Fire power is not what we need, we need modern units to have more hit points

[WhiteElephants]

10 % chances to do 5 damages is NO WAY the same than 50 % chances to do 1 damages. I hope this math rule will one day enter in the skull of people mislead by Soren's talk about firepower.

You are correct in your assertation, but have incorrectly applied it to the game. At no time does a unit ever have a base hit percentage as you have suggested -- i.e. 10% vs. 50%. To fit your example we would have to use a 1A 5F unit and a 9A 1F unit vs. a 9D unit.

The math for the 1A 5F unit -- (1/1+9) = 10% chance to hit.

The math for the 9A 1F unit -- (9/9+9) = 50% chance to hit.

Now being that one unit has 5 fire power I don't think it too much of a strech to assign each unit with a least 10 - 20 hit points (without the fire power you really don't need high amounts of hit points unless you are attempting to make combat more certain).

Now granted I don't have the math to calculate the exact odds for damage taken, I do know the math for calculating the chance that the units will go unscaythed.

Given that each unit would have 20 hit point --

The 1A 5F unit would have a (.10^4 = 0.0001 or a 1/100 percent chance of killing a 10D 20HP unit without taking damage.

The 9A 1F unit would have a (.5^20) = 0.00001 or a 1/1000 percent chance of killing a 10D 20HP unit without taking damage.

While I grant you the 1A 5F unit is 100 times more likely to go untouched, we're still not even in the realm of tenths of a percentage difference.

It would roughly be the equivelant of giving a unit a 10,000 Attack rating and another unit a 100,000 Attack rating and having them attack a unit with 1D expecting to see a noticable difference in the results. Is there a difference? Sure, but to notice the difference you would have to play Civ for decade upon decades, if not centuries, and compile the data to compare in the end -- I don't think this game has that kind of shelf life -- during the regular course of the game it makes very little difference.

[WhiteElephants]

Re: Re: Don't let the big numbers scare you

Originally posted by Akka le Vil
Ok, man, I am thankful that you try to help me, but you get me wrong : I can tweak Civ 3 to give the units the stats I want and make them able to hit more or less often during fight. That's not the point. I stated lenghtly about how HP/FP are useful for modding, for creating, and said that it has a DIFFERENT effect than changing the A/D rating.
There is a whole bunch of things in statistics, not only the end result. HP/FP allow to play on these subtle difference rather than just using a rough way of changing A/D and get an average result.
I require HP/FP back in the game for allowing more modding, more tweaking, more customisation. Because the customisation I can do right now does not satisfy me.

I would argue that you don't need to have fire power, but with a change of hit points AND attack/defense you would get the results you desire.

[Akka]

Re: Re: Re: Don't let the big numbers scare you

Gosh, it scare me to do so, because I plainly hate maths, but it seems that I'll have to do some precise exemples to prove anything. Well anyway the statistics and probabilities are part of the programm of this year, it'll help me to refresh them for the final exam

Ok, first :

Given that each unit would have 20 hit point --

The 1A 5F unit would have a (.10^4 = 0.0001 or a 1/100 percent chance of killing a 10D 20HP unit without taking damage.

The 9A 1F unit would have a (.5^20) = 0.00001 or a 1/1000 percent chance of killing a 10D 20HP unit without taking damage.

While I grant you the 1A 5F unit is 100 times more likely to go untouched, we're still not even in the realm of tenths of a percentage difference.

It would roughly be the equivelant of giving a unit a 10,000 Attack rating and another unit a 100,000 Attack rating and having them attack a unit with 1D expecting to see a noticable difference in the results. Is there a difference? Sure, but to notice the difference you would have to play Civ for decade upon decades, if not centuries, and compile the data to compare in the end -- I don't think this game has that kind of shelf life -- during the regular course of the game it makes very little difference.

I'll first just take a counter-example. I'll use yours, but changing the HP to 5 rather than 20.
First unit : 10 % chances to win flawlessly (one round).
Second unit : 0,5^4 = 0,0625 => 6,25 %.
Here we just come from simple to double. And here it's in the world of the 3 %, not the tenth of percent.

