Wait so he confirmed that Halberdiers are good vs paladins Skirmishers are good vs archers (I think he included it in another recent video too) I feel like there's a third counter we're missing that he hasn't done a video on... (I don't play AoEII so this isn't instinctive to me)
@@ruthswann88 Not sure if you're joking. Either way those are probably the hardest straightforward counters the game has. There's also, for example, onagers vs archers. Or hussars vs monks. Or some unique units (e.g teutonic knights against almost anything melee, huskarls against almost anything ranged).
@jocaguz18 Well is the sort of skill you need to practical math. At least in many fields. But not somethingyou really need to doctorate in. Engineering degree won't hurt however. ;)
@@Cythil I'm an engineer, and I'm not familiar with the formula he keeps using, so it's not an Engineering formula. :) Engineering helps me to understand what he's saying, but I'm guessing that formula only shows up in Statistics or advanced Math courses, specifically.
Now I pose another question pertaining to this hill conundrum: Why not take the heat and march your forces up the hill to fight on equal ground? Yes, you're taking free hits, but would that equalize with removing the hill bonus?
That depends highly on how good is your micro. WIth good micro you don't lose much dps when moving your units so you aren't even giving free hits or actually you maybe even dodging hits. Hard to measure. "It depends"
Beyond how good your micro is it depends on the speed of your units, the range of the other guy's units, and the balance between offense and defense in the situation. Speed is obvious if you can move up the hill faster they get less free hits. If they have shorter range they also get less free hits. If (assuming a mirror match-up like in the video) the units take a lot of hits to kill each other then getting a free hit or four matters less.
Anakin did not have anywhere near the +33% power needed. Chanches are Anakin had less then 100% of Obi-Wans Power at that moment. They were both clearly running low on HP then.
If Anakin was well rested he probably is a stronger unit than Obi-Wan. But again he basically lost his marbles after almost choking his wife to death so I would put a huge debuff multiplier on him for the equation.
While i am sure SotL would be capable majoring in mathematics, so far his videos have not gone beyond school maths. If you think university maths is anywhere near this simple, you are very mistaken.
@@EMDakka I'm not sure whether you are assuming that using an Obi-Wan joke would take research or that not using an Obi-Wan joke would take research, and I'm not sure which conclusion is worse.
1:04 I am so used to a green colour indicating buffs and red colour indicating debuffs that I have been staring at the screen for a good ten seconds in confusion, oops.
I had a similar problem when I was younger and used to play as blue in aoe1, the enemy in the campaign was almost always red, so when I played red alert as a Soviet whose faction is red (wonder why?) I assumed it was glitch and that my units were colored wrong.
man just recently I was thinking those Spirit of the law videos are not as math heavy as they used to be. Really cool to see an in-depth one again! Great job!
-All I learned from this is -_-Obi Wan-_- was wrong, it's not over for -*-Anakin-*- if he bring small army of his own- _-Obi Wan-_- should have fought -*-Anakin-*- in Arabia map, where there are lots of sand to insert more dominance- Fight only with trash units or if you have more numbers on downhill, got it xD
A terrible thought has crossed my mind. One day there will be "Thanks for watching, guys and I'll see you next time." But there will be no next time. Hope this never happens!
Congrats for playing with Hera. I know you have interviewed Hera and Tatoh in different ocassions. It would be cool to have more interviews with Pros now and then. Thanks SoTL
If I remember correctly, it's done before. So, for exemple one crossbow has 8 atttack one skirm has 4 def Assuming crossbow attack from uphill. 8*1.25 = 10 10-4 = 6 Something to test, though.
I had the same question, and it's AFTER. You can watch the video from SoL on the hill bonus to be sure: he uses archers who have 104 attack and 4 pierce armor. With the hill bonus, they do 125 damages ((104-4)*1.25=125). If the bonus was before armor, they would do 126 (104*1.25-4=126). So against really high armor, the hill bonus makes almost no difference if you have low damages. (+25% on 1 or 2 damages is really small, and it's maybe even rounded down...)
@Crimson51 Refer to 5:33 through 5:45 in the video. SotL mentioned it can be simplified into the alpha and beta variables (the ratio) in that equation based on the time it takes to kill a unit.
In general, with A on the hill and B below A, then if each A unit is z times stronger in attacking B than B is attacking A, then B will need to have (5z+3)/6 times as much units as A to get equal losses. Also, in order to win the fight, B will need to have at least [(1+5z/3)/(1+3/(5z))]^0.5 times as much units as A. This means if one's troops are two thirds (66.6666%) stronger, then engaging uphill is safe if one has the same amount of troops. If one has 50% more troops, it is not safe to fight uphill if the opponent's troops are 35% stronger.
I was watching the playlist, he was casually comparing a few unique units and all was good and all. I fell asleep for a few minutes, when I opened my eyes there were hecking equations and symbols on my screen. I thought I was dreaming and freaked out. It was an otherworldly experience
Liereyy does a few other things while taking fights. Not many can do the maneuver he makes, let alone he actually does this even with archers against skirmishers.
