"The expected number of top 100 players in a game would not matter if the idea is that we are merely looking for a mean of kills per game per player (or kills per appearance) and the top 100 is the largest sample available for a month."
>Yep, that's exactly what I had in mind.

"Deadliness would be a combination of inherent dangerousness and likelihood of encounter."
>I guess the best indicator of deadliness is then the kill count (if someone has already played enough games so that his k/g reflects his inherent dangerousness). :)

The likelihood of encountering a player should be proportional to the number of games they play in a month, if they play twice as many, a random encounter would be (roughly) twice as likely.

Btw. I don't think that many people think of deers as particularly "deadly" animals. Sure they cause a lot of accidents, but these collisions hurt them as well so they would try to avoid these if they could, so it's just an unintended consequence of their carelessness. Similarly, if an inherently "gentle" player plays a lot of games, they can amass a huge number of kills in a month, but few people would think of them as "deadly" fellows.

I think what most players would care about is NOT the a priori likelihood of getting killed by a certain player, but rather the likelihood of getting killed by them _provided_ they sat at the same table.

The likelihood of being killed by a particular player when you sit down at a game is a function of that player's kills per game stat and the confidence you can have in that stat, which goes at the square root of the number of games. It would not depend on whether that player's kills per game is above or below the mean kills per game.

KPG differs from the current incarnation of PPG in at least one crucial aspect. It's certainly not a zero-sum game, you can never get negative kills. You can (and will) get a negative PPG if you "lose" your first regular game, even if you start at 0 pts.

Before one person has even played one game you can be certain that the probability of getting killed by them is not zero.

If a robot is reliably capable of achieving a certain k/g ratio, its kprg will increase as its number of games increases, but its threat level will certainly not. Its kprg will (slowly) tend to infinity as its game count tends to infinity but the conditional probability of getting killed by it provided that both you & the robot sat at the same table should not increase as its number of games increases.

The robot's threat is kills per game. Your confidence about what the robot's true threat is goes as the square root of the number of games. Your best estimate of the relative threat of two robots who have a different number of games is their kills per game times the square root of the number of games, or kills per square root of number of games. In math lingo, stat divided by its standard deviation.

AFAIK (but correct me if I'm wrong) "relative threat" is not a well-defined concept in either mathematics or statistics, as opposed to "(conditional) probability", "likelihood" or "odds" that all have a stringent and universally accepted definition.

So could you please define what you really mean by "relative threat" - cause all those previous examples (savage deer and athletic tortoises) that you gave were going against my intuitions about what I would perceive as deadly (or quickly)*?

KPRG compresses information about killing efficiency and activity. It is highly correlated (0.744 in the top100 sample of Sept.) with #games. The correlation coefficient is not as high as the one between #kills and #games (0.905 in Sept.). It's only moderately correlated (0.490 in Sept.) with (#k/#g) - which would not be such a big problem**, but even you have admitted that someone's "natural" (or inherent) kills to games ratio could be an adequate indicator of killing efficiency if there was any way to measure that directly.

I know that it's not a convincing argument but I simply have an ill feeling that KPRG reveals a lot more about how active a player is than about their "threat level".

People with very few games invariably finish near the bottom of the KPRG rankings. I think it'd be wrong to assume that they would pose a minor (death) threat if they sat at the same table as you. It's more like you can only give an unreliable estimate about their threat level.
_____
*If I just wanted to place something at either the tails or near the peak of a bell curve, I would certainly demean it before dividing it by its std. error.
**After all, even KPG could be used to rank people according to their deadliness. I would even find that more meaningful than KPRG if people with a very low number of games are excluded from the rankings.

Kpg is the estimate of the measure of deadliness in a game. I think we three agree on that. The root of games played has two uses: 1) it contributes to the confidence level we can attach to the deadliness of a player in a game and 2) it is used in comparison of relative deadliness of players, incorporating their likelihood of appearing in a game.

Thanks, I see your point now. "2)" was something that I had been suspecting for a while, but I'm glad that you have confirmed it.

When I suggested subtracting E(k/g)*sqrt(g) from KPRG I specifically wanted to discard all information about someone's "likelihood of appearing in a game".

In my opinion, as soon as a game begins with both me and that other guy sitting at the table, the likelihood of an encounter becomes irrelevant (even if it was unlikely 5 minutes ago - it is now certain).

Suppose that the only piece of information you have about the guy is that his KPRG rank is very low (near 100). That could mean either of two things: a.) he plays infrequently; b.) he is relatively peaceful and rarely kills anyone. If b.) is the case he's only a minor kill threat, but a.) should suggest that he might even be a dark horse. As #games and KPRG are highly correlated, you could think that "a.)" might be the more likely reason.

OTOH, the alternative ranking is preserving more information about the K/G ratio (their correlation coefficient was 0.9 in Sept.), while #games is still correlated with the absolute value of "(k/g - E(k/g)*sqrt(g)". (Information about #games is stored in the absolute value of the variable, while information about k/g is stored in both the sign and the absolute value.)

If you see someone with a very low alt.deadliness ranking, you can be pretty sure that they either have a very low K/G or that they have a below average K/G ratio after a large number of games. Both possibilities suggest a low probability of getting killed by them.

I AM DEADLY.

You guys do realize that wertrew uses proxy accounts right?

You don't need a crystal ball to see it. Play a couple games with him. ;)

I will look into it. The easy way would be to spy on wertrew's games to see what other players may be his proxies. The hard way would be to look for players whose attack defend ratios sum to the modulus of wertrew's.