It would roughly be the equivelant of giving a unit a 10,000 Attack rating and another unit a 100,000 Attack rating and having them attack a unit with 1D expecting to see a noticable difference in the results.

Now, with the new results (that we obtained ONLY by changing the HP/FP), it's roughly equivalent of giving a unit a 24 in attack and another a 15. The difference between a modern armor and a unit inferior to tanks (remember, it's not EQUIVALENT, it's just to give a VAGUE idea about the outcome).

Why it changes is because X % of winning is not only this X % in stat.
To explain better, I'll take a practicable example : you have to measure the average height of a certain quantity of people.
Suppose that you have one who is 1,70 m then one who is 1,75 m then one who is 1,80 m then on who is 1,65 m then one who is 1,85 m. The average is 1,75 m.
Now take another population. They are five too, and they respectively are 2 m / 1,5 m / 1,95 m / 1,75 m / 1,55 m.
You can see that the average is the same. Though, you can't say that they are the same population. In one case, the biggest difference with the average is 10 cm. In the other, it's 25 cm. What it means is that though the average is the same, you tend to have greater differences in size in one group than in other. Which means that they are statistically different.

There is basically two things :
1 - The average : it's what we use the most. One 5A unit hit one 5D unit an AVERAGE of 50 % of the time (provided there is not any bonuses).
2 - The dispersion : it's how likely any result is about to be far from the average. In Civ 1, with only one HP, the dispersion was bigger than in Civ 2 => "bogus" results happened more often.

Now, changing the A/D rating is only affecting the average (if you double the attack rating for a unit, you double it's probability to hit). The dispersion is influenced by HP/FP : the more rounds there is, the more the outcome tend to favor the unit which has the better chances of winning.

Basically, HP/FP allow people to chose the "randomness" of the fight : the more the HP, the less the dispersion. The more the FP, the more the dispersion. Only giving HP would allow moders to reduce the overall dispersion of all units (or make a single unit more resistant to damage if putting more HP only to her). Giving the FP allow to CUSTOMIZE the dispersion/randomness of EVERY units. That's a MAJOR point for modders.

[WhiteElephants]

Re: Re: Re: Re: Don't let the big numbers scare you

Originally posted by Akka le Vil
Basically, HP/FP allow people to chose the "randomness" of the fight : the more the HP, the less the dispersion. The more the FP, the more the dispersion. Only giving HP would allow moders to reduce the overall dispersion of all units (or make a single unit more resistant to damage if putting more HP only to her). Giving the FP allow to CUSTOMIZE the dispersion/randomness of EVERY units. That's a MAJOR point for modders.

Right, but you don't need both HP and FP. You only need one or the other.

I would also like to point of that in your example you used a very low amount of hit point in relation to fire power that would therefore accentuate the differences. I don't think choosing twenty hit points was a ridiculous as choosing five given the fact that no unit in Civ2 had a fire power of 5 while some had over 30 hit points. I could do the same thing with your results by adding more hit points which would further demonstrate that there isn't much of a difference.

If you want 5FP unit with 5HP units your going to get extremely wild results, far stranger than the results put forth in this thread. As far as your arguement goes I think it's moot as you continually alter the numbers to suit the results. In all practicality no one is going to be interested in playing a game with units that have 5HP along side units with 5FP. It would result in a virtual crap shot where the lucky player, not skilled player, wins. If your going to post some convincing numbers I think it should be numbers within the realm of reality -- not reality as in realism, but reality as in someone might actually make a unit as such.

[Akka]

Re: Re: Re: Re: Re: Don't let the big numbers scare you

Originally posted by WhiteElephants


Right, but you don't need both HP and FP. You only need one or the other.

Look, Whiteelephant, you're constantly half-reading the posts you're answering to. One thing good to change would be to really read them, it's tiring to tell you ten times the same things. Read that :

"Only giving HP would allow moders to reduce the overall dispersion of all units (or make a single unit more resistant to damage if putting more HP only to her)."