A losing battle is fine if it helps you win the war. Throwing 44 crossbows away to 10 skirms is still a win if you have 44 more crossbows and they have nothing.
so is simply ordering your ranged units to the top of the hill the best way to nullify the hill bonus? or is it not worth it due to the time not spent firing back?
You lose 1-2 units till you get to the top of the hill. After that, you are on even ground. So, it's worth it. If you can, you can spam between Z and V to change stance while walking to avoid some arrows. That's what Viper does all the time.
Minimum dmg is always 1, and -I think it does 1.25 but the display rounds the hp value up. No data on the last part though- Edit: Just tested it, the bonus ends up rounded down to 1 as well.
@@DuckieMcduck if I'm reading the wiki right, there's a catch- if two armies of say 4 armor and 4 attack face each other, both sides will do 1 damage per hit whether they're on the hill or not If there are two armies with 4 attack and 3 armor, on level ground they do the same-1 damage per attack, and the army attacking uphill will do 1 damage per attack still, as damage can never drop below 1. But the army attacking downhill will gain an extra damage every 4 shots- the attack bonus only applies to "real" damage, not the pity 1 damage minimum possible- the minimum is applied after the rest of the damage calculations. If it's 4 attack 2 armor, both effects come unto play ageofempires.fandom.com/wiki/Attack
@@AngDavies Makes sense when the minimum of 1 damage is applied completely at the end of the calculation. So for 4 attack vs 4 defense you get 0 damage with downhill bonus is 0*1.25=0, which is changed to the minimum 1 damage.
@spiritofthelaw it seems like you did not include the "bug" where units that die before their projectile hits their target do full damage and remove the +/-25% damage modifier completely. I have no clue how it might be added mathematically, but i am certain it influenced that original 50% you were talking about.
Great video Spirit! You should definitely be invited to a symposium about "Learning Maths through videogames" if there ever was one. Idea on which I would love a dig in. How does ELO rating work in AoE2 DE? Just played a guy yesterday with 2 wins and 9 losses that had a 1345 1v1 elo... How is that even possible with such a limited amount of games?
If he only played against very high-rated players, that would mean he loses very little elo from his losses, and gains large amounts of elo from his wins.
I'd guess he started with a high unranked or TG score. Each ladder tries to place you, within 10 games, of a score reflective of your score on the other ladders. For example, someone with a 2500 TG score will only need a few 1v1s to reach 1600 1v1 elo, while someone who only plays 1v1s might take much longer to reach that point
@@Naverb That sounds reasonable. I wish I knew this before starting 1v1 from 1000 elo then. The guy has my same elo in TG, but he has like 150 elo more than me in 1v1 which does not make sense considering that we won the TG without much effort against a team of apparently better 1v1 players. In the end, you cannot trust the ELO system that much given the differential between TG and 1v1.
instead of "x - 10" it should be A - B, which leads to A^2 - 2AB + B^2 = A^2 - (b/a)B^2 => A = ((b/a + 1)/2)B So that's basically "cut their power advantage in half". In this case the power advantage is 66%, so the required numbers advantage is 33%.
Yeah, the 10 was just to remove a variable for a general audience and make it easier to follow. That's a nifty rearrangement to show why it'll always be exactly half, though.
1- With Cavalry Archers, I NEVER fight downhill. I just march them up the hill to fight. 2- If you are attacking elite skirmishers with crossbows from downhill. Start getting omega 3 supplements.
The video mentioned that you need a 33% unit advantage to come out even in an uphill fight in terms of units lost. This, however, assumes that both armies fight to the death. Is it possible to come out ahead with a 33% army advantage by engaging for a while, killing a few enemy troops, and then running? Or, conversely, if you're uphill and fighting with a troop disadvantage, is it possible to come out ahead by strategically deciding when to disengage?
Actually, turns out that a 33% advantage isn't enough for the downhill player if the uphill player can strategically retreat. Suppose player A is downhill and starts with 133 units, and player B is uphill with 100 units. What B can do is fight with A until B goes down to 32 units (10*sqrt(10) to be exact) and then escape. In this exchange, B loses 68 units. At the same time, A goes down to 53 units, which is an 80 unit loss for A. So B actually comes out ahead! More generally, B can fight on until A has a 66% unit advantage (66% is the magic number here) and then escape, and B will always come out on top. As a result, the downhill player needs to start out with at least 66% more units than the uphill player if they want to deny the uphill player an advantage from fighting a bit and running away.
