Mapmaker wrote:I like the idea of having solos weighted by more than just twice a 2-way draw. And I think that if you're increasing the k-factor, surely average points should increase as well - so everyone would start off at a higher score. Or is that unnecessary?
Wait. This could have very serious consequences: think about it - most people consider a loss to a solo or a loss by exclusion from a draw (presumably having already been eliminated first), equal losses. This schema seems to suggest that losing to a solo is WORSE than being eliminated and a draw being eventually reached. I think it's hard to make the case that these are not both complete losses, and as such should be scored the same. Moreover, any ranking system will have to be 0-sum, since otherwise we'd be favoring those who play more (otherwise we could just give "bonus" points for solos). So solos won't be able to be worth significantly more than draws, if we want to preserve the idea that a loss is a loss (though, it is still possible to "scale" wins, somewhat).
Two options seem to make the most sense, then, instead. One gives a *slightly* escalating value to solos/draws, and the other treats them all the same. Personally, I prefer option 1 strongly, but I suppose a case could be made for option 2, or some similar system. I go over the details and pros/cons for each below.
Option 1: 7 players enter the game. Anyone who loses (is not part of an N-way draw/solo) is charged 1/N losses (the number of players who won) to each of the winners. This ensures they always lose once and only once per game. The value of a win (or loss) against a certain player will be determined by the ELO formula (this holds for option 2 as well). This allows for scaling of the value of solos/draws in the fashion of the table below
# of winners 1 2 3 4 5 6 7
prop of solo points (per winner) 1 5/12 2/9 1/8 1/15 1/36 0
total "value" of game 1 5/6 4/6 3/6 2/6 1/6 0
So we can see that a draw (that you are involved in) will NEVER lower your rating, no matter how much "better" you are than your opponents. Whether this is good by discouraging ganging up on high-raters or bad by encouraging draws is not clear. It has the scaling of the "value" of the game many people hoped for, discouraging draws, especially many-player draws.
Option 2: 7 players enter the game. EVERYONE "pays" a loss to play, and loses equally amongst. Thus, take the (hopefully very hypothetical) situation of a 2-way draw. The two winners are each credited a half win gainst each loser. Then they each give each other half a win (and half a loss, of course). Thus the lower-ranked player gains significantly more. One possible drawback is that a highly rated player who draws with lower rated ones could very well see his rating drop, despite a decent (say, 3-way draw) finish - conversely, low ranked players have a lot to gain from draw-mongering. Another is that there is no "scaling" for making solos more than 3 times more desirable than a 3-way draw. While I'm fine with this, I'm not sure how many others are. On the plus side, this system is probably more intuitive than the system above.
But it is basically the system above, except that everyone loses to the winners, including the winners amongst themselves, whereas in the first system only the losers lose to the winners.
# of winners 1 2 3 4 5 6 7
prop of solo points (per winner)* 1 1/2 1/3 1/4 1/5 1/6 1/7
total "value" of game 1 1 1 1 1 1 1
* excludes the fact that they also lose some, depending on the size of the draw, as well.
PS As the only guy with a solo on the board, it may seem odd that I'm coming down so hard against rewarding them excessively, but I just don't think it's a teneble system, because it adds at least as many perverse incentives as the site's official system, and is one of the problems I have with another player-run ratings system, in the Diplomacy League here on the forum.
EDIT: ARGH the tables look miserable when posted but great before. It condensed my spaces