Understood ? Only HP would not allow to make a single unit deal a lot of damage compared to others. All units would inflict the same damages, they would just be able to bear more or less damages. Not inflict more.
Gotcha ?
Understanding the difference between ONE unit and ALL the units ?

Now read carefully, because I don't want to repeat myself : HP/FP are to the dispertion rate the exact equivalent of what A/D are about the average. Saying we can use only HP with a constant FP of 1 is about the dispersion like saying we can use only Attack rating with a constant Defense of 1 about the average.
Understood ?

I would also like to point of that in your example you used a very low amount of hit point in relation to fire power that would therefore accentuate the differences. I don't think choosing twenty hit points was a ridiculous as choosing five given the fact that no unit in Civ2 had a fire power of 5 while some had over 30 hit points. I could do the same thing with your results by adding more hit points which would further demonstrate that there isn't much of a difference.

Man, if you want to prove something with maths, then you're about using maths. What I proved was that FP/HP could NOT be simulated by improving the A/D ratings only. If you would adding more HP, it would prove MY explanation : that HP/FP does NOT influence the results in the same way than A/D.
I was not talking about a GAME example, I was talking about a MATH example. To explain that A/D and FP/MP are not the same thing.

If you want 5FP unit with 5HP units your going to get extremely wild results, far stranger than the results put forth in this thread. As far as your arguement goes I think it's moot as you continually alter the numbers to suit the results. In all practicality no one is going to be interested in playing a game with units that have 5HP along side units with 5FP. It would result in a virtual crap shot where the lucky player, not skilled player, wins. If your going to post some convincing numbers I think it should be numbers within the realm of reality -- not reality as in realism, but reality as in someone might actually make a unit as such.

Ok, dude, have you ever heard about modding ? You know, when you invent your own units, when you test your imagination, this kind of stuff.
I have an average HP of 5 and an average FP of 1. I want make a very DAMAGING unit (bomb, fireball, terrorist, toxic gas, flamethrower...). I want then this unit to be able to wipe out any other unit in one shot. Why ? Because it would fit in my mod and because I'm in the mood to do it.
I don't give a shît about the results becoming random, because it's the very PURPOSE of that unit. Yes, this unit, here. Not ALL the units of the game. One. Or two. Or whatever the number I want. It's called MODDING. i.e. giving the game special features.
If I want to create the Warp Gun which inflict obscene amounts of damage while hitting practically never and being extremely easy to destroy, I would use a FP of 10 or 15 and set it's HP to 1 and it's attack to 2. I can't just change it's Attack rating because the idea is that it's not about hitting often, it's about hitting nearly never. But killing in one shot. I just CAN'T create it without FP/HP.
Understood ?

[Sevorak]

karlmarx9001,

Good analysis with the warriors, tanks, production and maintenance costs.

Now, if you had only added in the savings for the warrior side concerning all the technology they didn't have to research, we may be on to something here.

Let's do that now.

Assume for the sake of simplicity that the advanced civilization gives away its tech to about half of the other civilizations in the game, and we can assume 8 civs. The tech multiplier based off of that is a simple 1/2 then.

Heading straight for Motorized Transportation, bypassing EVERY optional tech (simplicity's sake again) we end up with 47 techs at a total tech cost of 2196. Standard map makes the tech cost 24, so we get 24*2196*4/8 = 26,352 gold to research all of those technologies, assuming *no* beaker overflow (simplicity again).

Furthermore, let's assume that each side will have enough banked gold to maintain their army for a period of twenty turns.

So we change the example a bit:

473 warriors, 473/turn upkeep
+26,352 gold from not having to research tech
-9460 for 20 turns of upkeep

47 tanks, 47/turn upkeep
+12,543 gold from not having to maintain warriors
-940 for 20 turns of upkeep

The result is actually +5,289 for the warrior side, with which you could rush-build 88 more warriors (and keep them for 20 turns each).