You made me smile at the 3m 30s mark as a math geek myself. Stuff like the M.I.T. blackjack counting strategy I used math and hundreds of millions of simulations myself to literally find perfect blackjack (or more perfect) plays and counting strategies. I found a better basic one to +1 deuces through nines with faces and tens at negative one and aces at negative four and ran math and calculated about a 10% better rate of return playing this over the basic one they had. I don't really play much blackjack at all because I hate the game after running variance sets and then playing some. I have better ROI's where I use math in my profession of gambling that blackjack is a waste of time. I know I used a much different subject, but I do love math and computer programming.
I love your videos Spirit - I'm especially impressed by the high production values. I'm about to start trying to make UA-cam videos myself (not AoE). Do you mind if I ask what software you use to put them together?
I use obs to screen capture and powerdirector 12 to edit. It's pretty cheap compared to Vegas and Premiere Pro, and has the important functions. If you get it, make sure you experiment with shadow files and the preview quality to make your life easier while editing (depending on how good your computer is). Also, play around with the export settings a lot at first because you want to find something that looks okay after youtube's compression.
I appreciate your well written content. I've been following you since your very early videos and I'm always impressed with the quality of your scripts. Thanks for so much great information Mr Law
Thanks a lot for making this content that I asked on your last video. My approach was like this - Uphill unit size = u Downhill unit size = d Since all the units have equal attack and HP if the damage taken ( or HP loses) over time is same for both group, they will eliminate each other. So u/0.75d = d/1.25u --> d/u = root (5/3) = 1.291 or 29.1% more units. Honestly I'm really surprised to see that the theory applies so perfectly here in practice .
I'm currently on my 2nd year on mechanical engineering and seeing the dreaded differential equations being used on my favorite game is a unique kind of motivation
"Assuming you fell asleep at the first graph" hahaha you got me man, i m parallel with math. I don t even play AoE but i find myself watching matches like my father watches football lol. Ps. I m surprised I m this early to one of your videos.
Hey Spirit of the Law, instead of numerically solving it, you could just have solved your equation with setting A_f = A_0 - B_0. You can solve this and get: A_0 / B_0 = 1/2 * (1 + \beta / \alpha) With \beta / \alpha = 1,25/0,75 you get A_0 / B_0 = 4/3 , which is exactly what you got with your grafic calculator, as you showed in the video. The advantage of solving it analytically is, that then you have a more general result, which can be used for more cases. I hope you will see this. But nevertheless, this was a great video! Keep up the good work! (I am sorry for my dilettante english; it's not my first language)
What if they're both in a hill with a pit in the middle and viceversa? Maybe it's gonna be the same thing, no changes. Also, how many units do we have to kill with a mangonel/onager for it to be worth it? Thanks for everything SOTL :D!!!
Anyone know if the size of the hill matters at all? Do you only need to be 1 'elevation point' above the enemy for the buff to occur or is there some sort of sliding scale? Bigger hills == Bigger bonus? There was some cliffside bonus too... does that stack with this also?
Wait units deal more damage when attacking from on top of a hill? That's wild. Used to games like StarCraft where downhill units get a penalty to hit, but there's no uphill bonus.
Id like to know at which point its more efficient to just storm uphill to negate the malus/bonus while risking the damage taken until you reach the top.
>makes an entire video about holding the high ground > doesnt make a single Obi-wan Reference IM THROUGHLY DISSAPOINTED IN YOU SOTL.. YOU HAVE DISGRACED THY FAMILY, DISGRACED YOUR HONOR, DISGRACED YOUR COW! VERY DISHONORABIRU.
Quick bit of maths shows that for given attack advantages α,β and k as your weaker-army scale factor, you get a pretty simple answer: 2k-1 = α/β Plug this in for α=1.25, β=0.75 and you get the k=1⅓ answer which SotL found, but this works for **any** different strength army. For example, what's the value of a civ not having their last blacksmith upgrade? Well, the Halberdier has 6+4 standard attack and 3 melee armor, so if we compare that to 6+3 we have α/β = 7/6, and so k=13/12 or about 8.3%. So that means that the final attack upgrade for infantry makes your halbs 8.3% more efficient in a head-to-head encounter, at large numbers.
"Some motherfuckers are always trying to ice skate uphill" -Blade, 1999 "Don't attack skirmishers with crossbows from downhill" -Spirit of the Law, 2020 Spirit of the Law is Blade, confirmed
I was thinking if you could do a video with different champions fighting vs arbalest and raiding, like Celts (quicker), Aztecs (+4 attack), Malians (+3 Parmor) and don't remember another now but smth like that :D I need moar maths
5:37 That crossbowman got a shot off right before he died, but then it didn't register on the other crossbowman, is that the way it is for any projectile now, because, unless I'm mistaken, it wasn't like that in the HD edition.
6:55 - I'm still feeling dread about fighting up-hill... And then you show a flurry of Chu Ko Nu bolts flying FROM both sides! 'Twill be nightmares for tonight I guess.
Wait a minute... What! Aren't the Tatars too overpowered given their AoE stats? Their unique unit gives gold when killing enemies... They have extra hill damage... Needs nerf.
