Nabla

Don't worry guys. The default will be CMBO for the second round as well, unless all players want CMBB.

I don't think it's a problem for the first round of the tournament. However, if CMBB is available for the final (second) round we may have to vote whether we want it to be played with CMBO or CMBB. That shouldn't cause any defections, quite the opposite. To support this I'm designing the ideas for the final round games on paper, for abstract sides, and implement them and add local flavor with whatever version is chosen at the time. Yes, I think it can be done.

Remember that this can only be done once a scenario has been played by all players in both tournaments, this and the original Nordic Championships.

I have a question for you. Are you doing this analysis to 1. determine if the scenarios are balanced or 2. assess whether the scenarios have been fair from the point of view of this tournament? These are two different things. The scoring system is immune to unbalance (median different from 50), so from the point of view of this tournament a median (or mean) which differs from 50 is not a problem. However, if you want to use the scenarios in ordinary (non-tournament) play, then the situation is different. [ February 07, 2002, 02:56 AM: Message edited by: Nabla ]

Luckily this is not necessary any longer. Here are some thoughts about these issues that came to my mind. As John Kettler noticed above, standard deviation of the results is one possible additional measuring stick for scenarios. What would it measure? If the standard deviation of the results of a scenario is zero, the scenario does not differentiate the players in any way. At the other end, consider a scenario with maximal standard deviation: half of the Allied players score 0 and the other half +100 (this is still balanced). Does this scenario measure the goodness of the players in any way? The answer depends completely on the correlation between player skills and the end result. If the two are completely uncorrelated then the battle measures pure luck. Put two tanks head to head in an open field, facing one another. There's not much you can do to improve your chances. But if there is a positive correlation then the scenario does measure the goodness of players. If the correlation is negative then there is probably something wrong with the way CM calculates points or models battles. Of course, the real problem here is the determination of "player skills", since it is also done with the scenarios. If in the previous example we assume that the skills of the players follow a normal distribution, a maximal correlation is achieved if players below mean score 0 and players above mean score 100. Would such separation be preferable? Probably not, unless you want to have a cruel playoff system. What then would the optimal scenario be like with respect to the distribution of results and their correlation with player skills? First the correlation with player skills. This should probably be maximal, given the other attributes of the distribution. Minimize the **** happens -factor. Then the distribution. Keeping the same assumption that the skills of the players follow a normal distribution, the results should also probably follow a normal distribution. Why? I'm not sure... If we have a scoring system like the one we're using in this tournament, then the scoring curve maps normally distributed scores into uniformly distributed ones (at least approximately). It spreads results near the median and clumps them together further away. Such a mapping differentiates the scores maximally, that is, the standard deviation of the final scores will be maximal. This is reasonable as long as the standard deviation is the same for all scenarios. If it is not, which is of course the reality in all tournaments, then the scoring system should neutralize this difference. As someone may have noticed, I may have shot into my own leg with the previous argumentation. The scoring system should maybe normalize the results so that all scenarios have the same standard deviation. But I am a bit confused, and probably also confusing you with this post. I'm not sure why a uniform distribution of final scores would be optimal. I will think about this. [ February 07, 2002, 02:58 AM: Message edited by: Nabla ]

Wouldn't it be more fun to play until the end with no disturbing feelings of security? It shouldn't come as a surprise that I vote for blackout. Like the concept of (possibly) unbalanced scenarios, this would keep people on their toes. It's only a couple of weeks more... But the decision is really up to Treeburst155.

Sounds like an instance of a quite general psychological phenomenon (don't know if it has a diagnostic name yet ). Really, if some friend of mine is overenthusiastic about some subculture I'm not familiar with yet, there's a point beyond which his overenthusiasm lowers my interest to the subject. I've seen this happen a lot, both for myself and others. If you want to sell something like this you have to be subtle. Or perhaps I'm wrong, WineCape. Perhaps you weren't overenthusiastic at all. [ February 01, 2002, 09:48 AM: Message edited by: Nabla ]

<blockquote>quote:</font><hr>Originally posted by Treeburst155: It is a bit dicey with us using the actual tourney scores to decide on the formula parameters. It raises the question of me possibly manipulating the parameters to achieve a certain desired outcome in the Wild Bill tourney. I don't think I want this question popping up in the participants' heads. For this reason I will use the original Nabla curve I spelled out in detail on the WBW Tourney thread early on. The one fairly recent change I will implement is the splitting of points for contested VLs. Players will be more at ease with the results if the scoring method used was in place before the results were known. Let's continue work on the assymetrical curve using the WBW results (nothing beats actual results). We can use the new curve for the Nordic Championship, Nordic Wannabee, and future tournaments. This also gives us more time. Treeburst155 out.<hr></blockquote> Ok, loud and clear. This is the way it will be done. I will leave the question regarding Nordic Championship and Nordic Wannabee scoring parameters to your hands for now. We should probably decide those parameters before the first rounds of these tournaments are finished. Just in case anyone else is interested, the programs can be downloaded from here.

