Nabla Posted November 7, 2001 Author Share Posted November 7, 2001 As was suspected, the original algorithm is not optimal when the number of players is large. For eight players the new version of the program (which optimizes over all possible side changes) is able to find a schedule for which #3=0 and #4=4, so the comparisons are done evenly. The solution provided by the original algorithm has #3=4 and #4=2. The optimal solution is ================================ # Scenario_1 PlayerA PlayerB PlayerC PlayerH PlayerD PlayerG PlayerE PlayerF # Scenario_2 PlayerC PlayerA PlayerB PlayerD PlayerE PlayerH PlayerG PlayerF # Scenario_3 PlayerA PlayerD PlayerE PlayerC PlayerB PlayerF PlayerH PlayerG # Scenario_4 PlayerE PlayerA PlayerF PlayerD PlayerC PlayerG PlayerH PlayerB # Scenario_5 PlayerA PlayerF PlayerG PlayerE PlayerH PlayerD PlayerC PlayerB # Scenario_6 PlayerG PlayerA PlayerH PlayerF PlayerE PlayerB PlayerD PlayerC # Scenario_7 PlayerA PlayerH PlayerG PlayerB PlayerF PlayerC PlayerE PlayerD ================================ My friend working with combinatorial problems has provided me with a book which writes about these balanced schedules. It seems that our problem is related to a construction called balanced Room squares. I'll let you know if the book is of any use. Link to comment Share on other sites More sharing options...
Treeburst155 Posted November 7, 2001 Share Posted November 7, 2001 Great minds at work.....I love following it. NOw what are you trying to do to my scoring program?! :eek: I don't understand the problem with it. I can adjust the max possible score, and therefore the flatness of the curve simply by changing the value of "a". Where's the problem? Treeburst155 out. Link to comment Share on other sites More sharing options...
JPS Posted November 10, 2001 Share Posted November 10, 2001 Nabla (and Treeburst155), I would like to discuss the "proper" way to handle results in which some objective flags remain neutral (i.e. the scores sum to less than 100). First, I think scoring system should reward a player for (i) achieving own objectives, and (ii) preventing enemy to achieve objectives. Lets consider the following end scores of the same scenario: (1) 50-50 (2) 40-40 (3) 40-60 (4) 40-50 The Axis player in game 3 obviously should be rewarded most, as the current Nabla system does. However, one could argue that Allied player in game 2 did better than the one in game 4, which in turn did better than the one in game 3. This, I believe, is not reflected in the current Nabla scoring system. I bring this issue for discussion as the current system may encourage players to reach scores like in game 1 compared to game 2. I.e., it is better for _both players_ to divide objective evenly rather than fight to stalemate. In the extreme, this may result in gentlemen's agreements that divide contested flags in the last minutes. There are several ways to modify the Nabla system to remedy this issue. For example, scores could be normalized to sum to 100 before calculating the Nabla scores by dividing the "unallocated" points to both players evenly. Using the above example, the normalized scores would be (1) 50-50 (2) 50-50 (3) 40-60 (4) 45-55 Thus the Allied player in game 2 did better than in game 4 than in game 3. Also, Allied players in games 1 and 2 are considered equal for tournament scoring purposes. Finally, Axis player in game 3 is still rewarded most, whereas Axis player in game 4 is considered superior to player in game 1. I propose the above modification is taken into use in Nabla tournament scoring system in order to encourage competitive play to the very end. Time for peer review, comments please. JPS EDIT: minor typo [ 11-10-2001: Message edited by: JPS ]</p> Link to comment Share on other sites More sharing options...
Treeburst155 Posted November 10, 2001 Share Posted November 10, 2001 I think you're absolutely right JPS! That's very easy for me to implement, and involves no work for Nabla. I'm just correcting the input to his scoring program. Good thinking! How about it, Nabla? Do you see any flaws in JPS's thinking? Treeburst155 out. Link to comment Share on other sites More sharing options...