Fuck. I discovered Lanchester's square law by myself a few years ago and thought I had discovered something unique. I had no idea somebody else had come up with it first. The reason you square the army size is that you need to account for both hitpoints and attack. When you increase the army size by 30%, you increase both your attack by 30%, and the number the enemy needs to kill by 30%. That's why bringing your attack back up to even while the enemy does 25% more damage than you is balanced. You have 30% bigger army and they do 25% more damage.
"Don't attack skirmishers with crossbows from downhill"
Shit, he's not wrong.
Wait so he confirmed that
Halberdiers are good vs paladins
Skirmishers are good vs archers (I think he included it in another recent video too)
I feel like there's a third counter we're missing that he hasn't done a video on...
(I don't play AoEII so this isn't instinctive to me)
@@ruthswann88 Not sure if you're joking. Either way those are probably the hardest straightforward counters the game has. There's also, for example, onagers vs archers. Or hussars vs monks. Or some unique units (e.g teutonic knights against almost anything melee, huskarls against almost anything ranged).
@@ruthswann88 You are missing cavalry vs Archers and skirmishers.
@@karanchavda446 basically Cavalry archers are also archers
@@ruthswann88 halbs>paladin
skrims>archers
Archers+skirm>halbs?
Or
Paladins>archer halbs?
"that's a hill i'm prepared to die on" nice one
You'll need 1.33 Spirits of the Law to kill him consistently though, if I understood the video correctly. I think he's safe
truly hillarious
The puns are escalating 🤦♂️
*Insert Obi-Wan Kenobi meme here*
Hello there
Another happy landing
Oh, I am not brave enough for politics
I assume the meme was not including it, so we have to think about it ourselves.
A second order meme! To the publishing cave!
*It's over, archers! I have the high ground!
"What did you do with your math doctorat?"
"Over-analyzed a real time strategy game."
You mean the perfect amount.
He actually just learned maths on Skillshare. SOTL is only 13 years old.
High school maths is sufficient.
@jocaguz18 Well is the sort of skill you need to practical math. At least in many fields. But not somethingyou really need to doctorate in. Engineering degree won't hurt however. ;)
@@Cythil I'm an engineer, and I'm not familiar with the formula he keeps using, so it's not an Engineering formula. :) Engineering helps me to understand what he's saying, but I'm guessing that formula only shows up in Statistics or advanced Math courses, specifically.
Now I pose another question pertaining to this hill conundrum: Why not take the heat and march your forces up the hill to fight on equal ground? Yes, you're taking free hits, but would that equalize with removing the hill bonus?
That depends highly on how good is your micro. WIth good micro you don't lose much dps when moving your units so you aren't even giving free hits or actually you maybe even dodging hits. Hard to measure. "It depends"
Beyond how good your micro is it depends on the speed of your units, the range of the other guy's units, and the balance between offense and defense in the situation. Speed is obvious if you can move up the hill faster they get less free hits. If they have shorter range they also get less free hits. If (assuming a mirror match-up like in the video) the units take a lot of hits to kill each other then getting a free hit or four matters less.
Great question! It also begs the second one, how easy is it to keep the hill to yourself from an advancing army?
The answer is simple, you should always move up the hill, but you should attack while doing it.
@@Latexi95 When you add micro, all that math becomes rather pointless. He even showed that in the video :3
People : Math is boring
Spirit of the Law: Hold my AOE2 Graphs please
7:03 "Even if you won't be pulling out your calculator mid fight.."
Bold of you to assume that
🤣
You underestimated my power!
Legit Strategy when playing a campaign?
@@N1ghthavvk Just pause and spend 10 hours beating the campaign (due to the calculations)
"Alexa, do this calculation for me"
Anakin tried and it didn't end well.
Anakin did not have anywhere near the +33% power needed. Chanches are Anakin had less then 100% of Obi-Wans Power at that moment. They were both clearly running low on HP then.
Spoiler alert:
Im pretty sure anakin outlives Obiwan
@@HarbingerIV From a certain point of view...
If Anakin was well rested he probably is a stronger unit than Obi-Wan. But again he basically lost his marbles after almost choking his wife to death so I would put a huge debuff multiplier on him for the equation.
@@HarbingerIV Sure but he later got an upgrade while ObiWan was continuously nerfed over time.
"Don't fight with Crossbows against Skirms uphill" *laughs in larry*
ua-cam.com/video/Zw8w8SKBSjo/v-deo.html
I think you mean Liereyy
@@MetalKingII he is called larry a lot in the community
Who needs bodkin or hills or armor or counter units when you have the power of Larry on your side
@@MetalKingII /woosh
So that's the reason to take a major in Mathematics: Age of Empires videos
While i am sure SotL would be capable majoring in mathematics, so far his videos have not gone beyond school maths.
If you think university maths is anywhere near this simple, you are very mistaken.
