I recall a story that's been around for awhile. Something about a tortoise and a hare.

I guess you are talking about this tale: http://childhoodreading.com/?p=3

So you want to have an indicator where the hare is beaten by a tortoise? OK, I think we can agree to disagree at this point.

Let's sum up the most important facts about this KPRG and the alternative indicator that I've suggested.

___KPRG___
Formula:
Kills/SQRT(Games)

Characteristics:
Tortoises beat hares (Rewards people for both deadliness and diligence; a guy with a low-ish kill/games ratio of 0.1 can beat any score provided they play enough games.)

___Normalized KPRG (my proposal)___

Formula: (Kills - Global.Average*)/(Games^0.5)
_______
*Global.Average = (The sum of kills achieved by the players in the top 100)/(The sum of games the top 100 players played) = 8933/23668 = 0.377429440594896 in August)

Characteristics:
Hares beat tortoises (Players with a higher than average kill/games ratio always beat players with a lower than average kill/games ratio.)
Diligent hares beat lazy hares (Rewards people for diligence if they can consistently keep their high kill/games ratio; a guy with a k/g ratio of 0.5 and 100 games beats a guy with a k/g ratio of 0.5 and 50 games.)

I will also provide the alternative deadliness stats for August:

4.37 rednttautology
3.87 wertrew
2.99 Noobie
2.95 shirahoshi
2.42 greekboi
2.20 the die
2.14 bcmatteagles
2.12 TriG8
2.11 marcb
2.05 kdice 123
2.00 beyazguvercinus
1.99 W00PW00PW00P
1.56 michele
1.54 mrlee
1.40 BigDaddyKane
1.17 ugolino
1.17 OneShot7
1.13 morrinson
1.11 tajmtoedaj
1.04 jsonproxy
0.94 Whitehawk
0.91 ji-jo
0.88 Nokia3310
0.84 jf220
0.76 lipos
0.59 6v16to6111111to6
0.57 Honyo
0.56 Soromon
0.54 spanky6
0.50 special k dice
0.49 Berna
0.48 Chris_Fun
0.46 Beybi_Sistr_Hors
0.44 123
0.35 jurgen
0.32 joe2me
0.17 vino_en_carton
0.14 siccannibal1
0.07 peter luftig
0.01 Aken
0.00 twinky
-0.01 gogi
-0.04 stakaboo
-0.08 musetel
-0.08 Jan Paul Kraemer
-0.09 Beer Me!
-0.09 diceptr
-0.15 masticore
-0.17 Lex Lauher
-0.18 rocka09
-0.20 Voo
-0.21 themall
-0.22 danceswithdices
-0.25 Vermont
-0.32 TheKnightWalker
-0.34 GreGGwar
-0.36 integraI
-0.40 Kakkap
-0.40 shatteros
-0.42 SprintTx
-0.44 22 april
-0.45 LemonSong
-0.45 Monsanto
-0.46 rap1d
-0.52 Manfred Singh
-0.53 Ninjamonkey
-0.54 bivo
-0.55 alex_sfb
-0.57 Carloos
-0.60 fuzzymcfuzz
-0.63 svran
-0.68 Rebel9
-0.69 Gonna4v4U
-0.79 63 belly
-0.81 PureOdyssey
-0.92 no_name2
-0.96 Who'sNutz?
-1.06 farq
-1.12 mattz1
-1.17 Gurgi
-1.26 parsifal
-1.29 dr. zoidberg 69
-1.30 negramarta
-1.37 moulue
-1.38 franklyghost
-1.40 javanse
-1.40 ikoko
-1.50 Lil Johnson213
-1.57 {A}Monkey SLayer
-1.64 dalius1
-1.71 kdiceplaya!
-1.74 Ledexo
-1.84 gontis
-1.86 Slinus
-2.06 @jeremywright
-2.17 1a2b
-2.52 inipi
-2.69 sablja
-3.23 caesar-blue
-3.55 spman

Of course the ranking of caesar-blue is way too low, because (s)he played most of his/her games on 2-player tables.

Ew, sorry, the formula for my proposal is
Formula: (#Kills - Global.Average*#Games)/(#Games^0.5)

Where # is "the number of" and Global.Average is 0.377429440594896

Since your stat is the difference between two normal distributions, its variance will be twice as big so you have to divide each player's stat by an additional sqrt(2). The spread will be reduced but the relative positions of the players will be unchanged.

Hmm, that's a valid concern, but I'm not sure the exact numerical value would have a meaningful interpretation anyways. (E.g. it's not as if someone with double the score, or +2 score would be twice as skillful.)

Moreover, I think the variance would be twice as big if the two distributions are independent or at least uncorrelated. [Var(X-Y)=Var(X)+Var(Y)-2Cov(X,Y)].However, I'd assume that both should be positively correlated with #games, cause that's the reason I advocated including the second term in the first place.

But yeah, the stat can be divided by a constant and it wouldn't change the rankings. I'm more concerned about the validity of using the top 100 weighted k/g average as the global average, perhaps using a larger sample (averaged over more players and/or multiple months) to calculate the expected value of k/g would be better. Or not.

You are correct about the covariance. If you had stated your stat as kills/game minus global average, it would be stat minus a constant. Then multiply by sqrt of games and you have your current stat.

For September you will probably have to redo the global average to account for the difference in there not being any 1 on 1 games this month, but for later months you may not need to change it again, or the change will be small.

Congratulations on your new contributor badge.

Thanks! That's very kind of you!

All we have to do is offer a useful statistic analysis tool to get a badge these days?

Here I thought I had to make videos embarrassing myself...