Nabla Posted November 11, 2001 Author Share Posted November 11, 2001 It's the middle of the night over here so my thinking is not at its best, but the problem is real and the solution sounds good to me. I'll return to the issue tomorrow after I've slept a bit Link to comment Share on other sites More sharing options...
Nabla Posted November 12, 2001 Author Share Posted November 12, 2001 Ok, I'm back on-line. It seems that my brain still was able to function at least a bit even when deprived of sleep. The issue brought up by JPS is important, and his solution looks like a good one. Treeburst155: I think the solution should be coded into the scoring program. It is better to keep the original scores in the result file intact. I'll send a message here when I've implemented the changes (perhaps next week or so). Link to comment Share on other sites More sharing options...
Nabla Posted December 11, 2001 Author Share Posted December 11, 2001 Time to dig up this thread from the heap of dust. It's been quiet on this front for a while since first I had to take a break off CM after the Nordic Tournament had been started (way too much CM for a while). Then my win98 broke down and I was unable to play CM!! I had to install win2k from scratch, and now CM runs smoothly again Anyway, because of these breaks I have not yet written / compiled a new version of the schedule / scoring program. I'll do it pretty soon if the same compiler still works under win2k. The subject of this post, however, is the exact form of the scoring curve. I just think that the old curve was a bit too flat - some reward should be given even for the really big wins. I'll spare you (=Treeburst155) from the details for now, and I'll just let you choose between two different curves. These are depicted below. The green curve is just the "neutral" scoring curve plotted for comparison. The blue curve is the good old curve chosen by Treeburst155. The red curve is the new one I'm suggesting. So, Treeburst155, which one would you pick? [i changed the name of this thread to reflect my current feelings about the scoring system. Also edited a typo.] [ 12-11-2001: Message edited by: Nabla ]</p> Link to comment Share on other sites More sharing options...
Treeburst155 Posted December 11, 2001 Share Posted December 11, 2001 Hi Nabla! So we're back to the good old curve discussion again. I feel it is highly unlikely that many games will score over 40 points above the median making the curve after 40 inconsequential. Your proposed curve and mine are almost exactly the same in the range from 0-40 above the median. Of course, this is based on the curves' appearance which is affected some by the scale of the graph. One of the nice things about your system is that we can use any curve we want. I have no problem changing to a max 23 curve or thereabouts. I'm sure the players don't really care either. What exactly would you like to use for the value of "a" in the formula? BTW, don't forget I will be splitting any points not earned due to neutral flags between the players. If a final score is 60-30 it will be recorded as 65-35. As mentioned earlier in this thread, this fixes some "gamey" problems. Treeburst155 out. Link to comment Share on other sites More sharing options...
Nabla Posted December 12, 2001 Author Share Posted December 12, 2001 <blockquote>quote:</font><hr>Originally posted by Treeburst155: Hi Nabla! <hr></blockquote> Hi Mike! <blockquote>quote:</font><hr>Originally posted by Treeburst155: So we're back to the good old curve discussion again. I feel it is highly unlikely that many games will score over 40 points above the median making the curve after 40 inconsequential. Your proposed curve and mine are almost exactly the same in the range from 0-40 above the median. Of course, this is based on the curves' appearance which is affected some by the scale of the graph. <hr></blockquote> All of your observations are correct. (Actually, I designed the curve so that in the range 0-30 the curves would be identical.) However, we have to take a stand concerning very high scores. I mean, are they rewarded at all when compared with intermediate victories (and also, are big losses punished). The current choice is practically flat for victories which deviate more than 50 points from the median. This may be appropriate, since it is very effective in neutralizing very inconsistent play. But then again, if someone gets a very large victory even though the opponent tried to play seriously, he only gets an intermediate final score. This is the tradeoff in the current system. Also note that if someone knows that he's losing Big Time (when compared with the median), in the current system the motivation for the loser and the winner becomes very low. This is because the motivation is practically equal to the flatness of the curve. The new curve tries to give some reward for large victories as well, and motivates both players to keep on trying even if one side gains the upper hand. But if the new curve is adopted the cost is reduced protection against inconsistent play. In my previous post I said that the new curve is my suggestion, but this is actually false. The truth is that I don't have enough experiense to say which one would be better. We can modify these in the future, but for the current tournaments we have to select one. Treeburst155: you're the judge, really. <blockquote>quote:</font><hr>Originally posted by Treeburst155: One of the nice things about your system is that we can use any curve we want. I have no problem changing to a max 23 curve or thereabouts. I'm sure the players don't really care either. What exactly would you like to use for the value of "a" in the formula? <hr></blockquote> I said I'd spare you from the details Its a different formula, I'll give you the details if you decide to choose that one. <blockquote>quote:</font><hr>Originally posted by Treeburst155: BTW, don't forget I will be splitting any points not earned due to neutral flags between the players. If a final score is 60-30 it will be recorded as 65-35. As mentioned earlier in this thread, this fixes some "gamey" problems. <hr></blockquote> No, I won't forget that. But don't you forget that I said that I'll implement that into the scoring program so that you can leave the original results untouched [There's always at least one typo.] [ 12-12-2001: Message edited by: Nabla ]</p> Link to comment Share on other sites More sharing options...
