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Topic: 2012 Arimaa World League Roundtable (Read 20894 times) 

ChrisB
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Re: 2012 Arimaa World League Roundtable
« Reply #75 on: Aug 28^{th}, 2012, 7:46pm » 
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on Aug 28^{th}, 2012, 6:24pm, supersamu wrote: A question to ChrisB: So, if i understand correctly, the peak WHR rating of one of our players inceased too much since you submitted the roster? If not, from which day are the peak WHR ratings taken? I won a game against harren 5 hours before the AWL game, i hope this game didn't cost us one point. 
 No, your win over Harren had no effect on your team exceeding the upper limit of 6580 in Round 1. The peak WHR ratings for Round 1 were set well before you won that game.

« Last Edit: Aug 28^{th}, 2012, 7:47pm by ChrisB » 
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novacat
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Re: 2012 Arimaa World League Roundtable
« Reply #76 on: Aug 28^{th}, 2012, 11:19pm » 
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I have been thinking of another way to do the points/budget, which ends up being almost exactly what Fritz suggested here: on Aug 24^{th}, 2012, 1:34pm, Fritzlein wrote:An interesting addition to the standings (if megajester can autogenerate it without too much trouble) would be the amount over/under target budget divided by 350. For example, Let's say Europa wins two of three from the Rockies and thus leads by 7 points to 5. But Europa overspent the target by 720 and the Rockies underspent by 230, which is worth 2.06 and +0.66 respectively. So when you take budget into account, the standings would be 4.94 to 5.66, i.e. the Rockies would actually be leading. (Of course we need to win one to make this scenario come true. ) 
 Start with a budget of 0. No budget limits on any round either. All other rules stay the same. Optional: we can come up with a "rating to points" calculation if 350 doesn't work well. Thus (for 350 per point), a team who plays three 1500 rated players and loses would tie with a team who plays 2200 rated players and wins every game. Using Fritz's example, the Rockies would have been slightly ahead with 1 victory. On the other hand, the Rockies could have also played Aamir, balaclava, and Copac and won. The risk with this roster is if chessandgo wasn't on the roster, Europa would win. Advantage: Teams can play anyone and still be in the running. Disadvantage: There may be more lopsided games and less play for middle ranked players because teams will likely want to either assure victory with stronger players or lose with very low rated players. I'm sure there are other things I didn't think of, and I'm not sure I am ok with the disadvantages I did think of, but I wanted to share my thoughts.


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Fritzlein
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Re: 2012 Arimaa World League Roundtable
« Reply #77 on: Aug 29^{th}, 2012, 2:06pm » 
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Novacat, if I understand correctly, the main innovation you are proposing is that, instead of just penalizing teams for going over budget, we reward them in equal measure for going under budget. This would create problems. Assume for a moment that the Elo formula is correct. Assume that you, as a captain, know in advance the ratings of your three opponents are 1800, 2000, and 2200. Assume that you have an infinite roster to choose from, so you can field players of any rating. Assume that, as you propose, there is no budget, just an adjustment based on spending more or less than your opponent. What is your optimal strategy under your proposal? If you take the derivative of your expected (league score + budget bonus), you will find that it is always negative. That is to say, increasing the rating of the players you field always hurts you, and decreasing the rating of the players you field always helps you. Therefore your strategy should be to field the three lowestrated players you can find, every round, regardless of which three opponents you face. You'll lose every game but win on the budget bonus. Now you see why it is important that there be a penalty for going over, but no bonus for going under. Under the current rules, the negative derivative assures you that every point you spend over budget will hurt you, because the incremental increase in winning chances is worth less than the incremental increase in budget penalty. But if you are under budget, every additional point you spend helps you. You get increased winning chances and the penalty remains zero. Therefore the current system pressures the spending towards the middle. Everyone wants to exactly meet the budget without going over. This, in turn, makes highrated players exactly as valuable as lowrated players. Within that framework, however, there is still plenty of room to strategize. For example, consider a budget of 6000 and the following rosters: A: 1800, 2000, 2200 B: 1400, 2200, 2400 C: 1600, 1800, 2600 Roster B has positive expectation against roster A. Roster C has positive expectation against roster B. Roster A has positive expectation against roster C. So there is no optimal roster; there is a guessing game and an opportunity to psych out the opposing captain. Assuming, of course, you have enough volunteers to have options about who to field.

