I think that it's an important point and if you can find values that make it work, I am all for it.

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I think the +/- request isn't for tolerance, but for seeing more easily how big the change is. Or maybe just make the significant changes bold?

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Well, 9(Bb) aren't really weakened that much; they are only weakened in a fight against a 9(S/Bb). In a fight against a 10(S), they behave as well as any other 9(S). I think the specific change is not enough to worry over, as 9(Bb)vs9(S/Bb) are extremely rare. I mean, once there is again reason to fully upgrade defence, pretty much everyone will, and if you can get a 9(S), you generally can make a 10(S) too. In competitive games, at least; and if you're not tryharding, then a few % of difference won't impact your game.

By the way, in today's tournament game, I had empire and worldsavior skipped both defence promotions, and I still needed 5 hits to kill him. 2 expensive promotions, 4 iron 4 coal 1 gold total, and they can be skipped because they make no difference. I think that's the greatest argument in favor of my change so far.

On the other hand, I lost a handful of supersoldiers against sirver's weaker troops. Attacking with few supersoldiers isn't trivial. The easy solution is to attack with more than two soldiers, unfortunately those were all I could spare from worldsavior pushing on my other border... Still, all things considered, I think this change is good.

GunChleoc wrote:

I think that it's an important point and if you can find values that make it work, I am all for it.

Those values I suggested are the best that can be done with slight change. if we want to fine tune more, then we should completely change the values, probably nerfing attack and buffing defence overall, so that 10(S)vs10(S) will require 7 or 8 hits to kill. But I prefer to change as little as possible.

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First thing, I would like to see a statistic averaged over who's starting. So if for example 9(Bb)vs10(Bb)=51.6% and 10(Bb)vs(9(Bb)=57.7% I'd like to see a single box with ( 51.6 + ( 100 - 57.7 ) ) / 2 = 46.9%, which is easier to read than two similar numbers. 47% is a bit less a difference than I was hoping but at least it is a difference. Maybe adding 2 to barbarian helmet, bringing their total hp at 220, would be better.

Aside from that, I don't think the statistics about 2(S)vs10(S) are helpful. As I said, it would be more useful to see how many 2(S) it takes on average to kill a 10(S). I actually tried to calculate it from the number of kills and statistical considerations, but it didn't work, because the variation on the damage dealt is not the same as the amount of damage dealt. Though we can figure it out with other calculations; it takes 16-17 hits for a 2(S) to kill a 10(S), so if the 2(S) dies in 4 hits, four consecutive fights are a real danger to the 10(S), and even 3 can be if it's unlucky. A surprisingly small number. Now I see why my soldiers had so much trouble against sirver. If instead the 2(S) dies at the third blow, then it takes six of them to threaten the 10(S). That of course assuming equal evasion, so we're talking (S/Bb). Notice that 10(Bb) already kill 2(S) in three hits, but with their lower evade, they still take as much damage as anyone else.

well, four to six is a big difference. but how to fix that? one way to deal with it would be to nerf attack instead of buff it, so that 10(S/Bb) would kill each other in 6 hits rather than 5. Barbarian attack would also need to be nerfed to kill with 5 hits. But then, this would significantly nerf 10(Bb) when going against 2(S), because 10(Bb) would kill in 4 like anyone else, but they would die more easily for their lower evade.

I see no way out. We can accept my slight change and what it does to 2(S)vs10(S/Bb); or we can keep the current situation and accept that the pro players aren't going to use some of the promotions; or we can cmpletely rework all the values to keep the following constrains: 2(Bb)vs2(S/Bb)=20% to 30%, 10(S)vs10(S)=close to 50% for any tribe, 10(S) is stronger than 9(S) for any two tribes, it takes four to five 2(S/Bb) to kill a 10(S), and barbarian have lower evasion and higher attack.

Those three options.

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So finally I've recalculated all fights one more time, and got final results. For sure the hardest thing is about king's indecision: 1 or 2 HP for helmet? So I had to check both possibilities.

Table of Context:

Introduction

Here I provide full data I got from calculations. All of them are experimental ones, not pure mathematics probability. Of course the experiments are pseudo-random, as Python code allows.
The project I used is available here and introduced here.

For all data except the old ones I added percentage changes in brackets, as SirVer suggested here
The percentage is absolute change between old data and new one. For example, when old data shows 54.5% and the new one is 62.4%, the old data record will be pure "54.5%", but the new one will be "62.4% (+7.9%)". Changes +/-0.1% should be interpreted as 0% change (measurement uncertainty).