<blockquote>quote:</font><hr>Originally posted by JPS: I do not really wish to rush anyone, _but_ it would be extremely non-desirable situation if last minute tweaking of the scoring system parameters decides the finalists in RoW tournament. As most of the battle scores are already in, it is feasible to make reasonable educated guesses of what parameters would benefit the standing of certain players. I would suggest the following: Nabla proposes the most reasonable set of parameters (based on his current understanding of the scoring system) to Treeburst, and Treeburst makes his final parameter decision with no further input from other participants. IMO, this should be done with no further delay. <hr></blockquote> I agree. I was going to post a message with a similar idea today. At least we can't let any of the players in WBWRW participate in this discussion. I will post no further information about this subject to this board until the final parameters for WBWRW have been chosen. I will discuss their selection with Treeburst155 directly via email.

Time to dig up this thread from dust again. So we've got one last thing to take care of: the actual mathematical definition of the asymmetric curve. Already during Christmas I started to think about an optimal way of computing the curve, but it became way too difficult. So I came up with a very straightforward way of implementing our idea. This is my suggestion. When the tournament manager runs the scoring program he gives it three options. The two first ones are as before: type of nonlinearity used (either exp or asinh) and the single parameter of this nonlineary which determines the flatness of the curve. But the third parameter is new: it is the minimum slope of the curve on the negative side. Let me give you an example. Let's say we use the exponential nonlinearity, and a=.05, and the minimum slope is .5. Then the curve looks like this (for visual purposes only the part covering -60 to 60 difference from median is shown). The curve on the negative side follows the shape of the nonlinearity on the positive side until its slope reaches this minimum value. From that point on the curve has a constant slope. I don't know whether this is the best solution to the problem, but it's easy to implement and has only one extra parameter to play with. What we should remember all the time is that we will probably never see a deviation of -100 from the median. Let's say that in a tournament there is one game with median (80,20). One guy plays it bad, frustrates, surrenders and the game ends (20,80). The difference from median is 60. With the curve shown above the winner gets a final score of 19, while the loser gets -33. So with two big wins he's back in the game. Then again, if the minimum slope is .5, like above, then the asymmetry of the curve does not affect scoring for small deviations from the median. For example, for a difference of 20 points from the median the positive score is 12.6, while the negative score is -13.1. I know it's very difficult to state an opinion if you can't play with this system, so I'll start implementing it right away (it shouldn't take long, will be available latest tomorrow). I'll post a message here once the new version is ready for downloading. [ 01-26-2002: Message edited by: Nabla ]</p>

<blockquote>quote:</font><hr>Originally posted by The_Capt: "For games that do not add up to 100 points the difference will be split between the players. For example: A final score of 60-30 will be recorded as 65-35. If you can figure out why I am doing this then you have a devious and gamey mind. Treeburst155 out." To confirm, I was talking about this. Is it part of the scoring program?<hr></blockquote> Yup.

<blockquote>quote:</font><hr>Originally posted by The_Capt: Are you still adjusting the "less than 100 total scores"? I see that these ones haven't been.<hr></blockquote> They need not be adjusted - the scoring program takes care of this. Speaking of which, it seems that the program would be needed, let's see, about now. Treeburst155, I still have that one homework to do. I already tried to think of a very optimal solution, but didn't have enough data for it. I'll find a solution this weekend and post it to the scoring system thread. Ok? [ 01-25-2002: Message edited by: Nabla ]</p>

<blockquote>quote:</font><hr>Originally posted by Joseph Porta: Hmmm...The war is soon over for most, yet there is little noise on the front...Where is everyone ? :confused: <hr></blockquote> Perhaps (hopefully) this is because of the hush-hush policy concerning the scenarios. I'm pretty convinced that you will hear a lot of stories once the curtain is lifted for both this championship tournament and the Nordic Wannabe tournament.

Hello everyone! Just wanted to thank all of those who have already written some AARs: you've written some pretty darn interesting pieces of text. Excellent reasoning (if not hindsight ) for courses of action taken. Keep them texts coming! Oh, and if Treeburst155's mailbox can handle it, I would be completely knocked over if you wanted to include a screenshot or two (if you write Word documents).

Hello everyone! Just wanted to thank all of those who have already written some AARs: you've written some pretty darn interesting pieces of text. Excellent reasoning (if not hindsight ) for courses of action taken. Keep them texts coming! Oh, and if Treeburst155's mailbox can handle it, I would be completely knocked over if you wanted to include a screenshot or two (if you write Word documents).