jshandorf Posted December 13, 2001 Share Posted December 13, 2001 Wait a second... There is absolutely nothing wrong with the way games are scored in CM. If in a game you are unable or unwilling to take a flag(s) and it is left neutral then TOO BAD. You lose those points but also so does your opponent. The REAL solution to this problem is then for every MAP played you have an equal amount of flag points available for EACH map. Then each player in the tourney has the opportunity in each game to capture the same number of points. If a player fails to this then it is his/her fault. Too bad. So sorry. Game over. There is no need to modify someone's score, and thus elevate their average, because they were too inept to capture the flags but not inept enough to make them neutral. Gimme a break. Jeff Link to comment Share on other sites More sharing options...
Treeburst155 Posted December 13, 2001 Share Posted December 13, 2001 Nabla, Lets think for a moment in terms of line segments of different slopes rather than a curve. For example: +1 to +20 of median, 1/1 ratio tourney points to game points +21 to +30 of median, 1/2 ratio tourney points to game points +31 up, 1/3 ratio tourney points to game points The same would apply to below median scores. Let's see how this would work. I'm thinking aloud here. Player A scores 36 points above the median. He gets 20 pts. for his first 20 over median. He gets 5 pts. for his next 10 over median, and 2 points for his last 6 over median. His CM score of +36 over median would net him 20 + 5 + 2 = 27 tourney points. This sloping segments approach could be broken up into smaller segments for further refinement of "just rewards" for different levels of achievement over (under) the median. Your smooth curves are like having an infinite amount of segments, each at a different slope. Suppose we came up with a segmented graph that we liked, using about 5 different slopes; could you come up with a formula for a curve that would closely match it? If not, what about a program that simply does the arithmetic involved in my example above. I guess the real question is the reward for extremely high scores. The curve I decided on earlier is a fairly flat one. Beyond +40 of the median there is not much benefit. Let me study the many game results that have come in for the various tournaments so far. I want to look at the difference from the median of the extreme examples and the number of such instances. This will help determine what the best curve is. Shandorf, Go back a page or two and read JPS's post for the reasons behind splitting unclaimed VPs. Be sure you are familiar with the scoring system too. Treeburst155 out. [ 12-12-2001: Message edited by: Treeburst155 ]</p> Link to comment Share on other sites More sharing options...
Treeburst155 Posted December 13, 2001 Share Posted December 13, 2001 Nabla, Looking over the Wild Bill Tourney results that are in (about 70%), the distance from the median for any side of any scenario only goes beyond +/- 40 in three cases of extreme outliers. The vast majority of scores are within 30 of the median. How about something like this: +/- 0 to 10 from median, 1 tourney point for 2 CM points (1:2) +/- 11 to 20 from median, 1:3 +/- 21 to 30 from median, 1:4 +/- 31 to 100 from median, 1:5 A score of 40 above median would yield 5 + 3.33 + 2.5 + 2 = 12.83 tourney points. The whole graph here tends toward the horizontal to help keep the competition tough. At the same time in never flattens out more than the 1:5 ratio. Only overwhelming outlier losses or victories will ever see the 1:5 ratio. This one may be a bit too horizontal, but it sure would make for a tough fight for the championship. I'm for keeping the losers in the running more than rewarding the overwhelming victories. I like the idea of making the curve shallow near the median too. All the curves we've looked at so far have been steep in that area. I'm still thinking about all this. Treeburst155 out. [ 12-12-2001: Message edited by: Treeburst155 ]</p> Link to comment Share on other sites More sharing options...