7:08 Sometimes I wonder whether or not SotL do research for topic-related jokes
I would not put it past the scoundrel
He didnt used Obi-wan Kenobi, so no.
@@EMDakka I'm not sure whether you are assuming that using an Obi-Wan joke would take research or that not using an Obi-Wan joke would take research, and I'm not sure which conclusion is worse.
IT'S OVER ANAKIN, MY MEN HAVE THE HIGH GROUND!
Me with 50% larger army.
You underestimate my power
@@lordvoldemort917 what is your scout level?
1:04 I am so used to a green colour indicating buffs and red colour indicating debuffs that I have been staring at the screen for a good ten seconds in confusion, oops.
didn't even catch that
I had a similar problem when I was younger and used to play as blue in aoe1, the enemy in the campaign was almost always red, so when I played red alert as a Soviet whose faction is red (wonder why?) I assumed it was glitch and that my units were colored wrong.
red = strength
@@JNCressey Red = Speed
they're all just random stat modifiers when you're colourblind
The intro is back again! :D
Intro HYPE!
"You have two options:
Number 1: fight tartars elite skirmishers with crossbowers from downhill, or number 2:"
"Its enough! I choose Number 2"
or tatar emperial skirmisher ?
@@popopduck877 Or Tartar Genitours?
Tatar elite skirms with archers from downhill with a Tatar ram in front
The beautiful old intro is a gift from the gods.
no
Maybe.
man just recently I was thinking those Spirit of the law videos are not as math heavy as they used to be. Really cool to see an in-depth one again! Great job!
0:40 Ultra Instinct Villager wears orange clothes... Coincidence? I don't think so
falls asleep during video
sotl: "assuming that you fell asleep"
me: did he just read my mind
Me: It's over [name]! I have high ground!
[Name]: oh sh...
-All I learned from this is -_-Obi Wan-_- was wrong, it's not over for -*-Anakin-*- if he bring small army of his own-
_-Obi Wan-_- should have fought -*-Anakin-*- in Arabia map, where there are lots of sand to insert more dominance-
Fight only with trash units or if you have more numbers on downhill, got it xD
Obi-wan: "It's over Anakin! I have the high ground!"
A: "You underestimate my civ bonus!"
Glorious return of the intro song!
A terrible thought has crossed my mind. One day there will be "Thanks for watching, guys and I'll see you next time." But there will be no next time. Hope this never happens!
kind of dark...
... also, the Internet is forever.
Man, why you gotta go around putting those thoughts in my mind. I just now acknowledged Sotl's mortality and it's a sad thing.
bro, you just cursed the channel.. do you realize how many chickens I will have to sacrifice to make this right again?
Congrats for playing with Hera.
I know you have interviewed Hera and Tatoh in different ocassions. It would be cool to have more interviews with Pros now and then.
Thanks SoTL
Okay, so is anyone else curious how armor/attack bonuses etc. play into hill bonuses? Are they added before or after the hill bonus?
I'm pretty sure the added percent is after armor calculations, else the archers would do a lot more damage to skirms
If I remember correctly, it's done before. So, for exemple
one crossbow has 8 atttack
one skirm has 4 def
Assuming crossbow attack from uphill.
8*1.25 = 10
10-4 = 6
Something to test, though.
I had the same question, and it's AFTER. You can watch the video from SoL on the hill bonus to be sure: he uses archers who have 104 attack and 4 pierce armor. With the hill bonus, they do 125 damages ((104-4)*1.25=125). If the bonus was before armor, they would do 126 (104*1.25-4=126).
So against really high armor, the hill bonus makes almost no difference if you have low damages. (+25% on 1 or 2 damages is really small, and it's maybe even rounded down...)
@Crimson51 Refer to 5:33 through 5:45 in the video. SotL mentioned it can be simplified into the alpha and beta variables (the ratio) in that equation based on the time it takes to kill a unit.
@@wansdich It's calculated AFTER the armor calculation. So in your case it would do 5 damage (1.25 * (8 - 4) = 1.25 * 4 = 5).
It's over Anakin !
You underestimate my power!
Don’t try it
Sotl: Damage downhill can be calculated from Lanchester's square law.
Me (with 30 champions): TENNOHEIKA BANZAI!!!
Ah, I've that opening,thanks for bringing it back :)
In general, with A on the hill and B below A, then if each A unit is z times stronger in attacking B than B is attacking A, then B will need to have (5z+3)/6 times as much units as A to get equal losses. Also, in order to win the fight, B will need to have at least [(1+5z/3)/(1+3/(5z))]^0.5 times as much units as A.
This means if one's troops are two thirds (66.6666%) stronger, then engaging uphill is safe if one has the same amount of troops.
If one has 50% more troops, it is not safe to fight uphill if the opponent's troops are 35% stronger.