Thanks to Treeburst155 for handling the recruitment of replacements so well. I hope you are still having a lot of fun with the scenarios.

<blockquote>quote:</font><hr>Originally posted by Treeburst155: Are you telling me that ALL FOUR of these people have not sent a turn in three weeks to a month? <hr></blockquote> Come on guys, get your act together.

<blockquote>quote:</font><hr>Originally posted by Treeburst155: OK then, you go back to your study and come up with the new asymmetrical formula. When it's ready I'll start running hypothetical tourneys (and real ones) through the formula and play with the "a" parameter. Then we will meet here and discuss. It's gonna be good!! <hr></blockquote> This is a good plan. I'll get back to you when the first part is done. And a merry Christmas preparation time for everyone. :cool:

I think that the asymmetric curve fulfills all of our current goals. Let's go through these one at a time. <blockquote>quote:</font><hr>Originally posted by Treeburst155: 1) Overwhelming victories should not be too heavily rewarded for the following reason: A) Big victories could very well be the result of extremely poor play on the part of the opponent, such as surrendering or merely playing for "fun" once the battle turned against him. <hr></blockquote> The very flat (exponential) curve on the positive side takes care of this extremely efficiently. <blockquote>quote:</font><hr>Originally posted by Treeburst155: 2) Players should reap noticeable benefits from a successful withdrawal. This encourages more realistic play IMO. In CM players tend to surrender just to be done with a "failed" game. <hr></blockquote> The not-extremely-flat (asinh) curve on the negative side rewards successful withdrawal. (However, whether the benefit is "noticeable" should be analyzed more carefully using some examples.) <blockquote>quote:</font><hr>Originally posted by Treeburst155: 3) Related to #1 above, the curve should yield a competitive tight race. One big loss or victory should not take a player out of the running or win the tournament for him. <hr></blockquote> Since the curves on both sides are relatively flat the system takes very good care of this once we can define a correct value for a (the degree of flatness / the point where the curve turns flat). <blockquote>quote:</font><hr>Originally posted by Treeburst155: 4) The unbalanced nature of virtually all scenarios should be accounted for. (The median does this) <hr></blockquote> Agreed. <blockquote>quote:</font><hr>Originally posted by Treeburst155: 5) Players who are winning a game Big Time should have sufficient incentive to get all the points they can. <hr></blockquote> This is difficult, since it so easily conflicts with goal 1. As noted above, in addition to the minor direct incentive of getting a few more points, the asymmetric system creates a second incentive by lowering the score of the loser significantly if the winner gains more points. I think it's a very nice feature. Whether or not it will motivate the winners in real tournaments is a whole different question. So at this point I would say that we should go with the asymmetric system. If you agree, then I suggest that we will do the following: 1. A home exercise for me. The use of the asymmetric curve requires doing some math and some programming work. I have to compute the formula that relates the two parameters, and implement this into the program. The person running the tournament will only give parameter a for the flat curve on the positive side, and the program will compute the corresponding parameter for the negative side. The point of this computation is to a) ensure that the two curves have almost identical shapes near zero and define a reasonable point from which the two curves differ. 2. After the program has been written, we should generate a few results for imaginary tournaments, try to define a good value for the parameter a, and see how the whole thing works. What do you say, is this the plan? [ 12-21-2001: Message edited by: Nabla ]</p>

<blockquote>quote:</font><hr>Originally posted by Treeburst155: When you get a chance, give my your thoughts on my other suggestion, the one with linearity at 2:1 from -100 to +10 with the curve flattening out as victory levels increase. (Victory being defined in terms of relation to the median). <hr></blockquote> I think this would violate rule number 3: <blockquote>quote:</font><hr>Originally posted by Treeburst155: 3) Related to #1 above, the curve should yield a competitive tight race. One big loss or victory should not take a player out of the running or win the tournament for him. <hr></blockquote> If the curve was at its steepest all the way down to -100, a player who lost Big Time in one game would be practically out of the tournament. In order to compensate for this big loss he would have to win a large number of games. A few large victories would not do it since the curve is much flatter on the positive side. Do you agree?

<blockquote>quote:</font><hr>Originally posted by redwolf hates artillery: Did I understand your correctly that in an overwhelming victory - the looser is punished quite heavily, so that he is motivated to try a retreat from the map - but the winner doesn't gain very much, just barely enough to keep him motivated to maybe try a few points more If so, that sounds exactly like the right thing!<hr></blockquote> Yes, you have the basic idea. In the current plan the punishment on the looser is not heavy, but it is significant. In addition, part of the motivation for the winner will be to try to sink the loser a bit lower. Well, that's a nasty way of putting it, a more political way is to say that the winner tries to maximize his chances of winning the whole tournament by reducing the losers chance of winning. I'm glad to hear that you agree. Even if you didn't agree, I'd still be glad to hear your opinion. This system will probably/hopefully affect a number of tournaments, so input is very welcome at this point.

