Is it ever worth it to fight uphill?

In this video we'll crunch the numbers and see if an uphill fight is ever worth it. Thanks to Mubashir Ul Moula and Laurens Mertens for posing the question.
Previous Lanchester's Law video: • Lanchester's Laws in AoE2
Patreon: / spiritofthelaw
Full intro song: • Spirit of the Law Chan...
Background music from Epidemic Sound: www.epidemicsound.com
Game: Age of Empires 2 Definitive Edition, with Forgotten Empires, African Kingdoms, Rise the Rajas, and Last Khans expansions

[@emmyallen4582]

"Don't attack skirmishers with crossbows from downhill" Shit, he's not wrong.

[@ruthswann88]

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)

[@miguelinileugim]

@@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).

[@karanchavda446]

@@ruthswann88 You are missing cavalry vs Archers and skirmishers.

[@sauravtripathi4128]

@@karanchavda446 basically Cavalry archers are also archers

[@dogeofgreatness2222]

@@ruthswann88 halbs>paladin skrims>archers Archers+skirm>halbs? Or Paladins>archer halbs?

[@katerinakorcakova2085]

"that's a hill i'm prepared to die on" nice one

[@btarczy5067]

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

[@weenniethepoop5667]

truly hillarious

[@AlexThomson1000]

The puns are escalating 🤦‍♂️

[@trevorkoonce1473]

"What did you do with your math doctorat?" "Over-analyzed a real time strategy game."

[@rupert7565]

You mean the perfect amount.

[@oliverhughes610]

He actually just learned maths on Skillshare. SOTL is only 13 years old.

[@TPerm-hj4sf]

High school maths is sufficient.

[@Cythil]

@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. ;)

[@c182SkylaneRG]

@@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.

[@krishmakhecha6969]

7:03 "Even if you won't be pulling out your calculator mid fight.." Bold of you to assume that

[@shane87smith]

🤣

[@timchanux]

You underestimated my power!

[@N1ghthavvk]

Legit Strategy when playing a campaign?

[@krishmakhecha6969]

@@N1ghthavvk Just pause and spend 10 hours beating the campaign (due to the calculations)

[@devagr]

"Alexa, do this calculation for me"

[@edyslavico3761]

*Insert Obi-Wan Kenobi meme here*

[@javieryllanes1987]

Hello there

[@Ugapiku]

Another happy landing

[@ouvej4757]

Oh, I am not brave enough for politics

[@carlpult5235]

I assume the meme was not including it, so we have to think about it ourselves. A second order meme! To the publishing cave!

[@twohandedswordsman852]

*It's over, archers! I have the high ground!

[@nelsonmejiaslozada9362]

People : Math is boring Spirit of the Law: Hold my AOE2 Graphs please

[@mullerpotgieter]

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?

[@Latexi95]

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"

[@timwf11b]

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.

[@selkokieli843]

Great question! It also begs the second one, how easy is it to keep the hill to yourself from an advancing army?

[@oyuyuy]

The answer is simple, you should always move up the hill, but you should attack while doing it.

[@Bartoc1988]

@@Latexi95 When you add micro, all that math becomes rather pointless. He even showed that in the video :3

[@AgeofNoob]

"Don't fight with Crossbows against Skirms uphill" *laughs in larry*

[@nathangamble125]

kzbin.info/www/bejne/kKibqGuJgKeGoNE

[@MetalKingII]

I think you mean Liereyy

[@simonschaller7023]

@@MetalKingII he is called larry a lot in the community

[@Naverb]

Who needs bodkin or hills or armor or counter units when you have the power of Larry on your side

[@gamaxgbg]

@@MetalKingII /woosh

[@IorekMetal]

The beautiful old intro is a gift from the gods.

[@kodacv1612]

no

[@Bartoc1988]

Maybe.

[@baloonman5]

The intro is back again! :D

[@Marckillius]

Intro HYPE!

[@kabob0077]

IT'S OVER ANAKIN, MY MEN HAVE THE HIGH GROUND!

[@lordvoldemort917]

Me with 50% larger army. You underestimate my power

[@METALFREAK03]

@@lordvoldemort917 what is your scout level?

[@daddysidrak1330]

"You have two options: Number 1: fight tartars elite skirmishers with crossbowers from downhill, or number 2:" "Its enough! I choose Number 2"

[@popopduck877]

or tatar emperial skirmisher ?

[@matiasrisso5917]

@@popopduck877 Or Tartar Genitours?

[@punbug4721]

Tatar elite skirms with archers from downhill with a Tatar ram in front

[@SnarkyZazu]

So that's the reason to take a major in Mathematics: Age of Empires videos

[@Jonathanizer]

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.

[@williamsouth1847]

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.

[@dontspikemydrink9382]

didn't even catch that

[@ahmadtarek7763]

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.

[@JNCressey]

red = strength

[@PressA2Die]

@@JNCressey Red = Speed

[@selkokieli843]

they're all just random stat modifiers when you're colourblind

[@hylianrapsody7607]

7:08 Sometimes I wonder whether or not SotL do research for topic-related jokes

[@skumfisken]

I would not put it past the scoundrel

[@JKRevanBR]

He didnt used Obi-wan Kenobi, so no.