Nabla Posted December 13, 2001 Author Share Posted December 13, 2001 <blockquote>quote:</font><hr>Originally posted by jshandorf: Wait a second... There is absolutely nothing wrong with the way games are scored in CM. If in a game you are unable or unwilling to take a flag(s) and it is left neutral then TOO BAD. You lose those points but also so does your opponent. The REAL solution to this problem is then for every MAP played you have an equal amount of flag points available for EACH map. ... There is no need to modify someone's score, and thus elevate their average, because they were too inept to capture the flags but not inept enough to make them neutral. <hr></blockquote> Are you sure you've understood the problem? We're not saying that there is something wrong with the way CM handles neutral flags. However, the handling of neutral flags is not suitable for the purposes of the tournament scoring system under development. This is of course not the fault of CM because its scoring system was not designed for such unbalanced tournaments. About your signature: Current evolutionary theory emphasizes successful reproduction over survival. For example, there are a number of species in which the males let themselves be eaten after copulation because the chance that they get to copulate again is negligible, and the nourishment of the female increases the survival of the female and the offspring. Survival is important only as long as it increases reproductive success. Therefore, Evolution - Too Stupid To Reproduce. [ 12-13-2001: Message edited by: Nabla ]</p> Link to comment Share on other sites More sharing options...
Treeburst155 Posted December 13, 2001 Share Posted December 13, 2001 Nabla, In a recent post you said: "Also note that if someone knows that he's losing Big Time (when compared with the median), in the current system the motivation for the loser and the winner becomes very low. This is because the motivation is practically equal to the flatness of the curve." Players will not know where they stand in relation to the median since the median cannot even be determined until the end of the tournament. Also, I will not divulge scores beforehand, thereby allowing them to get an idea of the median. BTW, I suspect that at least some of the extreme victories are the result of surrendering rather than withdrawing as many as possible and letting the program surrender when the threshhold is reached. Some just do not like to play out battles they can't win. In these cases especially, the extreme victories should not be given too much weight. Unfortunately, it is not easy for me to determine why a huge victory occurred. Treeburst155 out. [ 12-13-2001: Message edited by: Treeburst155 ]</p> Link to comment Share on other sites More sharing options...
Treeburst155 Posted December 14, 2001 Share Posted December 14, 2001 More thoughts.... Based on further analysis of final game scores I feel confident in saying that a CM Grandmaster will average between 30-35 (probably closer to 30)above the median over the course of a tournament. Using the segmented curve mentioned above the Grandmaster would finish the tourney with a score of 10.8 - 11.8 tourney points. A very strong player who averages 20-25 above the median would finish with 8.33-9.58 tourney points. The Grandmaster will win the tournament if his play is consistent. The margin of victory (in tourney points) does not matter. First place is first place and takes the prize. In cases where a merely competent player (10-20 above median) manages a victory at 35 over the median in one instance, I would have to be very suspicious of a surrender being involved, OR an unusually weak opponent. I think these two possibilities are more likely than our competent player simply having an unusually brilliant game. With the "curve" described above, this aberration will not pay off much for our competent player. Consistent, or at least frequent, large victories must be achieved in order for a player to reap the benefits of such game results. You can see I'm arguing wholeheartedly for minimal reward for overwhelming victories. I don't want an unusually lucky game, or one against an unusually poor opponent (a person who surrenders is in this group), to boost a player well above the others. To stick out above the rest a player must perform at a consistent high level. Looking at my tourney scores there are such players. They consistently score well above the median. Such players will pull away from the pack inspite of the diminishing returns for scores in the high range. Comments and arguments against are always welcome. Nothing is engraved in stone yet. Do remember, Nabla, your new curve in your last graph is fine with me. I have no problem with your scoring program being based on that new curve/formula. I think it is sufficiently tough on extreme scores to accomplish what I've laid out above. I just like contemplating all this. Geez, I'm a real geek; just like my wife has always said. :0 Treeburst155 out. [ 12-13-2001: Message edited by: Treeburst155 ] [ 12-13-2001: Message edited by: Treeburst155 ]</p> Link to comment Share on other sites More sharing options...
