either used a weird calculation that confuses most people, or,
2. Their wording of the bonus is incorrect (and confusing) for most people.
So, it actually reduces the time it takes to do anything but since we measure the rate which attacks are done usually it's for example #attacks/time_taken, or units_produced/time_taken. what they do probably is time_taken=time_taken*mod. and they say mod=1-0.2 for 20%. so in the end the percentage is on the bottom of the division, while what we understand usually would be the percentage to be on top. So again both viewpoints stand true, but SotL and the game speak for different things. One says about time taken while the other says about "production" so it's something divided by the time taken.
About the argument "if you go over 100% you get negative numbers", that's a mathematician's and a programmer's job to know when you can and when you can't go over 100%, that's why they don't.
Nice intro! Now, tell me something: do you like Starwars Battlegrounds?
@6:01 you explain that a barracks increase of 20% should reduce the production time of a unit from 10 seconds to 8.3333333 seconds, and that if you would decrease it to 8 seconds that this would effectively be a 25% reduction. All fine I agree with this conclusion. However, you never explained what the actual production time in the game is with the 20% bonus applied. Is it 8 seconds or 8.333 seconds?
The old age of empires 2 it started by using the denominator to show that when it says 20% faster, you divide by 1.2 instead of multiply by 0.8, but the team bonuses corrected this mistake. Since dividing by 1.2 is same as multiplying by 8.3333 instead of just 0.8.
0:41, the Nazare math meme, I am brazilian and this meme became world wide!
Exactly. I lived to see Spirit use an image of Nazare Tedesco in one of his videos, lol.
BRASIL SIL SIL SIL
Love your videos, you have the best narrator/caster voice and bring forward interesting facts. I suppose a great fix for AoE2 tooltips, would be to display unit attack speed as number of shots/sec. I thought your slow-mo mongol cavalry archer segment was more understandable. Numeracy isn't a skill many have developed, including myself, hence why expressing risk in i.e. number needed to harm or ratios is more intuitive than percentages.
I LOVE your math videos. ♥ This one helped me A LOT in understanding!
If it says "Unit is created 20% faster", then the production time for that unit should go down by 20%, which result in 25% more units in the same time.
If it says "Building produces (Units) 20% faster", then the output of the building should go up by 20%.
It all comes down to wording, but while this seems correct for unit production, (at least the legionaries you showed in this video), for shooting speed it often is just worded wrong and should say "Unit reloads X% faster" instead.
Well it would be called "33% less time spent" would be 67%. If it's called "33% faster" its a completly diffrent formular anyway, since your % is going up and not down. So it's working on 133% of its speed, rather than it does need 33% less time spent.