All the experiments are made with 10 thousands of cases. I've measured percentage of wins (and lost), and also (as suggested here), percentage of left HP for attackers and defenders. That is why this post is rather like an article :). Hope it will answer all questions.

And as it was mentioned here, if two soldiers of the same level and tribe is fighting, the chance of win is always greater than 50% for the attacker. So this is not a mistake! It should be like that, because if A kills B, B can't kill A any more. And the attacker attacks first, so he has more chances to hit the defender.

Soldiers data

• AT - Attack level
• DF - Defence level
• EV - Evade level
• HP - Health level

All possible values are listed here, also you can find there how the fight works inside the game.

Barbarians

• bar_02
  • AT: 0
  • DF: 0
  • EV: 2
  • HP: 0
• bar_09
  • AT: 5
  • DF: 0
  • EV: 2
  • HP: 2
• bar_10
  • AT: 5
  • DF: 0
  • EV: 2
  • HP: 3

Empire

• emp_02
  • AT: 0
  • DF: 0
  • EV: 2
  • HP: 0
• emp_09
  • AT: 4
  • DF: 0
  • EV: 2
  • HP: 3
• emp_10
  • AT: 4
  • DF: 0
  • EV: 2
  • HP: 4

Atlanteans

• atl_02
  • AT: 0
  • DF: 0
  • EV: 2
  • HP: 0
• atl_09
  • AT: 4
  • DF: 1
  • EV: 2
  • HP: 1
• atl_10
  • AT: 4
  • DF: 2
  • EV: 2
  • HP: 1

Raw data

Old data

Battles win/lost:

Attackers health:

Defenders health:

New idea

General king_of_nowhere's idea is to change equations for attack for Empire and Atlanteans. Instead of +8 I used +9.2 (1.2 more), as he suggested. Also Barbarians needs some boost too: every helmet upgrade will be +29 instead of +28 (1.0 more).

Battles win/lost

Attackers health:

Defenders health:

Barbarian helmet +2

With another king's proposal, where every helmet has +2 more HP, I had to made another calculations. I will show only significant changes between the results (percentages are between this section and king_of_nowhere first idea):

Battles win/lost

Attackers health:

Defenders health:

Conclusion

As you can see above, adding +2 instead of +1 makes bigger difference between level 9 and level 10 Barbarians soldiers. I guess that this is what king_of_nowhere wants (and all here agreed about that). So in further points I will use data from this part of calculations and "forget" about idea of +1 for each helmet.

Another thing is surprise here: battle between Barbarians level 9 and level 10 soldiers, ends worse for level 10 soldier. He wins in more cases, but with bigger HP lost. So there is more cases when level 9 soldier almost win. In previous version level 9 soldier wins more cases, but other fights are definitely his lost.

Regardless the starting position

Here king_of_nowhere proposed to show the averaged values for winning the fight from both sides: attack + defence.

Old data

Battles win/lost

Health

New data

Battles win/lost

Health

Other statistics

I include here some smaller parts of the statistics above to show how everything works.

Level 9 vs. level10

Win / lost statistics

Old data

| vs. | bar_10 | | emp_10 | atl_10 | | --- | --- | --- | --- | | bar_09 | 54.6% | 52.2% | 50.6% | | emp_09 | 48.2% | 53.4% | 48.9% | | atl_09 | 52.3% | 56.8% | 52.9% |

New data

Level 10 vs. level 9

Win / lost statistics

Old data

New data

Level 10 vs. level 10

Win / lost statistics

Old data

New data

Level 9 or 10 vs. level 9 or 10

Win / lost statistics

Old data

New data

Level 2 against 9 or 10

Health statistics

Old data

Defenders health

Attackers health

New data

Defenders health

Attackers health

Conclusion

1. From given possibilities, best solution is to give +2 for every helmet (Barbarians)
2. Changes doesn't affect much level 10 soldiers balance
3. Changes does affect level 9 soldiers in an expected way
4. Changes makes Barbarian's level 9 soldier much weaker than others level 9 soldiers
5. Changes does affect level 2 vs level 10 soldiers balance in a minor way
6. Changes makes Atlantean's level 2 soldiers weaker against level 10 soldiers from Empire and Atlanteans

Epilogue

If I made a mistake, please tell me about that.
Also If you want to have any other comparison, write that too.

einstein13
calculations & maps packages: http://wuatek.no-ip.org/~rak/widelands/
backup website files: http://kartezjusz.ddns.net/upload/widelands/

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