« Last Edit: Aug 29^{th}, 2012, 2:08pm by Fritzlein » 
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novacat
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Re: 2012 Arimaa World League Roundtable
« Reply #78 on: Aug 30^{th}, 2012, 2:03am » 
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on Aug 29^{th}, 2012, 2:06pm, Fritzlein wrote:Assume that you, as a captain, know in advance the ratings of your three opponents are 1800, 2000, and 2200. Assume that you have an infinite roster to choose from, so you can field players of any rating. ... Assuming, of course, you have enough volunteers to have options about who to field. 
 Given these assumptions, great analysis. However, we are far from that, so I was trying to come up with something a little more forgiving for teams with low availability. First, let's take away the opponent's roster. You only want to play a lower ranked player if they are 700 points lower than their opponent, otherwise you want to play someone ranked higher that the opponent but not by more than 700 or you are losing. Given that we still have an infinite roster with any rating (including negative ), there is really no clear reason for any choice. Just get a random number generator and go. Putting back the opponent roster and removing the unlimited player selection, there is a limit to the lowest ranked player. Playing the three lowest ranked players in the league would still lose to your 1800, 2000, 2200 roster. Thus, my choice would actually be to play my top three players. Taking away both assumptions, I would look at the opponent's lowest three players and see who is less than but close to 700 rating points higher (2000 to 2200). With a little tweaking, this would be feasible against Europa and the Rockies. Since the Ring of Fire has a lot of higher ranked players, I would either play my strongest players or my weakest players against them. I could probably play all the players on the Atlantics right now, but as you can see, most players ranked between 1600 and 2000 would only get to play if no one else is available or if captains were hedging their bets. This is where you can reduce the ratings per points lost ratio. Going from 350 to 275 distributes the regions of preferred players around. Now the only unfavorable range is 1600 to 1850. Looking at some rosters: A) 1350, 1400, 1500 B) 1850, 1900, 2000 C) 2100, 2250, 2400 D) 1350, 1900, 2400 A beats C, loses to B B beats A, loses to C C beats B, loses to A D wins or loses based on the result of the table with the same ranking. All teams have the players to do at least 1 of these options, and most can do 2 and come close to 3. Even if you are forced to play a nonideal roster due to availability, you still have a decent chance of coming out ahead. For example, your roster this week (1820, 2110, 2660) would lose against A, be unfavorable against C, be almost 50/50 against B, and win against D. I remain unsure if this arrangement will indeed cause problems or turn out ok. Either way, the current arrangement will be the better one as participation increases.


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clyring
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Re: 2012 Arimaa World League Roundtable
« Reply #79 on: Aug 30^{th}, 2012, 7:23am » 
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on Aug 30^{th}, 2012, 2:03am, novacat wrote:First, let's take away the opponent's roster. You only want to play a lower ranked player if they are 700 points lower than their opponent, otherwise you want to play someone ranked higher that the opponent but not by more than 700 or you are losing. 
 This works under the assumption that the higherrated player will always win. This is simply not true. on Aug 29^{th}, 2012, 2:06pm, Fritzlein wrote:If you take the derivative of your expected (league score + budget bonus), you will find that it is always negative. 
 I'm afraid you have erred in your calculations here. The global maximum derivative for expected league points before the penalty is ln(10)/800, quite plainly greater than 1/350. on Aug 30^{th}, 2012, 2:03am, novacat wrote:This is where you can reduce the ratings per points lost ratio. Going from 350 to 275 distributes the regions of preferred players around. Now the only unfavorable range is 1600 to 1850. 
 Going from 350 to 275 brings about Fritz's doomsday scenario where the weaker player is always better in every single situation!

« Last Edit: Aug 30^{th}, 2012, 7:25am by clyring » 
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Fritzlein
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Re: 2012 Arimaa World League Roundtable
« Reply #80 on: Aug 30^{th}, 2012, 8:55am » 
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on Aug 30^{th}, 2012, 7:23am, clyring wrote:This works under the assumption that the higherrated player will always win. This is simply not true. 
 I am not making this assumption, only the assumption that the Elo formula holds, i.e. the probability of winning is 1/(1 + 10^(rating_diff/400)). Quote:I'm afraid you have erred in your calculations here. The global maximum derivative for expected league points before the penalty is ln(10)/800, quite plainly greater than 1/350. 
 You are correct; ln(10)/800 is actually 1/347.4, so the derivative is positive for a rating difference of 29 Elo or fewer. If you are very close to your opponent's rating, spending more on your own rating helps a little. Outside that narrow band, decreasing your rating would always help. Quote:Going from 350 to 275 brings about Fritz's doomsday scenario where the weaker player is always better in every single situation! 
 I believe that here is it you who have erred. Going from 350 to 347 (not 275) brings about the doomsday scenario. We are very close to it already. (In fact, that is how I chose the value of 350, although I forgot that I rounded up.) For example, although decreasing rating by one point wouldn't always help, decreasing rating by one hundred points always would. Therefore the strategy of "always field the three lowestrated players you can" would be essentially correct.

