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358Re: Scoring and league-position formulae for Perikles?

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  • macleodandrew
    Dec 16, 2007
      Funny that, Bob finally finds a game he wins every time and then he
      wants to set up a league table for it.

      No seriously I think its a good idea, I had once thought of
      suggesting we record the results of the games at each session and
      devise some sort of rating system along the lines you've suggested,
      but then thought it would be too complicated and would be taking it
      too seriously. However I think for a few games that we want to play
      semi frequently anyway, it would add an extra dimension to the play
      and the banter.

      One suggestion to the scoring system, without wishing it to become
      too complicated, I think the bonus a first time player gets should
      depend on how many others playing are first timers as well. This is
      just an extension of your rule that the bonus does not count if all
      are first timers. For example in a game of four players, if three are
      first timers they are at much less of a disadvantage (only up against
      one experienced player)than say a five player game where there is
      only one first timer up against four experienced players. However in
      both games they would all receive a +1.0 bonus. My suggestion is
      that a first time player should receive a 0.25 bonus for
      each "experienced" player he is up against. That would mean in the
      examples above the three first time players in the four player game
      get 0.25 whereas the one first timer in the five player game gets
      0.25x4 = 1.0

      In your game last week Dave and Michael would then get 0.25x2 = 0.50
      bonus. I think this would have made the table:

      Player Points Played Rating
      >
      > BobR 10 2 2.000
      > FelixK 3 1 1.000
      > DaveB 2.5 1 0.833
      > NeilP 4 2 0.800
      > AndrewM 2 1 0.667
      > MichaelY 1.5 1 0.500

      I think this would be slightly fairer and not much more complicated
      to calculate.

      One other suggestion would be that perhaps Apocalypse would be a
      better choice than Roborally for a league table. For two reasons,
      Roborally is a TEAM game with a significant element of luck so I'm
      not sure a league would be very meaningful or easy to score.
      Secondly Apocalypse is a game that gets a few airings a year anyway
      and it might add a further edge to the game in that as well as going
      after your target, you might want to nuke the guy at the top of the
      leaderboard to make sure he does not do well either!

      In fact this leads me on to the final thing I wanted to say, about
      tall poppy syndrome. You may in fact be introducing a different
      variant of it in that people may want to gang up on the league leader
      from the start of the game, but we'll just have to wait and see.

      Merry Christmas to everyone.

      Andrew


      --- In lbgc@..., "Founder." <bobroscow@...> wrote:
      >
      > Right, I've spent a fun hour or two playing at devising a scoring
      > system etc. for a Perikles "league". I enjoy devising such
      things.
      > I'm open to comment and suggestions.
      >
      > 1) It's only a league in the sense of keeping track of whoever
      plays
      > and how they do. There are no "fixtures", no game that you have to
      > show up for. Not everybody will play everybody. It just counts up
      > games you DO happen to be in, and cumulates scores and some kind of
      > average or rating.
      >
      > 2) I suggest we only play (or only count) games with 4 or 5
      > players. People can give it a try with 3 players (or 6?) but those
      > are outside the league keeping count.
      >
      > 3) I suggest points per game be as follows:
      >
      > 4 players: 1st gets 5 points, then 3,2,1 points.
      >
      > 5 players: 1st gets 6 points, then 4,3,2,1 points.
      >
      > [I know I'm rewarding a total defeat with 1 pt rather than zero,
      but
      > it's nicer that way; I hate to see people on zero].
      >
      > 4) What with our turnover, we'll always have SOME people playing a
      > game of Perikles for the first time, sometimes as the only new
      player
      > with 3 others who have played before. So, there is a bonus point
      if
      > it is your first game - one extra point - unless you are ALL
      > playing it for the first time, and only if you don't WIN. So, even
      > if you play your first game and come last, you'll still score 2
      pts,
      > not 1.
      >
      > 5) I do favour the above approach of points for positions. Rather
      > than cumulating vp-points scored in each game, eg, 65,64,53,41.
      And
      > rather than ONLY counting people's WINS, and ignoring whether they
      > finished 2nd, 3rd or 4th, as some leagues do. One reason for this
      > is, it will actually HELP the play within each game, IMHO. Y'see,
      > all conquest-type games are more or less prone to Tall Poppy
      > Syndrome, the 3 currently losing ganging up on whoever went ahead
      > early on... This approach tones down that effect a bit. Given the
      > league, you would, or should, care whether you ended second, and so
      > might try to overtake someone in the game to win second place
      rather
      > than all have equal incentive to take out the guy who is ahead
      early
      > on. Yep, a league system, points for position, helps to mitigate
      > Tall Poppy Syndrome.
      >
      > 6) OK, that makes it easy to award points across games, and put
      > people in order of total points scored across games played. OK so
      > far. EXCEPT: That favours whoever plays most often, cumulating
      most
      > points. So you need some kind of averaging : eg points earned
      > divided by games played... That is not as obvious as it sounds ...
      > (as many of you will know).
      >
      > 7) The biggest problem with simple averaging is this: a player
      who
      > just plays once only, and happens to win, gets a 100% record, and
      > sits at the top of the league, never to play again and impossible
      to
      > overtake.
      >
      > 8) There are various ways round this (as many of you will know).
      >
      > 9) I suggest a formula for "Rating", by which the league-table-
      > positions will be sorted:
      > The formula is:
      > Cumulated points earned, divided by [2X the number of games played,
      > +1].
      >
      > I've tried this (and other formulae) on our results to date, and
      > lokked ahead to see what effect playing another game would have, if
      > you came 1st or 2nd or 3rd or 4th in that game.
      >
      > " games so far:
      >
      > 2 Dec 07
      > BobR
      > FelixK
      > AndrewM
      > NeilP - ALL first time, therefore no +1 bonus
      >
      > 9 Dec 07
      > BobR
      > NeilP
      > DaveB - first time, therefore +1 bonus
      > MichaelY - first time, therefore +1 bonus
      >
      >
      >
      > Using the points system, with the bonuses for first-time playing,
      > plus the formula, the league would currently look like this:
      >
      > Player Points Played Rating
      >
      > BobR 10 2 2.000
      > FelixK 3 1 1.000
      > DaveB 3 1 1.000
      > NeilP 4 2 0.800
      > AndrewM 2 1 0.667
      > MichaelY 2 1 0.667
      >
      >
      > Note how this is closer to an average-per-game than to a cumulative
      > total? That's why Neil, having come 4th and 2nd, comes out lower
      > than Felix (a 2nd) or Dave (a 3rd, but first-time). Looks fair.
      >
      > It's quite variable over time. When Bob plays again, if he comes
      > 4th, his Rating will drop to 1.571. When Felix or Dave play again,
      > if either wins, their rating would go to 1.600 - thus topping the
      > table.
      >
      > It looks like it would work fairly over time. Not TOO dependent on
      > how many times you play, but not letting played 1/won 1/100% top
      the
      > charts forever.
      >
      > Any comments?
      >
      > AND, any suggestions on scoring and league-position formula
      (Rating)
      > for Formula De, and/or for Team RoboRally? Feel free to add to the
      > posts and suggest!
      >
      > Bob
      >
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