Final situation looks more like:

561 warriors, 561/turn upkeep
47 tanks, 47/turn upkeep

This allocates just under 12 warriors per tank. Assuming the tanks strike first, 47 of them kill two warriors each without trouble. Each tank has a 77% chance to take no damage in one attack, and a 59% chance to take no damage in two attacks. Therefore, of the total 47*4 = 188 hit points that the tank army contains, on average and at minimum (since 'damaged' results include results where the tank takes 2, 3, or 4 points of damage), 58 of them are lost in the attack phase. Then the warriors counter attack. There are now only 467 warriors. When a warrior attacks, a tank has only a 65% chance of escaping without damage. Therefore, 467 attacking warriors do a total of 163 damage to the tanks' remaining pool of 130. However, we are neglecting two important conditions here. First, the possibility that one of the 561 warriors deals two or more damage. We will assume the chance is two percent, combining attacking and defending percentages. With two percent of the warriors dealing two damage, we gain 11 points of damage to raise the total to 174. Then, we consider the probability of the tanks promoting to elite, which has a chance of 98%, meaning that 46 tanks promote, raising their hit points to 176.

So after that huge bloody battle of mutual destruction, a single tank lives at 2 hp. Note that in every case I have rounded up decimals in favour of the tanks and rounded down decimals against the warriors, so the results may be a little off. I'd call it a toss-up between the warriors and tanks, myself.

Of course, since this example involves great abstraction of a large number of variables, it, like the example before it, proves nothing. Just a different way of looking at the problem

-Sev

[WhiteElephants]

Re: Re: Re: Re: Re: Re: Don't let the big numbers scare you

Originally posted by Akka le Vil


Look, Whiteelephant, you're constantly half-reading the posts you're answering to. One thing good to change would be to really read them, it's tiring to tell you ten times the same things.

Understood ? Only HP would not allow to make a single unit deal a lot of damage compared to others. All units would inflict the same damages, they would just be able to bear more or less damages. Not inflict more.
Gotcha ?
Understanding the difference between ONE unit and ALL the units ?

No, I don't understand, because you could increase attack and get the same results. Meaning a unit would hit more often thus causing more damage in the same proportion of a unit that hits less often and causes more damage.

Now read carefully, because I don't want to repeat myself : HP/FP are to the dispertion rate the exact equivalent of what A/D are about the average. Saying we can use only HP with a constant FP of 1 is about the dispersion like saying we can use only Attack rating with a constant Defense of 1 about the average.
Understood ?

No I don't understand why you need both when one (hit points) is sufficent. No need to repeat yourself.

Man, if you want to prove something with maths, then you're about using maths.

I can not make heads or tails of this sentence.

What I proved was that FP/HP could NOT be simulated by improving the A/D ratings only. If you would adding more HP, it would prove MY explanation : that HP/FP does NOT influence the results in the same way than A/D.

I never claimed adjusting A/D would compensate for FP/HP, only that A is equivelent to FP.

Ok, dude, have you ever heard about modding ? You know, when you invent your own units, when you test your imagination, this kind of stuff.
I have an average HP of 5 and an average FP of 1. I want make a very DAMAGING unit (bomb, fireball, terrorist, toxic gas, flamethrower...). I want then this unit to be able to wipe out any other unit in one shot. Why ? Because it would fit in my mod and because I'm in the mood to do it.

Give the unit an extremely high attack rating. Problem solved.

I don't give a shît about the results becoming random, because it's the very PURPOSE of that unit.

Well, look how far we've come from the original arguement.

Yes, this unit, here. Not ALL the units of the game. One. Or two. Or whatever the number I want. It's called MODDING. i.e. giving the game special features.
If I want to create the Warp Gun which inflict obscene amounts of damage while hitting practically never and being extremely easy to destroy, I would use a FP of 10 or 15 and set it's HP to 1 and it's attack to 2. I can't just change it's Attack rating because the idea is that it's not about hitting often, it's about hitting nearly never. But killing in one shot. I just CAN'T create it without FP/HP.
Understood ?

Point taken considering modding, but haven't you taken this arguement to the extreme to prove your point?