I was watching the playlist, he was casually comparing a few unique units and all was good and all. I fell asleep for a few minutes, when I opened my eyes there were hecking equations and symbols on my screen. I thought I was dreaming and freaked out. It was an otherworldly experience
so if we want to take your hill we would need at least 1 1/3 SotL's to be equal...
good to know ;)
When uphill crossbowman sees downhill skirmisher closing in to attack: :my time has come:
Hi @Spirit Of The Law, please do a video of Cumman 2 TC boom vs regular 3 TC boom
nice to see some graphs in a SoTL video it feels like it has been a while :)
There were zero Obi Wan having the high ground memes and I am disappointed. Otherwise great video.
SOTL: "You should never fight with equal numbers uphill"
Liereyy: "I'm gonna pretend I didn't see that"
Liereyy does a few other things while taking fights. Not many can do the maneuver he makes, let alone he actually does this even with archers against skirmishers.
A losing battle is fine if it helps you win the war. Throwing 44 crossbows away to 10 skirms is still a win if you have 44 more crossbows and they have nothing.
It also helps if you have a track record of just not losing units doing that.
@@pointynives that is very brutal example
Stupid question: Do towers/castles also have the uphill advantage?
1
Yes, ships as well
@@TheSirBrainbug Thank you!
Is AoE2 an excuse to talk about math or is math and excuse to talk about AoE2 ? 😂
The intro music
Ooh, percentage based math. Something about it always appeals to me. I like the way SotL explains this too.
so is simply ordering your ranged units to the top of the hill the best way to nullify the hill bonus? or is it not worth it due to the time not spent firing back?
Great question
Also, when it's worth to send melee units uphill to take the fight?
You lose 1-2 units till you get to the top of the hill. After that, you are on even ground. So, it's worth it. If you can, you can spam between Z and V to change stance while walking to avoid some arrows. That's what Viper does all the time.
@@meunomenaoediego It's never worth it. You will need siege units or cavalry to deal with archers on hill
@@karanchavda446 cavalry (with the exception of cav archers and a few unique units) _are_ melee units
@@meunomenaoediego When you have Eagles, Huskarls or have a big numbers/tech advantage.
What id like to know is how do 1 dmg attacks factor into this?
Minimum dmg is always 1, and -I think it does 1.25 but the display rounds the hp value up. No data on the last part though-
Edit: Just tested it, the bonus ends up rounded down to 1 as well.
@@DuckieMcduck if I'm reading the wiki right, there's a catch- if two armies of say 4 armor and 4 attack face each other, both sides will do 1 damage per hit whether they're on the hill or not
If there are two armies with 4 attack and 3 armor, on level ground they do the same-1 damage per attack, and the army attacking uphill will do 1 damage per attack still, as damage can never drop below 1.
But the army attacking downhill will gain an extra damage every 4 shots- the attack bonus only applies to "real" damage, not the pity 1 damage minimum possible- the minimum is applied after the rest of the damage calculations.
If it's 4 attack 2 armor, both effects come unto play
ageofempires.fandom.com/wiki/Attack
@@AngDavies Makes sense when the minimum of 1 damage is applied completely at the end of the calculation. So for 4 attack vs 4 defense you get 0 damage with downhill bonus is 0*1.25=0, which is changed to the minimum 1 damage.
Good stuff, thank you!
So in order to beat Obi-Wan comfortably, we need another Anakin.
Or a youngling, mathematically speaking...
@spiritofthelaw it seems like you did not include the "bug" where units that die before their projectile hits their target do full damage and remove the +/-25% damage modifier completely. I have no clue how it might be added mathematically, but i am certain it influenced that original 50% you were talking about.
2:37 so if I choose to not square root at the end, I can greatly increase my army size!
I'm sure T90 & Th Viper learned something here😂
Great video Spirit! You should definitely be invited to a symposium about "Learning Maths through videogames" if there ever was one. Idea on which I would love a dig in. How does ELO rating work in AoE2 DE? Just played a guy yesterday with 2 wins and 9 losses that had a 1345 1v1 elo... How is that even possible with such a limited amount of games?
The first 10 matches in DE don't give an ELO rating it works out where you sit then the 11th give the ELO. You were his 11th so he didn't have an ELO.
@@HazmanFTW That's... not what he said, and also not an explanation for the thing he did say.
If he only played against very high-rated players, that would mean he loses very little elo from his losses, and gains large amounts of elo from his wins.
I'd guess he started with a high unranked or TG score. Each ladder tries to place you, within 10 games, of a score reflective of your score on the other ladders. For example, someone with a 2500 TG score will only need a few 1v1s to reach 1600 1v1 elo, while someone who only plays 1v1s might take much longer to reach that point
@@Naverb That sounds reasonable. I wish I knew this before starting 1v1 from 1000 elo then. The guy has my same elo in TG, but he has like 150 elo more than me in 1v1 which does not make sense considering that we won the TG without much effort against a team of apparently better 1v1 players. In the end, you cannot trust the ELO system that much given the differential between TG and 1v1.
