An simple math analysis of "Leadership vs. Attack" leve up dilemma

[maltz]

I've been troubled by the Leadership vs. Attack dilemma if they are both presented in the level-up choice.

I just realized that each extra attack converts to 3.3% of damage. Now the comparison is really simple:

Is the extra leadership better or worse than 3.3% of your army strength? The answer is YES! The leadership bonuses are always about 10%-20% of your current leadership. So it is MUCH BETTER to pick leadership than attack.

But we all know the early-level leadership bonus are much less compared to what you get later. It seems that those early leadership picks should be spent on Attack. So where is the cut off that you should switch from Attack to Leadership? From the game's default high score list I can see that Leadership in end game is about 20K. 3.3% of that is 660 - this is the cut off even from the end-game perspective. Any leadership bonus above 660 is an automatic priority.

The actual cutoff should be even lower than 660 because your attack is already higher than the target's defense. Let me give you an example. Let's say your unit X's raw damage is 10. They are usually asked to attack creatures with a lower defense due to game design puts more Attack than Defense on creatures, say 5 points lower than their attack ratings. Your character already have an attack of 10 just from equipments.

So your gross attack is 10 dmg x (1 + 3.3% (100+5+10)) = 15 dmg. So what's 1 extra ATK doing for you? 10 dmg x (1 + 3.3% (100+5+11)) = 15.28 dmg. Basically you are only getting 0.28/15 = 1.9% of the bonus from this one extra Attack point (much less than 3.3% as advertised.) The actual case varies - just that the actual bonus you receive from each point of Attack gets less and less when your Attack goes higher and higher.

If an average bonus of 2% (guessed from the 1.9% from the example above) per Attack is used, you should start taking Leadership ALWAYS when they reach 400 points. This is around level 7 - 8 as a warrior. Needless to say they are important for survival at higher difficulties, too.

p.s. I think defense is much less useful than attack. If you are good you shouldn't be hit very often at all.

[BuffaloX]

Thank you Very useful information.
This means i completely misjudged all my mage upgrades, except when I chose inteligence.

[Ryastar]

What's the formula you are using? Because each point of att is 3.3% more damage, no matter what.

[Stepsongrapes]

What's the formula you are using? Because each point of att is 3.3% more damage, no matter what.

He's talking about the impact of each point of attack being 3.3% more of the base damage rather than the adjusted damage.

The issue with his calculation is that he assumes that player attack generally excedes mob defense. Admittedly in this case, the percentage increase in modified damage is less than 3.3%.

However, in the case when defense excedes defense, it's an advantage to have the multiplier affect base damage rather than modified damage.

So, the question really is whether player army attack generally excedes mob defense.

I wouldn't be so quick to assume that it is. Yes, the player has a lot of modifiers. But depending on your playstyle, you may actually use low level units (having very low base attacks) much later into the game than the enemy. In other words, I for one commonly use level 1 and 2 units well into the end game.

So, while the situation described in the OP is useful, it isn't such a cut and dry calculation. As OP mentions, despite leadership being less "optimal" from an end point calculation, the % bonus is generally much higher than even the base 3.3%. This leads to a more immediate benefit that immediately loses value over the long run. But, that early kick is nice.

[Dabrinko]

Man, I chose Leadership almost always through levels 1-10 or so. Bummer.

Better luck next time, I suppose.

[maltz]

There is another issue about the timing of taking Leadership during a level up. Here comes a few assumptions (hopefully everybody agrees on them):

1) Nobody ever reaches Lv31 because of the insane exp requirement.
2) The amount of Leadership increase is proportional to level.

Therefore, it is better to take Leadership at level 30, 28, 26.... than at level 29, 27, 25..., because you get 60(w)/50(p)/40(m) more leadership per two levels. The difference can be high as 900/750/600 leadership at the end.

Yet we know the game is highly random. In my game I found two General's Baton. After upgrading them both I walk around with 2000 extra leadership and a bunch of happy human.

[jwallstone]

Thanks for the analysis, maltz. I have to disagree with you on one point though, but I agree with you on everything else. Your conclusion that adding 1 attack increases damage by 2% is a bit misleading. The 3.3% increase is always over base damage, and is always advertised as such, and in your example, it still holds true (+15 attack gives +49.5%, +16 attack gives 52.8%, a difference of 3.3%). If you expect attack to CONTINUALLY increase your damage by 3.3%, then you are expecting an EXPONENTIAL increase in power from attack. This would be easily unbalanced and might suggest a strategy of always picking attack to get exponential increases. This is definitely not what should be the case and is not what the designers wanted.

Note that the same holds true for leadership. It is NOT exponential. You get a set increase in army power, regardless of how much leadership you already have. According to your analysis, if you already have 10,000 leadership, increasing it by 1000 gives you a 10% increase in army power. However, after getting 11000, the next 1000 only helps you by ~9%. Therefore, according to this analysis, leadership is steadily devalued throughout the game.

I would argue that this is an incorrect way to think about it. You are MEANT to increase army power linearly, not exponentially, so that sort of thinking can lead to the wrong conclusion. Attack and leadership both scale linearly, the difference is that the same attack point chosen early has the same effect on the late game as one chosen later, but the leadership choice offered grows throughout the game.

[maltz]

Upon further actual playing experience and some Russian-decoding from the fan manual, I notice some pattern in the options given. In short:

1) Leadership is offered every 2 levels. If you do not take it when it is offered, it is still available in the next level.

2) Leadership bonus is 60xlevel for warriors (50 paladin, 40 mage)

The best theoretical scenario is therefore:

Leadership -> Attack/Rage/Mana -> Leadership -> Attack/Rage/Mana...

In my game I actually got into a very bad situation:

Leadership/Attack -> Other craps -> Leadership/Attack -> Other craps

So I purposely ignored Leadership for one level and take Attack. And then everything falls to normal.

So the general idea is if you see Leadership and Attack offered together (a dilemma), there is a high chance that it will happen again 2 levels later. Plus you will again have to pick between 2 craps in the level between. To avoid this, pick Attack and postpone Leadership to the next level.

The tricky part is you want to pick Leaderships on the even levels so you land on a high point at level 30, as explained in the previous post. I just use the cheat "levelup X" to map out a good progress line... :P