Nabla Posted December 18, 2001 Author Share Posted December 18, 2001 Hi Treeburst155! A status report. I've implemented both the neutral point distribution (evenly to both players) and the second scoring curve into the program. Now you can choose on command line which of the curves you want to use. Both curves have one parameter which determines the flatness of the curve. I've compiled and tested the current version under Linux, but I still have to compile it under win2k. I will try to do this today or tomorrow. In addition, I still have to write one small program and an Excel macro with which you can plot and see the different curves. I will also return to some of the points you've made above later on. Link to comment Share on other sites More sharing options...
Treeburst155 Posted December 18, 2001 Share Posted December 18, 2001 That sounds great, Nabla! If I understand correctly you say I will be able to use either curve (formula), and each one has a variable to adjust the flatness? That really is marvelous! I do foresee one problem however. I don't have Excel so I may not be able to generate graphs. This is not critical however. If I can get numbers I can plot my own on graph paper if I really want to. Just the numbers themselves is enough to visualize the graph, really. Thanks again for all your work on this project. Treeburst155 out. Link to comment Share on other sites More sharing options...
Nabla Posted December 18, 2001 Author Share Posted December 18, 2001 Ok, I've compiled the new versions for DOS (there were some problems with win2k, but I could make the compiler stable for a while). New features: 1. The -o option for nabla-tournament-schedule. It tries to optimize the schedule over all possible side changes (see posts above for description of the criteria over which the optimization is done). This can be pretty slow if the number of players is bigger than six. For eight players it takes 7 minutes on my computer. 2. Even without the -o flag nabla-tournament-schedule now prints the value of the criteria measuring the goodness of the created schedule. 3. nabla-score-tournament now distributes neutral points (for example, points from neutral flags) evenly to both players. By default it does this silently, but with -d option you can see what it does. 4. nabla-score-tournament now requires as its first argument the form of the score function to be used (the nonlinearity). It is either exp, which is the old one, or asinh, which is sgn(d)1/a*asinh(a*|d|). Here asinh is the hyperbolic arc sine, which for low values of d behaves very much like the old function, but for larger values is not as flat. See posts above for a picture showing the difference. A reasonable parameter value for this curve is 0.14, which for low values of d follows closely the curve corresponding to the older curve with Treeburst155's parameter value 0.055. Get the new versions here. Treeburst155: I will make a program which will simply plot the d,score value pairs, so that you can view them with any program you want. PS. nabla-curve-parameter is practically obsolete by now, but its still there just in case. [ 12-18-2001: Message edited by: Nabla ]</p> Link to comment Share on other sites More sharing options...
Treeburst155 Posted December 19, 2001 Share Posted December 19, 2001 Woohoo! Hyperbolic arcsines!! I love it. What is it? No, don't tell me. I don't want to know. Really, I don't. I understand how to use the new program, and what it is capable of. That's all I need. I may have some questions after I play with it for awhile, but your explanation above seems clear enough. I'll be working with the new program as I get some time over the next few days. Hyperbolic arcsines....hehehe...it must be good. Treeburst155 out. Link to comment Share on other sites More sharing options...
Treeburst155 Posted December 19, 2001 Share Posted December 19, 2001 Nabla, I don't have permission to access the machine where your programs are stashed. Somebody must have beefed up security on you. :eek: Treeburst155 out. Link to comment Share on other sites More sharing options...
