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Compiled by Andrew ":8:Quetzal" Plucker
Reference: ngWorldStats FAQ

Number of times a player kills another player.
Note: While individual game stats include bots, overall ranking exclude bot kills.

Number of times a player dies as a result of their own action such as splash damage from their own weapon, falling, drowning, being shot into space, etc.

Kills minus Suicides and Team Kills.

Number of times a Player is killed by another player (does not include suicides or being killed by a teammate).

Number of times a player kills someone on their own team.

Number of times a player is killed by someone on their own team.

7 points per Flag Capture
4 points per Flag Kill
1 point per Frag
Flag Captures
Number of times a player touches the opposing flag with their own flag.
Flag Kills
Number of times a  player kills an opposing player who is carrying your flag.
Flag Assists
Number of times a  player  carries the flag at least once during a successful capture, but does not actually capture it themself.
Flag Saves
Number of times a  player picks their own flag up causing it to return to base.
Flag Pickups
Number of times a  player picks up the flag, either in the field or from the opposing base.
Flag Drops
Number of times a Player drops the flag regardless of cause.

For Kills :  Kills / (Kills+Deaths+Suicides+Team Kills)
For vs another Player : Kills vs Player / (Kills vs Player + Deaths by Player)
For a Weapon :  Kills with Weapon / (Kills with Weapon + Deaths while holding the Weapon + Suicides with the Weapon)

Frags divided by hours played.
Frags Per Hour can be used as a relative indicator of skill in a game where different players entered the game at different times.

A players Average Time to Live.
Average amount of time in seconds a player lives live after each respawn in a game.

The average ping of a player during a game. Ping is the round trip delay in milliseconds that your computer has to the game server. Although there are other factors that contribute to the overall quality of your connection, in general the lower your ping the better.

Time in individual game stats is minutes played.  In Total Game Stats it is expressed in hours.

In Unreal Tournament, a Player who kills a large number of enemies without dying gains the special status of being on a "Killing Spree." List of the consecutive Frag counts at which various spree status is granted:
5 = Killing Spree!
10 = Rampage!
15 = Dominating!
20 = Unstoppable!
25 = God Like!
Sprees are promoted to the next level when obtained, meaning a single instance of 10 kills without dying counts as a single Rampage, not as a Killing Spree and a Rampage. Individual Sprees and  why they ended during a particular game are listed in the Game Summaries section of that games ngStats.

Multi Kills are noted for each player. Every time a player makes a kill they have up to 3 seconds to make another kill. Go from one kill to two in less than 3 seconds and it is a Double Kill, get another kill in less than 3 seconds and it is a Multi kill, etc. The complete list in order is:
Double Kill
Multi Kill
Ultra Kill
Monster Kill
Just as with Killing Sprees, Multi Kills are promoted to the next level.  This means if you kill 5 or 15 Players with a single Redeemer shot for instance they both will be recorded as a single Monster Kill.

Kills due to a precise shot to the head of the Victim, causing instant death.

First player to get a kill in a game.