<blockquote>quote:</font><hr>Originally posted by Rollstoy: WOW, you completely forgot that in the case of CMBO the credit cards were charged as soon as the product left the house, not months before (Anything else would not be very moral in my opinion)!<hr></blockquote> Well, that must mean that many of us, the customers, have really low moral

One preorder from here, yes. Why don't you change the topic of this thread to "Post here if you'd like to preorder CMBB now, knowing that you'd pay now and receive the goods whenever it's done." [ 12-20-2001: Message edited by: Nabla ]</p>

<blockquote>quote:</font><hr>Originally posted by Treeburst155: I understand what you mean now that I think about it. Any linear "curve" is just like any other linear "curve" in regards to the final outcome of the tourney. <hr></blockquote> Exactly. <blockquote>quote:</font><hr>Originally posted by Treeburst155: For the same reasons I understand why 1:1 is fine around the median. It's what we do before and after the median in relation to that 1:1 that matters. In fact, I believe the actual ratio around the median does not matter much. What really matters is how the ratio at the median compares with the rest of the curve on both sides. <hr></blockquote> Exactly 2 A 1:1 start ratio is just easy to compare with a neutral 1:1 linear curve. <blockquote>quote:</font><hr>Originally posted by Treeburst155: When you get a chance, give my your thoughts on my other suggestion, the one with linearity at 2:1 from -100 to +10 with the curve flattening out as victory levels increase. (Victory being defined in terms of relation to the median). <hr></blockquote> I will do that. <blockquote>quote:</font><hr>Originally posted by Treeburst155: EDIT: You know, Nabla, you are much more qualified to determine a curve that accurately measures a player's skill than I am. <hr></blockquote> Definitely not! I'm your analyst. (Reading this message through once more I had to add that I am still happy to see that our opinions on the priorities agree practically completely. ) I can tell you what can be done, and pinpoint pitfalls, locations where problems might arise. But you're the customer. You have much better knowledge about tournaments, knowledge of what we finally want to achive with this system. And this cooperation has worked very well It's been very easy for both sides to understand what the other person has been saying. This is quite an accomplishment since we can only interact through this board. <blockquote>quote:</font><hr>Originally posted by Treeburst155: Let's restate our goals for the system: 1) Overwhelming victories should not be too heavily rewarded for the following reason: A) Big victories could very well be the result of extremely poor play on the part of the opponent, such as surrendering or merely playing for "fun" once the battle turned against him. 2) Players should reap noticeable benefits from a successful withdrawal. This encourages more realistic play IMO. In CM players tend to surrender just to be done with a "failed" game. 3) Related to #1 above, the curve should yield a competitive tight race. One big loss or victory should not take a player out of the running or win the tournament for him. 4) The unbalanced nature of virtually all scenarios should be accounted for. (The median does this) 5) Players who are winning a game Big Time should have sufficient incentive to get all the points they can. I think if the curve was fairly steep on the negative side of the median and shallower on the positive side, but never becoming virtually flat, we would achieve what we want. When deciding on this curve it should be kept in mind that only rarely will any portion of the curve >|40| be utilized. The vast majority of scores from both sides of a scenario will be <|30| from the median for that side. <hr></blockquote> See, this is what I was talking about. You have stated here exactly what I wanted to know. This is how it works. Now, with these clear priorities, I will retreat to my study room for a while to think about the situation. [ 12-20-2001: Message edited by: Nabla ]</p>

<blockquote>quote:</font><hr>Originally posted by Treeburst155: Even simpler, what if the "curve" was linear all the way from -100 to 100 at a low slope, say 4:1? <hr></blockquote> A lot of stuff here, but I have some social responsibilities to attend to right now so I'll just comment on this one shortly. In a previous post you've also made a similar suggestion that the curve should start out more flat. I think - I'll try to prove this another day - that because finally the scoring system is used only to order the players from worst to best, we can multiply the slope with any positive value and we still get the same ordering. The differences between the final scores will be different, but the ordering will be the same. Therefore I think that a curve with a 4:1 slope all the way produces the same order as a curve with a 1:1 slope. This is also the reason why we can agree to always start with a 1:1 slope in those curves in which the slope decreases. Ok, social responsibilities can wait for one minute, here's an informal proof. Let i and j be game indices, and a_i and b_j denote the differences from median for players A and B in games i and j (here _ denotes subscript). Now let f(a_i) denote final score for curve f, and sum_i f(a_i) be the final score of player A (sum over scores of all individual games). If sum_i f(a_i) > sum_j f(b_j), player A is better than B using curve f. If we multiply f by some positive number, say X, the clearly still sum_i X*f(a_i) > sum_j X*f(b_j). So the ordering is the same.