[@benjaminmiddaugh2729]

@@JKRevanBR 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.

[@avalanchas336]

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!

[@alexwendler5479]

Glorious return of the intro song!

[@ChargingEve]

Anakin tried and it didn't end well.

[@christopherg2347]

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.

[@HarbingerIV]

Spoiler alert: Im pretty sure anakin outlives Obiwan

[@jacobweeks777]

@@HarbingerIV From a certain point of view...

[@zchen27]

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.

[@HomoErectusIsAFunnyName]

@@HarbingerIV Sure but he later got an upgrade while ObiWan was continuously nerfed over time.

[@speedyf40]

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

[@yrret1996]

falls asleep during video sotl: "assuming that you fell asleep" me: did he just read my mind

[@westupt850]

Me: It's over [name]! I have high ground! [Name]: oh sh...

[@HarrisNMeo]

The intro music

[@SWEm4rt1n]

You manage to make your videos about applied mathematics in games both enjoyable and informative at the same time, every time! More videos with numbers and graphs please!!

[@readyup9926]

Great video keep up the good work!

[@gustavoguerra7865]

U are the best! Spirit of the law, whem i see a fun video in youtube about aoe 2, its ever of ur channel. Thanx! From Bogotá, Colombia. New sub =D

[@rat488]

nice to see some graphs in a SoTL video it feels like it has been a while :)

[@canyildiz7708]

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

[@alejandroromero6464]

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

[@chtyldubreux5950]

Great content! I had that 50% in mind as a guess when the video started, turned out my intuition was right!

[@calebshonk5838]

Obi-wan: "It's over Anakin! I have the high ground!" A: "You underestimate my civ bonus!"

[@Zooooch1989]

Ah, I've that opening,thanks for bringing it back :)

[@Arbmosal]

Man the memes in your videos are on fire lately. Thanos balance really cracked me up :D

[@Creeping_Shadow]

Great video!

[@zTayx]

God I love that intro so much. Never change

[@richardlittlejohn8184]

Classic SOTL video! I love these types!

[@dreamsteraoe7596]

The way this guy explains stuff and still adds in humour is amazing.

[@gonzalocoelho8468]

Great video!!!!!

[@bcpratt6979]

People are going to love you for bringing your old intro back

[@kafelek7126]

I hope you won't run out of ideas cause I love your videos

[@samsam-un3cq]

Nice video!!

[@heckinmemes6430]

I haven't played this game in months, but I still watch these videos as they come out.

[@bruhwicked620]

OMG THE INTRO!!

[@ColinTimmins]

That was really interesting to see the numbers behind that question...

[@tiolavara13]

wonderfull video, congrats

[@bfernandeslopes]

amazing video

[@mubashirulmoula1798]

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 .

[@rahuldsouza1985]

Can't wait for your Cuman and Tatar civ overview

[@GiorgosKoukoubagia]

When uphill crossbowman sees downhill skirmisher closing in to attack: :my time has come:

[@thunderrowan737]

Just started play aoe for the first time your videos have really helped me deal with my friends who have played this for many years thanks.

[@admiralrooster]

I didn’t fall asleep at the first graph but I was picking my brain up off the floor so I appreciate the summary at the end lol

[@20gdetitane]

How can you still find relevant subjects that help us improve at the game after so long... it amazes me.

[@MrMercuryW]

0:40 Ultra Instinct Villager wears orange clothes... Coincidence? I don't think so

[@AcZe1188]

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

[@sauravtripathi4128]

Being a math major student myself, I just love those graphs, formulae, explanations etc.

[@pierre-mariecaulliez6285]

7:10 the brave trading cart charging the enemy for glory !

[@bombalas]

Please do a video covering Turkish spearmen or other "unusable" unit lines like Persian swordsman. Let's we if they have situationally any use

[@unimportantcommenter4356]

No, a better idea: Reviewing bottom of the barrel units, like Korean, Malay and Viking cavarly, Hunnic and Tatar infantry and Celtic Cavarly. Like, how bad are they and do they have situational use. Like Viking cavarly, which can only be used to snipe siege, nothing else.

[@alexbrowne9566]

@@unimportantcommenter4356 the other day I went viking cavalier to fight cataphracts and it won me the game. People just need to remember when and where it's appripriate to use these sub optimal units. The viking cavalier is obviously no match for paladin civs, but it's still a good stat powerful unit that has situational use

[@manu85345]

Dude, nice!

[@baizen1]

"Hill bonuses are no joke" Queue Riut's hill castle against MbL in megarandom

[@wsk1124]

The math, you are so good at it

[@federicoedoardomariabarber3598]

2000 - Learning history with Age of Empires 2020 - Learning math with Age of Empires Glad that my favorite game of all time never dies.