« Last Edit: Aug 30^{th}, 2012, 9:16am by Fritzlein » 
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Fritzlein
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Re: 2012 Arimaa World League Roundtable
« Reply #81 on: Aug 30^{th}, 2012, 9:14am » 
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on Aug 30^{th}, 2012, 2:03am, novacat wrote:First, let's take away the opponent's roster. You only want to play a lower ranked player if they are 700 points lower than their opponent, otherwise you want to play someone ranked higher that the opponent but not by more than 700 or you are losing. 
 OK, I understand the confusion. I understood you to be saying that instead of having a just penalty for overspending, you would also have a bonus for underspending. But apparently you meant, by removing the budget, that there would be only one adjustment, i.e. either the weaker team would get a bonus, or the stronger team would get a penalty, but not both. I infer this because if the weaker team gets a bonus and the stronger team gets a penalty, then fielding a player rated 350 points lower (not 700 as you say) is an automatic win. Now that I understand what you mean, I have a different objection: your proposal is not zerosum. If, say, the weaker team gets a bonus and the stronger team gets no penalty, then the teams both benefit from being mismatched. Say each board has a difference of 700 rating points; then the two teams combined would score 12 league points. If the other two teams were evenly matched on every board, those two teams combined would score 6 league points. So the way to win would be to call up the opposing captain and agree who "goes high" and who "goes low" to maximize the total points scored.


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clyring
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Re: 2012 Arimaa World League Roundtable
« Reply #82 on: Aug 30^{th}, 2012, 4:23pm » 
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on Aug 30^{th}, 2012, 8:55am, Fritzlein wrote:I believe that here is it you who have erred. Going from 350 to 347 (not 275) brings about the doomsday scenario. We are very close to it already. (In fact, that is how I chose the value of 350, although I forgot that I rounded up.) For example, although decreasing rating by one point wouldn't always help, decreasing rating by one hundred points always would. Therefore the strategy of "always field the three lowestrated players you can" would be essentially correct. 
 Going from 350 to 347 would indeed already bring about the doomsday scenario you suggested, going further to 275 does not change this. If you look my actual post it should be clear that my use of 275 refers to a different value suggested by novacat and is not the result of a terrible miscalculation.


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aaaa
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Re: 2012 Arimaa World League Roundtable
« Reply #83 on: Sep 3^{rd}, 2012, 10:30am » 
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megajester, on the wiki, you keep duplicating one wrong URL as the supposed link to the comment pages of all the games. You even undid my correction of the first round.


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megajester
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Re: 2012 Arimaa World League Roundtable
« Reply #84 on: Sep 3^{rd}, 2012, 11:51am » 
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I just realized that myself. I'm copying and pasting the entire page each time from an Excel worksheet, which means that I'm pasting on top of any changes anybody else has made. Thanks for the help though. If anyone else sees an error, please let me know, and I'll change it.


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Fritzlein
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Re: 2012 Arimaa World League Roundtable
« Reply #85 on: Sep 3^{rd}, 2012, 12:35pm » 
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on Sep 3^{rd}, 2012, 11:51am, megajester wrote:Thanks for the help though. If anyone else sees an error, please let me know, and I'll change it. 
 The Atlantics didn't forfeit twice last round; they made two substitutions. I can't imagine what you would have to do to get those results picked up (and correctly included in budget calculations) automatically. Maybe substitutions will always be a manual task for you?


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novacat
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Re: 2012 Arimaa World League Roundtable
« Reply #86 on: Sep 3^{rd}, 2012, 6:23pm » 
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The Atlantics sub games were: #242998 clyring vs woh #243005 browni3141 vs supersamu


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megajester
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Re: 2012 Arimaa World League Roundtable
« Reply #87 on: Sep 4^{th}, 2012, 1:28am » 
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Thanks guys I will make the necessary changes


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Fritzlein
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Re: 2012 Arimaa World League Roundtable
« Reply #88 on: Sep 4^{th}, 2012, 8:39am » 
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on Sep 4^{th}, 2012, 1:28am, megajester wrote:Thanks guys I will make the necessary changes 
 Thank you for doing all the grunt work behind the scenes to make the league run smoothly! It's a true gift the Arimaa community. (Oh, and the round 2 Rockies games still all have the same link. )


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megajester
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Re: 2012 Arimaa World League Roundtable
« Reply #89 on: Sep 6^{th}, 2012, 4:35pm » 
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on Sep 4^{th}, 2012, 8:39am, Fritzlein wrote: Thank you for doing all the grunt work behind the scenes to make the league run smoothly! It's a true gift the Arimaa community. (Oh, and the round 2 Rockies games still all have the same link. ) 
 OK NOW I've made the necessary changes... I like the way you basically do this to my ego whenever you find a problem Please carry on...

« Last Edit: Sep 6^{th}, 2012, 4:35pm by megajester » 
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