[Hunter Hutchins]

"modern times, it is superior technology that wins wars, not superior numbers."

Cortez 1519: 200 vs 60,000

Hmm.

[N. Machiavelli]

Let's try this.....

WhiteElephants, try this for an example using what Akka le Vil is saying about FP Let's pit two units against one another; a Rifleman (with a rifle, not an AT missle) and a tank (we'll even use an American WWII Sherman, so no advanced targeting systems). Now, we can agree (I hope) that attack/defense ONLY means the percentage that one unit has of hitting the other, right? Ok. Considering that the tank is slow as **** and is not going anywhere in a hurry, we can assume that from a range of 100 yards, the average rifleman could shoot hit it nearly every time, ok? In contrast, the rifleman himself is more agile and is harder to hit with that cannon, agree? Therefor is not resonable that the rifleman would have a higher attack rating than the tank, since his odds are better at hitting the tank than vice versa? Ok, good. Still with me?

Now, this is where FP comes in. Sure, the rifleman can hit the tank with ease, but I'm sure we can agree that the bullet isn't going to do jack against that plating? In contrast, if that tank shell scores a direct hit on the rifleman, he will cease to exist. I hope we can agree that a .40 bullet does not deal the same destruction as a 105 mm tank shell. (NOTE: we'll assume 10 HP each unit in this scenario, the HP is adjustable as long as it's in scale with the FP) Therefor, using FP, we could assign the rifleman a FP of 1 and the Tank a FP of 10. Agree?

Ok, using this model we have a situation where the rifleman could hit the tank whenever he wants to, but can only scratch the paint as opposed to the tank which has a real hard time hitting that infantryman, but will kill him in one hit. Got that? Using the current Civ3 model, you cannot reach the same results by simply raising the tank's attack level higher. The whole point is to create a sort of all-or-nothing chance for the rifleman. The rifleman even has odds on his side at defeating the tank, but if the tank ever actually gets lucky enough to hit him, it's over. You raise the tanks attack to astronomical levels and ensure that he's going to win every time, but you don't want that, you want a unit that is going to achieve NO damage ata ll except for the few times it scores a hit. Then BAM, game over.

[Nuke gay whales]

Originally posted by Sevorak
karlmarx9001,

This allocates just under 12 warriors per tank. Assuming the tanks strike first, 47 of them kill two warriors each without trouble. Each tank has a 77% chance to take no damage in one attack, and a 59% chance to take no damage in two attacks. Therefore, of the total 47*4 = 188 hit points that the tank army contains, on average and at minimum (since 'damaged' results include results where the tank takes 2, 3, or 4 points of damage), 58 of them are lost in the attack phase. Then the warriors counter attack. There are now only 467 warriors. When a warrior attacks, a tank has only a 65% chance of escaping without damage. Therefore, 467 attacking warriors do a total of 163 damage to the tanks' remaining pool of 130. However, we are neglecting two important conditions here. First, the possibility that one of the 561 warriors deals two or more damage. We will assume the chance is two percent, combining attacking and defending percentages. With two percent of the warriors dealing two damage, we gain 11 points of damage to raise the total to 174. Then, we consider the probability of the tanks promoting to elite, which has a chance of 98%, meaning that 46 tanks promote, raising their hit points to 176.

So after that huge bloody battle of mutual destruction, a single tank lives at 2 hp. Note that in every case I have rounded up decimals in favour of the tanks and rounded down decimals against the warriors, so the results may be a little off. I'd call it a toss-up between the warriors and tanks, myself.

-Sev

Wow... If all this math and calculations are correct, then doesn't this PROVE the original point? Something MUST be wrong with the combat system if a battle between warriors (bare-chested men with rusty axes in loin cloths) and tanks (with armour plating, cannons and mounted machine guns) ends up being a draw??? Please, I don't care how many of these "warriors" there were, the only thing that would slow the tanks down would be the time it would take to clean the body parts from the tank's tread... just running the hairy buggers over would be sufficient, you wouldn't even need to fire any of the tanks cannons or machine guns - it would be a waste of ammo…

[Sevorak]

As I said initially, the calculations prove nothing.

