What is the formula for calculating the value of a kill or an assist? Is it worth more gold for a team to get an assist and kill (AKA KS=kill securing) or is it better to allow the carry to get the whole kill with no assists?
First blood - first kill of the game - is worth 400 gold to the person who gets the kill.
After that, a kill's base value is 300 gold for the person who gets the kill. This number is then modified based on a "death streak", by 15% (iirc) for each consecutive death. This is to reduce the effect a bad player has on a game. So a person who dies 5 straight times (without themselves getting a kill) is worth less than 300 gold. I think that's 133 gold. Note that if a player on a death streak gets a kill their value resets. Conversely, players who rack up kill streaks become worth more money. They accrue a bounty that is awarded to whoever kills them and end their kill streak. You can see the bounty values here.
Note that executions (deaths to a turret, minion, or neutral creep) do not count as kills.
Assists are trickier. Anyone who does damage in the last 10 seconds splits money from the "assist pool", which is 58% of the value of the kill. The assist pool is divied up among all assisters. Also, other things can earn an assist, like healing the person who gets the kills. Other buffs might contribute as well but I am unsure.
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