# Calculate your Maximum Possible Respect!

Did you know that there is now a maximum respect you can earn that is based on your skill level?

In the old system, dying made you lose a fixed amount of respect. As long as you could earn more than that fixed amount before you died, your total respect level would rise. This increase in respect could continue forever, as long as you kept playing. There was no practical limit to the amount of respect you could earn. However, since the update, you now lose 2% of your current respect when you die. This presents an interesting situation.

Think about how much respect you usually earn before you die. If the amount you earn is more than 2% of your total respect (which you lose on death), you end up with more respect then you had since your last death. Unfortunately, if the respect earned during those kills is less than 2% of your total, you end up losing more respect than you earned before you died. The more respect you have, the more you lose, since 2% of a bigger number is, well, bigger... so...

To put it simply, your respect will eventually be so high that you cannot earn more than 2% of your total between deaths with your personal level of skill, and your respect - although transient - caps out and remains within a few tens of thousand.

So where will your respect max out? That can be calculated. You need to find the point where 2% of your respect is equal to the number of kills you get on average between deaths (your K/D) times the amount of respect you get per kill, on average.

[MAX RESPECT] x .02 = (RESPECT PER KILL) x (K/D)

Based on (for me):

Kills: 712
K/D: 26.4
Total respect: 280,000

The next variable we need to know is how much respect you get per kill, on average. This can be roughly estimated by dividing your current respect by the number of kills you have, but keep in mind that this is inaccurate since you lost 2% of your respect every time you died. A much better estimation can be done with the sum of a convergent series: For those who are unfamilar, this expression sets the total of your current respect to the sum of [your respect - 2% of your respect] iterated the number of times you have died. Solving for n, we get:

n ≈ 401

Note that the simple estimate would have given only 393, and that although 401 is still an estimate (it assumes you always get K kills per D deaths in your K/D), it is a much better estimate. The only way to calculate this exactly is to process the server logs, but this estimation will be quite close.

Understanding this, the rest of the math is easy using the equation above:

[MAX RESPECT] x .02 = (RESPECT PER KILL) x (K/D)

[MAX RESPECT] x .02 = (401) x (26.4)

[MAX RESPECT] = 529,320

This means that if I continue to average 400-ish respect per kill, and my K/D continues to be around 26, I can never achieve more than 529,320 ± 10,586 respect regardless of the number of kills I get or time I play. Further, it would take an infinite amount of kills at this level of performance to reach that number, so practically speaking I will never see this number, only creep closer and closer to it. It will become harder and harder to gain respect as I approach the maximum theoretically achievable (with infinite kills) of 529,320 ± 10,586 with my current skill and play style.

Of course, I could change this trend by increasing my K/D and respect per kill, but with a dataset of over 700 kills, the confidence interval around this value is pretty small for my style of play, which is to say that this number will remain quite accurate unless I decide to kill myself 50 times or something dumb like that.

This is corroborated by using some newer personal stats of 377,000 respect, a K/D of 30.9, and 1080 kills. My max respect based on these numbers is now 551,000 ± 11,021, showing that I have slightly improved my skill as a player (but only by 4%)!

In conclusion, the respect system is interesting now because it is more of a metric to gauge how well you perform rather than how long you have been on the server, and everyone will eventually cap out based on their total performance.

Neat!

For giggles, I have built a small Google spreadsheet that will estimate this number for you, minus the calculus but with a "fudge multiplier" that will keep the solutions more accurate to the real math (which Google nor Excel have the capability of doing concisely.)