Among the many factors I abstracted:

-City improvements of any kind, including Wonders of the World.
-Type of government.
-Optional techs researched.
-Effect on one or both civilizations due to war with a third (fourth, fifth etc.) civilization.
-Any tactical application of the troops involved (such as parking the tanks on mountains)
-Money needed to be spent on entertainment.
-More or less civilizations in the game.
-Size of map.
-Amount of cities.
-Any trade at all with another civilization.
-Effect of barbarians.
-Difficulty level.
-Turns in revolution.
-Civilization strengths.
-Promotions before the battle.
-Naval, air, and artillery considerations.
-The effect of armies and/or the creation of Great Leaders.
-Strategic resource availability.

Just a sampler. My point was less that 561 warriors tie 47 tanks than the fact that within limits, you can throw numbers around whatever way you like and get something out of it. Perhaps the sarcasm in the initial comments in my first post was mis-appreciated?

-Sev

[Setsuna]

Originally posted by Hunter Hutchins
"modern times, it is superior technology that wins wars, not superior numbers."

Cortez 1519: 200 vs 60,000

Hmm.

As I've mentioned before, the numbers were way more even than that. The bulk of Cortez's forces came from various factions whom the Aztecs had subjugated. Since they didn't bother to assimilate them or control them in any way other than the fear that the Aztecs could destroy them, they were easy to recruit. Even after that, the Aztecs still almost managed to win (Not to mention they almost killed Cortez.)

That said, I hate undermining those I agree with. >_<

[Akka]

Re: Re: Re: Re: Re: Re: Re: Don't let the big numbers scare you

Originally posted by WhiteElephants
No, I don't understand, because you could increase attack and get the same results. Meaning a unit would hit more often thus causing more damage in the same proportion of a unit that hits less often and causes more damage.

Ok. I spent several posts ONLY to try to explain you that it's NOT THE SAME AT ALL. What it means is either :
- you don't read my posts
- you're mentally challenged and don't understand them
- you're basically trolling

Anyhow, I see no point to continu. I already explained you the difference one thousand times, if you want answers then just scroll back and pay more attention at what I already told you.

No I don't understand why you need both when one (hit points) is sufficent. No need to repeat yourself.

Same as above. Go back reading or stop trolling or buy a brain.

I never claimed adjusting A/D would compensate for FP/HP, only that A is equivelent to FP.

Give the unit an extremely high attack rating. Problem solved.

Same as above.

[woody]

Originally posted by Nuke gay whales
I don't give a flying duck about the math... COMMON SENSE tells me that a group of men with pointed sticks could NEVER, EVER successfully defend against a group of tanks - period. If you like to get your calculator out every time you feel the need to rationalize the results - fine, but I can simply observe this occurring, and KNOW that it is wrong.

Your problem is that you expect Civ3 to be a tactical combat simulator. It isn't. It's an epic strategy game. Combat is only a small part, and it has to be balanced well enough to make the overall game fun. If tanks were invincible to more primitive units the game wouldn't be fun. If you can't suspend your "realism" 1% of the time that a spearman beats an armor attack, then Civ type games are not for you. You should be playing a tactical wargame, where different ages don't overlap.

Maybe Firaxis should allow units to have their own hitpoint multipliers (you don't need firepower). Then you can change the rules to be more like Civ2, which is what you seem to prefer. Just don't expect a balanced game to come out of it.

[Barnacle Bill]

Originally posted by Setsuna


As I've mentioned before, the numbers were way more even than that. The bulk of Cortez's forces came from various factions whom the Aztecs had subjugated. Since they didn't bother to assimilate them or control them in any way other than the fear that the Aztecs could destroy them, they were easy to recruit. Even after that, the Aztecs still almost managed to win (Not to mention they almost killed Cortez.)