Hey do you watch anime as it's japanese and you love japanese?
Lovin' the content but when are we getting the top 5 petard civs vid?
instead of "x - 10" it should be A - B, which leads to A^2 - 2AB + B^2 = A^2 - (b/a)B^2 => A = ((b/a + 1)/2)B
So that's basically "cut their power advantage in half". In this case the power advantage is 66%, so the required numbers advantage is 33%.
Yeah, the 10 was just to remove a variable for a general audience and make it easier to follow. That's a nifty rearrangement to show why it'll always be exactly half, though.
Math: It's a beautiful thing.
"Hill bonuses are no joke"
Queue Riut's hill castle against MbL in megarandom
You had the perfect chance to use the meme
1- With Cavalry Archers, I NEVER fight downhill. I just march them up the hill to fight.
2- If you are attacking elite skirmishers with crossbows from downhill. Start getting omega 3 supplements.
The video mentioned that you need a 33% unit advantage to come out even in an uphill fight in terms of units lost. This, however, assumes that both armies fight to the death. Is it possible to come out ahead with a 33% army advantage by engaging for a while, killing a few enemy troops, and then running? Or, conversely, if you're uphill and fighting with a troop disadvantage, is it possible to come out ahead by strategically deciding when to disengage?
Actually, turns out that a 33% advantage isn't enough for the downhill player if the uphill player can strategically retreat. Suppose player A is downhill and starts with 133 units, and player B is uphill with 100 units. What B can do is fight with A until B goes down to 32 units (10*sqrt(10) to be exact) and then escape. In this exchange, B loses 68 units. At the same time, A goes down to 53 units, which is an 80 unit loss for A. So B actually comes out ahead!
More generally, B can fight on until A has a 66% unit advantage (66% is the magic number here) and then escape, and B will always come out on top. As a result, the downhill player needs to start out with at least 66% more units than the uphill player if they want to deny the uphill player an advantage from fighting a bit and running away.
You made me smile at the 3m 30s mark as a math geek myself. Stuff like the M.I.T. blackjack counting strategy I used math and hundreds of millions of simulations myself to literally find perfect blackjack (or more perfect) plays and counting strategies. I found a better basic one to +1 deuces through nines with faces and tens at negative one and aces at negative four and ran math and calculated about a 10% better rate of return playing this over the basic one they had. I don't really play much blackjack at all because I hate the game after running variance sets and then playing some. I have better ROI's where I use math in my profession of gambling that blackjack is a waste of time. I know I used a much different subject, but I do love math and computer programming.
I love your videos Spirit - I'm especially impressed by the high production values.
I'm about to start trying to make UA-cam videos myself (not AoE). Do you mind if I ask what software you use to put them together?
I use obs to screen capture and powerdirector 12 to edit. It's pretty cheap compared to Vegas and Premiere Pro, and has the important functions. If you get it, make sure you experiment with shadow files and the preview quality to make your life easier while editing (depending on how good your computer is). Also, play around with the export settings a lot at first because you want to find something that looks okay after youtube's compression.
@@SpiritOfTheLaw thanks so much! I'll give all that a try!
OMG THE INTRO!!
Probably not, but people do it anyway.
never fight uphill me boys
Are the last 2 civ overviews coming up soon?
Seeing the enemy uphill
"They can't do that! Shoot them.....or something"
0:10 no SW pun? Disappointed :(
3:21 PERFECTLY BALANCED AS ALL THING SHOULD BE
Did corpses always disappear this quickly in Age of Empires 2? Yes, that's my takeaway from this video.
they seem to disappear more quickly in DE. They went through different decomposition phases eventually becoming skeletons in classic
I appreciate your well written content. I've been following you since your very early videos and I'm always impressed with the quality of your scripts. Thanks for so much great information Mr Law
Thanks a lot for making this content that I asked on your last video. My approach was like this -
Uphill unit size = u
Downhill unit size = d
Since all the units have equal attack and HP if the damage taken ( or HP loses) over time is same for both group, they will eliminate each other.
So u/0.75d = d/1.25u --> d/u = root (5/3) = 1.291 or 29.1% more units.
Honestly I'm really surprised to see that the theory applies so perfectly here in practice .
I'm currently on my 2nd year on mechanical engineering and seeing the dreaded differential equations being used on my favorite game is a unique kind of motivation
"Anakin, I have the high ground.. you can't win!"
"Assuming you fell asleep at the first graph" hahaha you got me man, i m parallel with math. I don t even play AoE but i find myself watching matches like my father watches football lol.
Ps. I m surprised I m this early to one of your videos.
"i m parallel with math."
Not too bad at geometry though.
Hey Spirit of the Law,
instead of numerically solving it, you could just have solved your equation with setting A_f = A_0 - B_0.
