[Seducer]

I was playing Call of Duty Modern Warfare 2 when I was thinking that in order for some people to have positive kill/death spreads (killed more often than they died), other people absolutely MUST have negative kill/death spreads (died more often than they killed).

Kill/death spread = number of people you killed - number of times you died

My intuition tells me that in any given death match, in order for some people to have positive kd spreads, some others must have negative kd spreads. I challenge you to prove this with logic in a more or less formal way and also see what rules exist for this situation. I mean it seems like it would be true, but can you show with logic that it absolutely is true? Also I want it to be shown for the situation of more than two people playing, because if it's just two people, then it's too simple. I think the "team death match" game type usually has 16 people playing.

[cannotseethe]

Originally Posted by Seducer To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

I was playing Call of Duty Modern Warfare 2 when I was thinking that in order for some people to have positive kill/death spreads (killed more often than they died), other people absolutely MUST have negative kill/death spreads (died more often than they killed). Kill/death spread = number of people you killed - number of times you died My intuition tells me that in any given death match, in order for some people to have positive kd spreads, some others must have negative kd spreads. I challenge you to prove this with logic in a more or less formal way and also see what rules exist for this situation. I mean it seems like it would be true, but can you show with logic that it absolutely is true? Also I want it to be shown for the situation of more than two people playing, because if it's just two people, then it's too simple. I think the "team death match" game type usually has 16 people playing.

[HIDE="the reasoning"]The key insight is that when you sum the kill/death spreads of all players, the result is 0.

You can see this by induction, for instance. At the very beginning of the game when no one's killed and no one's been killed, everybody's kill/death spread is 0 so the sum of kill/death spread over all players is also 0. Now, say player A kills player B. Player A then has a kill/death spread of 1 (1 kill, 0 deaths), and player B has a kill/death spread of -1 (0 kills, 1 death). 1 + -1 = 0. More generally if, at any point in the game, player A has k kills and l deaths and player B has m kills and n deaths, when player A kills player B, player A now has k+1 kills and l deaths while player B has m kills and n+1 deaths. The +1 for player A and the -1 for player B (deaths are subtracted) sum to 0, and if the overall sum of kill/death spreads was already 0, it will remain so. Essentially, the sum of the kill/death spreads of all the players remains constant throughout the game, and since it begins at 0, it remains at 0 throughout. This assumes, of course, that the number of players in the game is not changing (players can't join or quit in the middle).

Given that fact, it immediately follows that if one player has a positive kill/death spread, there must be at least one other player who has a negative one. A sum of positive or 0 kill/death spreads (with at least one positive one) cannot be 0.[/HIDE]

[Vagrant]

Thus, a 1:1 k/d ratio is considered "good" in a game -- because you are capable of balancing every death for a kill, meaning that you surpass 50% of the population.

Last I remember, my K/D spread was 14500 Kills:8000 Deaths, or a K:D ratio of 1.81:1. My headshot percentage was around 11-12%. And while I think I'm a good player, I've fought players who are far better than me (being sniped in the head through a wall sucks).

[Akzis]

99% of the people in MW2 do not go for headshots; you simply do not have enough time to get a headshot reliably. Especially given the low amount of damage a player can take before he dies.

K/D spreads tend to be averaged around the middle: most people have something ranging from 1.3 to 0.7. It gets rare and rarer to see people past such points.

[Vagrant]

	Originally Posted by Akzis To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	99% of the people in MW2 do not go for headshots; you simply do not have enough time to get a headshot reliably. Especially given the low amount of damage a player can take before he dies.

Particularly in hardcore mode, I just aim for torsos (1-3 bullets to drop someone). Non-hardcore mode, I aim up a bit more.

[SirJac]

I don't know the mechanics of MW2, but suicides/friendly fire usually upset kill/death spreads from being strictly zero sum. For every kill there is a death, but there isn't always a kill for every death.

[DewFuel]

Originally Posted by Seducer To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

I was playing Call of Duty Modern Warfare 2 when I was thinking that in order for some people to have positive kill/death spreads (killed more often than they died), other people absolutely MUST have negative kill/death spreads (died more often than they killed). Kill/death spread = number of people you killed - number of times you died My intuition tells me that in any given death match, in order for some people to have positive kd spreads, some others must have negative kd spreads. I challenge you to prove this with logic in a more or less formal way and also see what rules exist for this situation. I mean it seems like it would be true, but can you show with logic that it absolutely is true? Also I want it to be shown for the situation of more than two people playing, because if it's just two people, then it's too simple. I think the "team death match" game type usually has 16 people playing.

True to some extent, since the sum of all kills subtracted from all the deaths must be less than or equal to zero (suicides count as -1). also, if people with negative kd spreads leave the server, you can have positive k/d spreads without someone having negatives.

if you are talking about global statistics, then you would be correct.

[Photolysis]

Kills are zero sum, as long as you consider all the players who played in that particular game, even if they left the server, so yes, for anyone to get a positive spread it requires that the sums of the K/D spreads for all opponents who be negative, unless someone on your team is doing equally bad or worse to counter this.