That said, I hate undermining those I agree with. >_<

Yes, but Cortez basically had nothing by European standards of the day. Properly understood, Cortez would not even have 1 unit on the Civ3 scale. Let's consider what would have happened if the Spanish had deployed an full Civ3 unit to invade the Aztec Empire instead.

In modern times, "unit=division" fits the scale of the game very well, in terms of the size of the map and number of units in play. A 20th Century division is typically about 10 combat battalions, about 500 guys in a battalion (of infantry, anyway). Coincidentally, a Roman Legion was 10 Cohorts of about 500 guys (480, really, but that is "about 500"). So, going up from a Roman Legion to a modern division is (in addition to re-equipping the infantrymen) a matter of adding a big wad of support troops - a modern division's 10,000-15,000 (depending on the army) guys is 2/3-3/4 support troops.

BTW, Roman Legions routinely defeated hordes of barbarian warriors, greatly outnumbering the legionaries, whose arms & armor were as "modern" as their own. This was a matter of being trained to operate as a mutually-supporting formation of "soldiers" as opposed to a mass of "warriors". This tactical organization & coordination stuff is "technology", too, in the Civ sense.

A 16th Century Spanish Tercio consisted of 10 companies of 300 men or 12 companies of 250 men (3000 guys either way). Two companies were harquebusiers (guys with matchlock firearms) and the rest were pikemen with significant portions of their bodies covered by plate armor. This was a combined arms formation trained to manuever together, and was the building block of then-contemporaty Spanish armies (and the very much terror of Europe to the same extent as the German Panzers c. 1940). I would consider this the least that could be represented by one "unit" in Civ3 - but really a unit is more like two Tercios. Tercio companies are a bit light to be considered battalion equivalents, so you could reasonably say a Legion upgrades to a unit consisting of 2 Tercios and that unit eventually upgrades to a 20th Century infantry division.

OK, so now let's look at the Aztecs. The elite Jaguar "knights" had quilted cotton armor, light shields and wooden clubs set with obsidian (volcanic glass) to produce the stone-age functional equivalent of a sword. The masses had stone-tipped spears or relatively weak bows firing stone-tipped arrows. Their tactical sophistication was about on par with those Gauls Caesar beat up on with great regularity.

A steel sword or pike head can readily penetrate quilted cotton armor, especially if you thrust with the point. Stone or obsidian is not going to penetrate steel plate armor, so the Aztecs have to aim for unarmored parts of the Spaniards. Aztec armor is useless against the matcklocks, while an arrow that hits a Spaniard probaly has <50% chance of hitting a part not covered by steel, and lots of those parts an arrow would not take out the victim (a ball from a matchlock will shatter the bones in an arm or let, etc...). So even if the effective range of the two weapons (considered as mass fire aimed at an enemy formation rather than a particular enemy soldier) is equal, the Spanish have a huge qualitative edge.

So, a single "unit" of 16th Century Spanish infantry should have no problem polishing of 60,000 Aztecs (let's call that 10-12 units, assume 1 in 5 are Jaguar Knights and the rest are spearmen). In fact, Caesar's 10 Legion could probably handle them.

Now let's replace our 2 Tercios with a WWI Infantry division. OK, now all of our troopies have 5 shot (10 for Brits) bolt-action rifles, and every company has a belt-fed, water-cooled heavy machinegun (neglecting divisional artillery). The Brits lost something like 100,000 guys charging in machinegun fire on the first day of the Somme offensive. What do you think happens to our Aztecs? Then fast-forward to WWII - add in mortars at the company level, light automatic weapons at the squad level. Then fast-forward to modern - all the riflemen now have automatic weapons. Now make it an armored division - about 1 battalion in 3 is now replaced by tanks (call it 25 or more tanks per battalion), and each infantry squad is mounted in an IFV. Tanks & IFV's mount coaxial machineguns on the main weapon turret, plus probably a heavy machinegun on the commander's hatch. Plus, if you are fighting an enemy without tanks the loadout for the main gun will be beehive rounds - think of it as a 120mm bore shotgun (Isreali tankers on the march like to keep one of those up the spout to deal with wire-guided AT missile crews). Get the picture?