To Lieu- valiant effort. I couldn't resist taking a stab at it myself

I think that people who are arguing against the 32% swing are failing to understand some main concepts, so let me see if I can provide some insight.

1. The flag rarely, if ever, is neutral. This means that at almost any point in the game, one of side will have control of the flag and receive the buff. Because of this, one needs to take into consideration the loss of the buff by one side and the gain of the buff by the other side when calculating the *advantage* of completely capturing a flag.

2. Yes, one side loses the 15% buff and the other side gains the 15% buff, so when you capture a flag, you only gain 15% of your health, while the other side is returned to baseline, but Lieu- is talking about the relative change in *relative* strength, somewhat of a confusing idea. This is one way of looking at things, you could also talk about the absolute change in relative strength.

Example 1:

suppose TB has T_0=1410HP (lvl 1, no items) and Rook (lvl 1, no items), who has control of the flag has R_1=2185HP. TB's relative strength to Rook is

a) str_0 = T_0/R_1 = 1410/2185 = 64.53%

Now, suppose that TB makes the flag neutral. Rook loses his 15% bonus, Rook goes down to his baseline health (call it R_0). we have

b ) 2185 = 1.15*R_0 ==> R_0 = 1900

Next, suppose that TB remains near the flag, and completes the capture. TB (and his team) gain the 15% bonus. TB's new health is given by

c) T_1 = 1.15*T_0 = 1.15*1410 = 1621.5

Now TB's relative strength to Rook is given by

d) str_1 = T_1/R_0 = 1621.5/1900 = 85.34%

So the absolute change in relative strength is

e) **Abs_1** = str_1-str_0 = 85.34% - 64.53% = **20.81%**

and the relative change in relative strength is

f) **Rel_1** = str_1/str_0 = 85.34%/64.53% = 132.24% = 100% + **32.24%**

Example 2:

suppose TB has T_0=3500HP (lvl 20, no items) and Sedna (lvl 20, no items), who has control of the flag has S_1=4352.75HP. Then TB's relative strength to Sedna is

a) str_0 = T_0/S_1 = 3500/4352.75 = 80.41%

Now, suppose that TB makes the flag neutral. Sedna loses his 15% bonus, Sedna goes down to her baseline health (call it S_0). we have

b ) 4352.75 = 1.15*S_0 ==> S_0 = 3785

Next, suppose that TB remains near the flag, and completes the capture. TB (and his team) gain the 15% bonus. TB's new health is given by

c) T_1 = 1.15*T_0 = 1.15*3500 = 4025

Now TB's relative strength to Sedna is given by

d) str_1 = T_1/S_0 = 4025/3785 = 106.34%

So the absolute change in relative strength is

e) **Abs_2** = str_1-str_0 = 106.34% - 80.41% = **25.93%**

and the relative change in relative strength is

f) **Rel_2** = str_1/str_0 = 106.34%/80.41% = 132.25% = 100% + **32.25%**

So as you can see, the absolute change in relative strength depends on the exact numbers, while the relative change in relative strength is a constant, and therefore a very useful number. It's useful because it gives you an easy way to compare your HP to another hero's HP before and after the flag capture. The 15% is only useful for comparing your HP to another's if you have a calculator with you.

Here's how to use the 32% in practice:

Suppose TB has about 3/4 (75%) of the health of Sedna, who controls the health flag. TB knows that if he captures the health flag, they will have the about the same health. Why? because he knows that his relative strength will increase by a factor of 32% (about a third). One third of 75 is 25, and 75+25=100. His final relative strength to Sedna will be about 100%, meaning they both have the same HP.

This tells us that the higher your relative strength to the enemy, the more you stand to gain if you captures the flag, and the more you stand to lose if your enemy captures the flag.

Conclusion: Flags are important.

Edit: For those of you who may doubt these numbers, let me say that I am currently working toward a Ph.D. in math, and was a math major in undergrad. I solve many math problems on a daily basis. I also tutor high school student in math regularly, so I know the high school curriculum in and out, and I can tell you that this problem has about an 8th grade level (give or take a year or two, depending on the student's ability). If you disagree with the numbers, then I suggest you reread my post, because there is something you don't understand. If you read it a second time and still don't agree with the numbers, please feel free to PM me with whatever your complaints are.