I play some teams who buy flag locks early, like levels 1 - 3.
I think this is a waste of money. 250 GP is important early when you're racing towards your 1500GPish item. Unless a specific flag is required for your strategy (short cooldown on TB), don't waste your money so early when gold is sparse.
A good time to start locking is when enemy buys priests. You invest 250GP to lock the middle flag in Cataract. This buys you the time to go farm the priests in another lane and earn back your gold. Flag lock allows you to hold two flags for effectively 0 cost.
no, I'm afraid it has been added to the annals of shame, and all your favor has been revoked.
edit: new demigod idea -- Quantitactician: throws numbers at opponents until they feel ashamed for not understanding them, then end up using their own abilities to finish themselves off.
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%.
2 statements about the math:
1) Lieu is basically correct but has presented the conclusion very poorly by leaving out many intermediate steps.
2) the best way to understand the action is to break down the events into 2 stages (which is what happens in game anyway), where each stage affects a different quantity. you can then go ahead and combine the net effect of the 2 stages and get Lieu's numbers, but thats not particularly helpful in my opinion.
stage 1: flag goes from opponent control to neutral
what happens?: opponent loses the bonus, so if its a health flag the ratio of change is 100/115 with respect to opponent health.
stage 2: flag goes from neutral to friendly control
what happens?: you gain the bonus. so if its a health flag the ratio of change is 115/100 with respect to friendly health.
i see no point in combining those 2 numbers because the 2 events are affecting separate, independent quantities. the only conclusion statement that we need to know can be said in plain english. your opponent loses something and you gain something. the effect is 2 way swing.
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%.
I guess it depends if the flag is neutral or not when considering what the difference is. /Big booming voice: The Forces of Neutrality have Won the Thread!
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.
Beat me to it.
(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!
However, if you do not lock the flag, you're still likely to hold it 50% of the time, unless the other team locks. Thus, capping the flag is really only a 15% boost as a whole, given in large doses and delayed.
If the other team locks it, it's a whole new ballgame.
Simply put, flag locks ARE important. No matter what the OP thinks.
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.
No, your real advantage in owning the flag is 32% more hp. It's been explained arleady to full extent in this thread. There are two possible states, either you have the flag or the enemy has the flag. Those are the starting and end points. It's one or the other and going from one point to the other point gives you two 15% advantages.
For the last time, the real advantage in having that flag over your opponent is not 15%.
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.
The number "32%" that you keep waving around is wrong. Due simply to the fact that each side has a different health number. If you have one player with 1000hp and another with 2000hp you can see the jump in the difference become more substantial. From 850hp if the lower health character has the flag to 1300hp if the higher health character has the flag.
More so, your calculations are still off. This is also due to non constant dps between enemies as well. Even with Erebus' bite. If Erebus does 250dmg and heals 250dmg that does not mean he "has hit for ~500dmg". If you out dps Erebus then those 250dmg he healed are worth less.
Anyway, if someone lost 1150hp to 1000hp due to flag and the other gained 150hp to get up to 1150hp from 1000hp then no matter how much you sugar coat it, the difference is no where near 32%. Factor in a constant 100dps and one survives for 11.5 seconds while the other for 10 seconds.
Capturing the flag for the first time IS EXACTLY EQUIVALENT to recapturing the flag (one side has the flag, the other does not). In the first case (given the same starting hp) you get 15% more than your opponent. In the second case you also get *gasp* 15%. The loss of the potential to own the flag does NOT factor in a negative bonus therefore making your bonus seem "larger".
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.
Im going to repeat myself because this is the neverending story...
If u answer this question u will see easily the reality.
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)
The reality is that if you do not have the advantage, HE DOES. You are only taking the bonus it gives you into account, and not that you are depriving him of the hp bonus as well. Unless you play against people who only uncap flags and do not cap them for themselves.
Yes, you have a 15% advantage. But if you didn't have the flag, it wouldn't be even, you would have a 15% DISadvantage. So the net difference is 30%. Got it?
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.
Nitpicking, but it's 32.25% (1.15<sup>2</sup>). Don't want people to get the wrong idea.
30% might imply it's 15%+15% when it's not. Crucial difference in understanding. For flags like xp it's 44% rather than 40%, which is a big difference.
Edit: Yes, DeadlyShoe. It would be making the assumption that every point of hp helps you win exactly as much as the last, which of course we know isn't true because of burst, healing, regen, etc. It's roughly true, however. The main thing is that when you state it, you have to be very careful to say "32% more hp relative to your opponent" which is accurate (it makes no other claims, including how much health you actually have). Said that way, there is nothing wrong with it, you just need to be careful when making inferences from it such as "32% more time to live", which would be dependent on other damage factors and such.
I've been very careful to try and state the flag hp advantage as such.
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.
Ok, a ~30% hp swing specifically is what I meant. Not a 30% advantage across the board. I thought that was assumed.
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.
Actually, are you sure about those values? Looking at hard numbers...
If you and your opponent have 1000 hp each. You cap the flag first so now you have 1150 hp. Then you're forced to retreat, so your opponent caps the flag. He now has 1150 hp and you're back to 1000. So, the absolute value of the gain/loss is 300hp which = 30% of the initial 1000hp
However, say your opponent has more hp than you? Like 2000. Now they gain 300hp while you lose 150. So the swing is 45% of your life? It's difficult to assign a number to this flag capping at all everyone's hp is unique and relevant to what?
Anyway, all I'm agreeing with is there is a gain and loss aspect of capping flags that shouldn't be overlooked.
Just because you don't understand the 32% it doesn't mean it means nothing. If you're calling them "weird calculations" then that's no argument at all.
I don't know how you have failed to understand this simple concept. The flag does not simply give you 15% more hp. At the same time you are also depriving the enemy of 15% hp. At one, single point in time both these things are taking place. How can you just flat-out state your only combat advantage is 15%? If you were both 100 and then you went to 115 then that's a 15% advantage, right? Well the situation is that you aren't both at 100. When you are at 100 the enemy is at 115. Explain how there is only your own personal 15% going on.
Ok, maxxy. You seem to be completely hung up on absolute values of hp. No one is saying you have 100 hp and then you go to 132 hp. I'm using the word 'relative' here. I am and have been talking about your hp as it compares to your opponent's. One hp value is not changing the other's value which you say is the flaw. Of course they are not dependent on each other. What I am doing is expressing one hp value in terms of the other value. We are working in percentage hp advantage here. This is just expressing your own hp as a percentage of your opponent's. When we want to figure out how much of a % benefit the flag gives you this is the comparison we want to look at. If we wanted to find how much stronger capping the flag made you in relation to grunts then the 32% would not apply. It is simply a measure between you and your opponent. A ratio.
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