[@PigmeoMoral]

The best intro

[@yonokhanman654]

3:21 PERFECTLY BALANCED AS ALL THING SHOULD BE

[@StRodeNL]

SOTL: "You should never fight with equal numbers uphill" Liereyy: "I'm gonna pretend I didn't see that"

[@spd-kv6sd]

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.

[@pointynives]

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.

[@lagg1e]

It also helps if you have a track record of just not losing units doing that.

[@nightelf4161]

@@pointynives that is very brutal example

[@fads90]

Lovin' the content but when are we getting the top 5 petard civs vid?

[@langleyzor7547]

"Anakin, I have the high ground.. you can't win!"

[@lorenzo6868]

You're welcome, thanks for making the video. :-)

[@tomaszsmol3920]

"Don't attack smirmishers with crossbows from downhill" Unless you're name is Hera

[@devagr]

I think you mean Larry

[@emerson685]

The fact that you calculated an army size of 13 v 10 would equalize the advantage, and the simulated result matched that perfect, is why I FREAKIN LOVE YOU CHANNEL! Thanks for consistently being a boss

[@Moosbeuren1]

Marvelous

[@Sean.Vosler]

Good news, your doctorate in age of empires 2 has been approved, congratulations!

[@justincronkright5025]

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.

[@PriyabrataHalder]

Sotl: Damage downhill can be calculated from Lanchester's square law. Me (with 30 champions): TENNOHEIKA BANZAI!!!

[@m1st87]

that Hi-res Intro!

[@adramm3097]

It's over Anakin !

[@ayushtiwari2959]

You underestimate my power!

[@onetrucksizedsalmon2962]

Don’t try it

[@legion2590]

I would love to see some tests with melee units. It gets messy. One army starts with the high ground but the armies start to mix units with both sides having the high ground over enemy units. I imagine the army that starts with the high ground has an advantage that holds throughout the battle and especially in the first few seconds of the engagement but not as large as ranged units who always maintain the high ground.

[@Klepske]

Thumbs up for the intro.

[@Aynshtaynn]

Oh my god the intro!!

[@rezazorro00]

Seeing the enemy uphill "They can't do that! Shoot them.....or something"

[@yeeterskeeter2066]

You said "High Ground" in the beginning and I was really hoping for an obi wan meme, but your content is good, I'll overlook this minor mistake Xp

[@anwyl42]

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%.

[@SpiritOfTheLaw]

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.

[@jimd9053]

You had the perfect chance to use the meme

[@shdba]

"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.

[@nathangamble125]

"i m parallel with math." Not too bad at geometry though.

[@ilPOMPO95]

I love doing it with the scout vs scout at the beginning of the game agahah

[@theotv5522]

Congrats on bring back the old intro.

[@llamabeast1]

I love your videos Spirit - I'm especially impressed by the high production values. I'm about to start trying to make KZbin videos myself (not AoE). Do you mind if I ask what software you use to put them together?

[@SpiritOfTheLaw]

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.

[@llamabeast1]

@@SpiritOfTheLaw thanks so much! I'll give all that a try!

[@Code002x]

Extrañaba esa intro

[@binzero3935]

I smell the Tatars overview coming next. :))

[@adiwannenobi]

Spirit of the law : is it worth it to fight uphill? Obiwan Kenobi : [visible confusion]

[@terrestunicorn3782]

*trebuchet flings a rock at a castle* Spirit of the Law: *squints* yeah I can calculate that

[@erwinjohannarndt4166]

INTRO! F YEAH!

[@ShinkaTHPC]

Finally, full intro, Definitive Edition.

[@fidrewe99]

The 33%/50% - rule of thumb is a nice one to work with, thanks.

[@lostinthewoods3918]

I didn't even know hills give an advantage! But it sure does explain alot. Amazing how old this game is and it had hidden mechanics like this all along. No wonder my dad always won. Bastard probably knew all of them.

[@MinisterSW]

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?

[@HazmanFTW]

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.

[@nathangamble125]

@@HazmanFTW That's... not what he said, and also not an explanation for the thing he did say.

[@nathangamble125]

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.

[@Naverb]

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

[@MinisterSW]

@@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.

[@maukku1572]

KZbin recommended this and I thought it was in real world and not in a game but whatever still good vid.

[@dontspikemydrink9382]

What do you mean, game. Nobody said this was a game?

[@Dr.CaveCurinas]

Okay, so is anyone else curious how armor/attack bonuses etc. play into hill bonuses? Are they added before or after the hill bonus?

[@clonator5097]

I'm pretty sure the added percent is after armor calculations, else the archers would do a lot more damage to skirms

[@wansdich]

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.

[@MrMorvana]

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...)

[@nothanks7475]

@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.

[@devagr]

@@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).

[@40gomez]

Hi @Spirit Of The Law, please do a video of Cumman 2 TC boom vs regular 3 TC boom

[@Tcg8136]

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.

[@KristofThePaladin]

Have you ever done a top 5 navy civilizations video? I am asking because I want to know how to get a good navy to help my friend in his Huskarl rush

[@raynmanshorts9275]

Math: It's a beautiful thing.