I don't bother with capture locking flags right off the bat because I spend my money elsewhere and my starting items don't leave room for buying locks.

However, once creeps begin being purchased (and often times dropped, as in priests, angels and catapults are all purchased one after the other, or all the way to giants sometimes) it is time to start capping portal flags.

About the math... 

When you first take the flag, theres a net change of 15% health, since no side had the flag at the start.

From then on out, the net change is 30%. One side loses 15% and the other side gains 15%.

I dont think that is was particularily poorly presented.  Some people just werent thinking much.

If you lose 15% health and your opponent gains 15% health, the swing in health is NOT 15%. Its a bit more than 30%.

As with any description, the final goal is to be 'useful', helping our brains to a state where we can evaluate things best because we are nowhere near perfect information processing machines. On to the actual point: expressing things in different terms is often useful to us.

I don't mean you take 32% instead of regarding the flags as two events. They are both true simultaneously, just from different 'viewpoints'. One is in terms of relative hp to your opponent between start and finish, the other is in terms of absolute health.

I think it's useful to understanding to keep in mind the bonus^2 representation when wanting to comprehend both 15% bonuses together. "I know the opponent loses something and I gain something, and I evaluate both events together as roughly 2x the benefit, but what is it exactly?" It goes from a rough 2x 'benefit' - that's both imprecise and has no well-defined unit - to 32.25% relative hp difference.

I'd get into information theory here (the 32.25% relative hp does not contain the information about the two events. That's both good and bad) but then it would be getting too long.

But, overall, 32% is a useful value to know as well as everything else.

(You can skip past everything and just read the bold stuff...I think that's what's really important)

Well, here's another way to look at it (numbers are close to Lieu-'s, but I'm rounding here and there):

Suppose both players have a base 100hp.

Opponent has the flag, so opponent is at 115 hp, you have 100 hp.  You have roughly 87% as much hp as the opponent.

Now, suppose you get the boost and opponent loses the boost.  You are now at 115 hp, opponent has 100 hp.  You now have 115% as much hp as the opponent.  Your status now compared to your previous status is 115% of opponents hp vs the previous  having 87% of the opponent's hp, so 1.15/.87 ~ roughly 1.32 ==> 132% improvement between the two states ==> capping flag is good!

LoL what a mess with a simple problem.

If u take a flag is true, u gain 15% and ur opponent loose 15% so its a 30% of variation thats right... BUT this cannot be counted as a complete advantage in combat terms, P1 115 vs P2 100 is a 15% of advantage in the combat time no matters that 30 seconds ago the difference was -15% or -1500% now in the moment of combat I have 15% more (whatever) than my opponent thats the simple reality.

Lets put a silly example, if i had 30 seconds ago -1500% of life less than my opponent and now in combat I have +15% im not having a +1515% more than him, the fact is that the combat is going to be as +15% so this is the real advantage.

So... if u start a fight with 15% more health than ur opponent because u have the flag and he is not... what is exactly the advantage that u have in the fight? is a simple question.

Your theory has been explained but not accepted, your numbers are wrong and is so easy to see if u can answer the question above.

I'm siding with the ~30% net advantage of owning the flag.  Basically you have 15% more, and your opponent has 15% less than they would otherwise.  On the flip side, by losing the flag, you are losing the 15%, and they are gaining 15%.  It's double-edged. 

If capping the flag was merely a 15% advantage, then when they capped your flag you would lose your 15% advantage and they would gain nothing.  But since they also gain 15%, the swing is more along the lines of 30%.  If they for whatever reason uncapped your flag but did not cap it for themselves, that would be a 15% change.

Wow, people are worse at understanding than I thought. No, it's not "sugar-coating", the calculations are not "off". You two are are trying to apply intuition to a problem and it is failing. Ever heard of the monty hall problem?

Ok, anyway. I'll describe a simple situation in a moment, but first:

No one has ever said that your advantage in the fight is more than 15% hp. What has been said is the advantage you gain from capping a flag from your opponent is more than 15% relative hp. That's the advantage you gain in a fight over your opponent compared to before.