Nabla Posted December 19, 2001 Author Share Posted December 19, 2001 <blockquote>quote:</font><hr>Originally posted by Treeburst155: Nabla, I don't have permission to access the machine where your programs are stashed. Somebody must have beefed up security on you. :eek: <hr></blockquote> Try now. Link to comment Share on other sites More sharing options...
Nabla Posted December 19, 2001 Author Share Posted December 19, 2001 I think I have a great idea. I even contemplated for a while on my own signature, and I still think the idea is great. Above I've mentioned several times that I'm worried about the motivation of the players when they reach the flat part of the (old) curve. As Treeburst155 wrote above, it is difficult to know whether you're in this part, since you don't know the median of the scenario. But sometimes you really do now. Let's say you've let the other guy kill (n+4) tanks with one AT gun, or you've been ambushed by some schreck times, or let your guys get stuck in arty fire in the open. We've already seen players surrender in the Nordic and Nordic Wannabee tournaments. So let us for now assume that the two players - call them A and B - both know that they are on the flat part of the curve. A is on the positive side, and B on the negative. With the old curve neither player really has a motivation to play, unless B has a major plan which can swing him over to the non-flat part of the curve (or A assumes that B has one). So A can play defensively and B can try something insane. But if B has no grand plan, as is usually the case if you've been beaten for a while, he might as well surrender. He loses nothing by doing so. And A might just as well stop playing, because he has nothing to accomplish. If someone gains a point it makes no change for the tournament. This is not a good thing. Now here's the new twist. Let's make the curve asymmetric. On the positive side we use the old, flat curve. On the negative side we use the new curve which is not quite as flat. Now A is still on a flat curve, but B is not. To see how this affects the motivation of the players let us now think about what happens if either of the players gains a point. Obviously, since the curve is not flat on B's side, if B gains a point his score will become better. B has a motivation to play. In particular, B has a clear motivation not to surrender. What about A? If A gains a point, his own score will not improve. But it will affect B's score. Therefore, by gaining a point A will improve his own chances of winning the tournament by reducing B's chances. Furthermore, and here's the real beauty, A will not gain an additional advantage with respect to other players in the tournament. B's score is so low with respect to the median that if B loses more it will not affect the median of B's side. A's score does not change, the median of A's side does not change, and the median of B's side does not change. Therefore, there is no change in the scores of A and the other players in the tournament. Only B's score changes. So we have the following properties. 1. B has a motivation to gain additional points. 2. B has a clear motivation not to surrender. 3. A has a motivation to gain additional points. 4. An overwhelming victory of A over B will not decide the whole tournament. But it will reduce B's chances of winning the tournament. I think this is what we want. Problem solved? Link to comment Share on other sites More sharing options...
Redwolf Posted December 19, 2001 Share Posted December 19, 2001 Nabla, I'm not sure you cure the right problem, for two reasons: 1) I think that people will mostly surrender when they have lost motivation because of this game, not their standing in the tournament. So I think that tuning the scoring does not prevent them from surrendering. If your twist does not prevent them from surrendering, your twist makes the surrender worse for the whole tournament score, although as you say not much. 2) I kinda like it that the "winner" can't gain much anymore and the "looser" can try something insane. That may open great game moments and maybe turn the game. The latter is especially important in possibly unbalanced scenarios, since even if you have been beaten badly you still don't know how much your enemy has left, especially ammunition. Link to comment Share on other sites More sharing options...