You can solve this and get:
A_0 / B_0 = 1/2 * (1 + \beta / \alpha)
With \beta / \alpha = 1,25/0,75 you get A_0 / B_0 = 4/3 , which is exactly what you got with your grafic calculator, as you showed in the video. The advantage of solving it analytically is, that then you have a more general result, which can be used for more cases. I hope you will see this.
But nevertheless, this was a great video! Keep up the good work!
(I am sorry for my dilettante english; it's not my first language)
I just feel everything working up to Tatar civ overview but it doesn't come 🥺 this suspense is killing me
the real question here is, what bonus do you get from being on a moral highground?
It's over, Mayans! I have the high ground!
YOU UNDERESTIMATE MY PLUMED ARCHERS
"Don't attack smirmishers with crossbows from downhill"
Unless you're name is Hera
I think you mean Larry
What if they're both in a hill with a pit in the middle and viceversa? Maybe it's gonna be the same thing, no changes. Also, how many units do we have to kill with a mangonel/onager for it to be worth it? Thanks for everything SOTL :D!!!
If starwars has taught me anything its to always fight with the high ground
But to never be to selfconfident on thw high ground, or you lose like Darth Maul did.
Dude, again... Start making some Command & Conquer Remastered videos... People are playing that now and want to see that.
Everyone commenting about hills but you all forgot most important thing
INTRO IS BACK!!! IN HDDDDDDD!!!
0:40 that female villager can see the code!!!
Anyone know if the size of the hill matters at all? Do you only need to be 1 'elevation point' above the enemy for the buff to occur or is there some sort of sliding scale? Bigger hills == Bigger bonus?
There was some cliffside bonus too... does that stack with this also?
Wait units deal more damage when attacking from on top of a hill? That's wild. Used to games like StarCraft where downhill units get a penalty to hit, but there's no uphill bonus.
Id like to know at which point its more efficient to just storm uphill to negate the malus/bonus while risking the damage taken until you reach the top.
>makes an entire video about holding the high ground
> doesnt make a single Obi-wan Reference
IM THROUGHLY DISSAPOINTED IN YOU SOTL.. YOU HAVE DISGRACED THY FAMILY, DISGRACED YOUR HONOR, DISGRACED YOUR COW! VERY DISHONORABIRU.
But when units shoot downhill, they are much more clumped together than on a flat surface. So they are more vulnerable to catapults.
Good news, your doctorate in age of empires 2 has been approved, congratulations!
Quick bit of maths shows that for given attack advantages α,β and k as your weaker-army scale factor, you get a pretty simple answer:
2k-1 = α/β
Plug this in for α=1.25, β=0.75 and you get the k=1⅓ answer which SotL found, but this works for **any** different strength army. For example, what's the value of a civ not having their last blacksmith upgrade? Well, the Halberdier has 6+4 standard attack and 3 melee armor, so if we compare that to 6+3 we have α/β = 7/6, and so k=13/12 or about 8.3%. So that means that the final attack upgrade for infantry makes your halbs 8.3% more efficient in a head-to-head encounter, at large numbers.
"Some motherfuckers are always trying to ice skate uphill" -Blade, 1999
"Don't attack skirmishers with crossbows from downhill" -Spirit of the Law, 2020
Spirit of the Law is Blade, confirmed
I was thinking if you could do a video with different champions fighting vs arbalest and raiding, like Celts (quicker), Aztecs (+4 attack), Malians (+3 Parmor) and don't remember another now but smth like that :D
I need moar maths
5:37 That crossbowman got a shot off right before he died, but then it didn't register on the other crossbowman, is that the way it is for any projectile now, because, unless I'm mistaken, it wasn't like that in the HD edition.
Spirit of the law : is it worth it to fight uphill?
Obiwan Kenobi : [visible confusion]
6:55 - I'm still feeling dread about fighting up-hill... And then you show a flurry of Chu Ko Nu bolts flying FROM both sides! 'Twill be nightmares for tonight I guess.
Wait a minute... What!
Aren't the Tatars too overpowered given their AoE stats?
Their unique unit gives gold when killing enemies... They have extra hill damage...
Needs nerf.
Fuck. I discovered Lanchester's square law by myself a few years ago and thought I had discovered something unique. I had no idea somebody else had come up with it first.
The reason you square the army size is that you need to account for both hitpoints and attack. When you increase the army size by 30%, you increase both your attack by 30%, and the number the enemy needs to kill by 30%. That's why bringing your attack back up to even while the enemy does 25% more damage than you is balanced. You have 30% bigger army and they do 25% more damage.
Now I want to try out a mod that replaces all the in-game music with the non-AoE stuff SotL plays on his videos.
What do you do for a living, Spirit? Didn't you say you were a lawyer? Why tf do you play around with math so much
my brain hurts...
5:20 doesn't it change alpha to 1.5? Brta should be 0.75 right?
Spirit of the Law discovers the Unreasonable Effectiveness of Mathematics in Age of Empires