That's hilariously wrong. You state it with so much confidence and the numbers are right in front of your face. Before flag, as you said, player x has 1150 hp and player y has 1000. Player x survives 11.5 seconds, player y survives 10. Now player y caps the flag. x now survives 10 seconds, y survives 11.5 seconds.

x had 10 / 11.5 of the survival time of y. That how strong he is compared to his opponent.

now x has 11.5 / 10 of the survival time of y.

(11.5 / 10) / (10 / 11.5) = ~1.32

Ok, if you still don't understand, imagine this situation. x's opponent, y, has the flag capped. The hp values right now are 2000 hp for x and 2000 hp for y. That's after the 15% bonus that y is getting. The point is, they both have the same hp and are evenly matched. This should make an easier to understand baseline for the comparison.

Now, x caps the flag away from y. x's hp goes up to 2300 and y's hp goes back down to 1739 where it started. So, now tell me what x's hp advantage is. 2300 is 32% more than 1739. There you go.

- Before the cap, is was an even fight. They were exactly the same.

- After the cap, x has 32% more hp than y.

- Ergo, the act of capping the flag from your opponent results in a 32% benefit to your hp between you and your opponent

Q.E.D.

If it "seems" wrong then it's just you. (or, you might be confused about the terms used - possibly understandable depending on maths background)

you can't really term it a '30% advantage'.  The game is not really about flat HP/DPS blocks going at eachother - there are too many other variables.  Maxxy showed how those numbers don't work even in a basic autoattack contest, let alone when abilities/positioning/tactics enter the mix.

then there is that many fights are not straight up, but rather endurance/attrition games where health regen and mana management are typically more important.  Sheer health mostly just prevents ganking.

at the extremes, some builds derive little benefit from health increases. This is especially the case for non-burst damage builds like Ice TBs and Shield/Mulch QoTs/

finally, in terms of sheer fighting power, a 15% increase in HP is only a 7% increase in power.

if that doesn't make sense to you, game it out

Unit A has 100 HP and 20 DPS. Unit B has 200 HP and 20 DPS. Theoretically unit B is twice as powerful as unit A. So lets match 10 unit A against 5 unit B. 

second 1 - side A has dealt 200 damage, side B does 100 damage. One A and one B die.

second 2 - side A has dealt 380 damage, side B has dealt 180 damage.

second 3 - side A has dealt 580 damage, side B has dealt 260 damage. One A and one B die.

second 4 - side A has dealt 740 damage, side B has dealt 320 damage. One A and one B die.

second 5 - side A has dealt 880 damage, side B has dealt 360 damage. One B dies.

second 6 - side A has dealt 1020 damage, side B has dealt 380 damage. Side B is dead, side A wins in a landslide.

the best approximate power of a unit is the square root of the health times the square root of the damage.

If you think that spouting out QED makes you right then you are mistaken. My maths background I assure you is fine enough (BSc. in Comp Sci). You are looking at 2 things as if they are dependent but they are NOT. This is the FLAW in your calculations. First thing, you are comparing past to present when at each given time your enemy has X hp and you have Y hp. You should compare each time frame for survivability.

I am sorry you think you are all high and mighty and instead you should think about proving yourself the way you prove math statements (meaning in both directions, not only in one direction).

In the case of your calculation 2300/1739 = ~1.322, this is indeed 32%. Now lets look back at the other direction: if the lower health party grabs the flag again. We are back to square one: an equal 2000/2000 = 1. Where is your 32% bonus now?

If you have a proper statement with knowledge on how to prove it, please go ahead and prove me wrong. I have no problem admitting I am mistaken. If you are going to act like you are some kind of sureshot, then please stop posting in this thread. In the academy this isn't the way that things go.

The 32% of ilusional advantage that u say means nothing, if ur theory with ur weird calculations give to u a 32% its ok but means nothing.

The fact and the ONLY fact is that if u take a flag from an oponent of 15% HP u have 15% more HP that u had before and ur opponent have +0%. Lets explain it more easy, if u get a 15% HP flag from ur opponent and both have 100 HP now u have 115 and ur opponent have 100 this is the only reality, a 15% over your oponent this is the ONLY advantage u have over him.

U said "No one has ever said that your advantage in the fight is more than 15% hp" so who the f.. cares of ur 32% meansnothing numbers? cant be aplied anywere so whats the point?

U can develop any smartass weird theory and tell ppl that the problem is their "maths background" but this dont make u be right, for your information.