Nabla Posted December 19, 2001 Author Share Posted December 19, 2001 <blockquote>quote:</font><hr>Originally posted by redwolf hates artillery: 1) I think that people will mostly surrender when they have lost motivation because of this game, not their standing in the tournament. So I think that tuning the scoring does not prevent them from surrendering. If your twist does not prevent them from surrendering, your twist makes the surrender worse for the whole tournament score, although as you say not much. 2) I kinda like it that the "winner" can't gain much anymore and the "looser" can try something insane. That may open great game moments and maybe turn the game. The latter is especially important in possibly unbalanced scenarios, since even if you have been beaten badly you still don't know how much your enemy has left, especially ammunition.<hr></blockquote> Both of your points are logically correct - this is really just a question of what kind of gameplay is encouraged. If we want to give the loser a free ride to surrender, or encourage him to take big risks then we definitely should not use the kind of asymmetric system I've depicted in my previous post. Heck, I don't know. At least we have a lot of options. I think that at this point I have to wait for input from Da Tournament Man aka Treeburst155. But your point is correct in that now we have to identify the biggest problems with respect to reward and motivation. That is what has to be done next. Back to the drawing board for that exercise. [Edited cause this is still evolving.] [ 12-19-2001: Message edited by: Nabla ]</p> Link to comment Share on other sites More sharing options...
Treeburst155 Posted December 19, 2001 Share Posted December 19, 2001 An assymetrical curve.....interesting. Let's analyze the "old" curves for a minute. Player A plays Player B in a scenario that ends up with a median of 50, a perfectly balanced scenario. Player B has rotten luck in the first 10 turns and surrenders rather than withdraw the still numerous units he has that could have escaped. Because of the surrender, player B loses the game 90-10. Let's assume the score could have been 80-20 had player B withdrawn and let the program surrender for him. This surrender places player B forty points below the median, and player A forty above. Using even the flattest curve, the one with (a=.055) in the first formula; how much would player B have gained in tourney points had he achieved the 80-20 outcome through withdrawal? What is the real reward for not surrendering in this case? At 90-10 both players' calculated tourney scores for the game would be |16.17|. At 80-20 the scores would be |14.69|. Is this 1.48 points significant when looking at the big picture from the perspective of either player? I think it might be because the tourney winner's final score will only be 14-15 tourney points. Maybe I'm just hyper-competitive, but I'd want the 1.48 extra points for that scenario. I'd also want to deny those 1.48 points to the guy who is beating me. This extra 1.48 points may not come out to a great deal in the end when averaged with the other games, but it would still be enough to motivate me to withdraw rather than surrender. Keep in mind that this is using the flat curve (.055) with the original formula. The new formula would make withdrawal over surrender even more preferable. The players may not see it this way because they probably haven't put in the time to understand the scoring formula and/or they aren't as competitive as I would be when faced with a lost game. To sum up, I think the new hyperbolic arcsine curve is fine. However, your assymetric curve may be even better. Let's move on to that idea. Here's an assymetrical proposal constructed of sloping line segments again. What if the "curve" was linear from -100 to +10 at a 2:1 ratio (2 CM points = 1 tourney point), then dropped to 3:1 from 11-20, 4:1 from 21-30, and 5:1 from 31-100? Unless a player is doing significantly better than the median he will always be on the steepest part of the curve. At the same time a big winner will never actually hit a flat spot on the curve. The whole curve is somewhat horizontal again, being 2:1 around the median instead of the 1:1 we have with the two previous formulae. Even simpler, what if the "curve" was linear all the way from -100 to 100 at a low slope, say 4:1? I will take my now substantial Wild Bill tourney results and plug them into these two curve ideas, just to get a better idea of the end effects of such curves. I think Redwolf is correct in that the players for the most part only look at individual games as opposed to the big picture. We can't really expect them to have the same enthusiasm for this elaborate scoring system that we do. They are just happy that it takes into account the unbalanced nature of virtually all scenarios. They trust us with the details. I think we have made it clear in both Nordic tournaments that surrender is not a good thing for their score. Some just aren't competitive enough to want to carry on in a losing game when all they will be doing is withdrawing. An assymetrical, withdrawal friendly curve may help with this but I think there would still be some surrenders. That's why it's probably best to have the curve fall off substantially for large victories. An assymetrical curve in favor of low scores is better, but getting the players to take advantage of it is another thing. I'm going to plug my Wild Bill scores into the assymetrical curves I described above and see what it looks like. Treeburst155 out. [ 12-19-2001: Message edited by: Treeburst155 ]</p> Link to comment Share on other sites More sharing options...
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