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Tips and Hints Different solutions, tips and hints.

 
 
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  #29  
Old 04-28-2009, 09:46 PM
jwallstone jwallstone is offline
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That's the wrong way to think about Attack and Defense. You can't simply subtract the bonuses. Between 100 and 33%, there is indeed a 66% difference. But you need Defense-Attack=60 in order to get that 66% reduction. Why? Because each point of defense gives a smaller % than the previous one. Having D-A=60 reduces damage to 33.3%, while D-A=59 gives 33.7%, only a 0.4% difference.

Now, you're probably thinking that means Defense is worth less the more you have. But that's completely the wrong way to think about it. In fact, this system is completely fair and values Defense and Attack equally. Like I said, you can't just take the DIFFERENCE between the percents. For example, with A-D=30, you get a 100% bonus to damage, doubling your damage. But if D-A=30 gave a 100% reduction, that means you get ZERO damage, making you invincible against that troop. Clearly, this is not equal and would make Defense much more useful than Attack.

In fact, both Defense and Attack are equally valued. Attack increases damage output by 3.3% per point, while Defense increase how long you live by 3.3%. Give a troop 30 more defense, it'll live 100% longer against all attacks. It's very simple. In fact, the whole business about having different equations if D<A and if D>A can be misleading. They both ALWAYS give 3.3% more damage or 3.3% more life, regardless of what the other troop's stats are.

If you look at it mathematically, Attack helps as follows: Damage = BaseDamage * (1+A/30). Now, if Defense equals Attack, then the troop should do BaseDamage, right? So you divide by (1 + D/30), and voila, you have Damage=BaseDamage. This also tells you what the formula for defense should be: Damage = BaseDamage / (1+D/30). That's why Defense gives less % difference the more you have: because it gives a factor of 1/(1+D/30). You can see for yourself that if you take the derivative, you get 1/(30*(1+D/30)^2). But the % difference doesn't matter, it's still giving you 3.3% more life with each point! In fact, if Defense modified the unit's life instead of the attacker's damage, you could have it simply increase hit points by 3.3% for the purposes of that attack rather than reduce damage and get the exact same overall effect.

Last edited by jwallstone; 04-28-2009 at 09:53 PM.
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