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The "Analysis of Nabla scoring system" thread


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Originally posted by Cpl Carrot:

The deviation from the median is going to be positive or negative anyway so why include it? Seems to me you can just ingore it? :-/

What value of alpha do you recoomend?

I think you want to make sure the deviation always becomes positive. By multiplying a -1 times a negative deviation, you do this. Something to do with absolute value later in the formula?

I would use .8 for and "exp" curve and 2.3 for an "asinh" curve, with .42 for "minslope".

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"minslope" does not appear to be in the formula, although a minslope value entered in the command line will modify the curve on the losing side.

Be aware you are working with the "normalized deviation from the median". This may be an absolute value by nature. "Sign" means to manually enter whether it is a positive or negative deviation from the median, I think.

EDIT: "Normalized deviation (or difference) from the median" is a score's difference from the median divided by the standard deviation. Standard deviation is ALWAYS positive...I think. That's why you must manually enter "sign" into the formula....I think.

Treeburst155 out.

[ June 15, 2005, 09:32 PM: Message edited by: Treeburst155 ]

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As it understand it 'normalized deviation from the median' is what is being displayed HERE (the raw score minus the median then devided by the sd). So I just need to take that result and plug into the the Nabla formula using alpha of .8 and that should give the Nabla score for the battle? Add them up for the player and divide by 5 and that is their tourny score yes?

[ June 15, 2005, 09:32 PM: Message edited by: Cpl Carrot ]

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Originally posted by Cpl Carrot:

As it understand it 'normalized deviation from the median' is what is being displayed HERE (the raw score minus the median then devided by the sd). So I just need to take that result and plug into the the Nabla formula using alpha of .8 and that should give the Nabla score for the battle? Add them up for the player and divide by 5 and that is their tourny score yes?

This sounds right to me. Just be sure you put the "sign" in there. If a score is less than the median use "-". If not, nothing is necessary for "sign".
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Originally posted by Treeburst155:

I missed this post earlier. Think this one through, GaJ. If there was an Axis champ chosen only from those who played Axis, and an Allied champ chosen from those who played Allied, the problem of one side having a better scoring opportunity (due to balance) would be alleviated.

Doh - you are absolutely correct.

It sounds like a fun solution as well. I can relate to being one one side or the other!

GaJ

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Originally posted by Kingfish:

Therein lies a problem, because I know for a fact that neither scenario was designed to be unbalanced, and the huge win/losses that we witnessed did not come up in testing.

I was the designer for Push, and I made sure that whatever advantage one side had was offset to a certain degree by advantages to the other side.

So, how does one ensure a scenario is not unbalanced, even borderline?

Indeed - a truly vexing problem, one that I've been pondering. There's more to it than just "how do we know it's balanced?". There's also the point that a scenario that's perfectly balanced but with no real chance for either side to score a win is worse than one slightly imbalaned, but with a reasonable chance for both sides to win!

I think that Push actually falls into the latter category. A lot of matches of that scenario, resulted in an imbalanced looking median but a good win was possible from both sides (it appears). I can't see how the apparent imbalance could have been predicted. Even if it could have, I think that it is worth it from the point of view of the opportunity for both sides to win. I withdraw my "borderline" comment, which was made purely on the basis of the published median. (Wet is a different kind of thing altogther, but staying on topic...)

I can conceive of a very balanced scenario of forces opposing each other in trenches and grinding away at each other. Always results in 50/50 outcome and is boring as heck. The need to provide the opportunity for each side to win opens the possibility for one side having an easier time to do that.

Which just goes to show how awesomely difficult is the art of of coming up with good scenarios, and just deepens my (and I hope everyone's) appreciation of the designers who attempt it for us.

It also emphasises the importance of geting Nabla right, because scenario with imbalance are an inevitable and even desireable part of tourneys.

GaJ.

[ June 16, 2005, 01:04 AM: Message edited by: GreenAsJade ]

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(Mostly for Walpurgis benefit, but maybe other latecomers to the thread too...)

Originally posted by Walpurgis Nacht:

I'm not sure I understand who's been wronged here to inspire this thread? I've heard my game with BigDog (Maleme) mentioned repeatedly with little mention of anyone else save a few. So what that that score gave me that many Nabla points . . . .who exactly was cheated out of a section victory by it?

This question, while already partly answered, deserves reinforcement of its anwers.

1) No-one is saying anyone was cheated. Many people have specifically made a big point of saying this already in this thread. We all signed up for ROW with the rules how they are. The winners of round 1 are all deserving winners.

2) The high scores that outstanding players such as yourself were able to acheive from the underdog position in an unbalanced scenario have shone a spotlight on an unexpected aspect of the current scoring system - one that people find less than ideal once they really think about it.

If you haven't gethered, it's this: people assigned to the underdog side of an unbalanced scenario have a much larger scoring potential than people on the favourable side.

This means that you can conceivably be an excellent player, but end up assigned to the favourable side of all scenarios, and simply be unable to score as much as your opponents EVEN IF YOU GET 100% in every battle.

Yes - you can end up in the middle of the field in ROW even if you got 100% in every battle, if you happened to have the favourable side of 5 unbalanced scenarios.

That is what this discussion is all about.

Obviouusly, the example above is extreme, and because mostly people end up with a share of favourable and unfavourable psotions in scenarios the truely excellent players bubble to the top. This is demonstrably the case in ROW V.

Nonetheless, the players hot on their heels, with aspirations to do well, and those who just want their efforts fairly represented, are now realising that the current ROW scoring has some shortcomings in that respect.

That's why we're talking it through.

While I'm here, I would strongly advise against applying any other formula to the ROW V scores. It's much better to take a hypothetical set of scores and work with those. Rearranging existing real people and their scores is almost guaranteed to cause unintended hurt.

GaJ

[ June 16, 2005, 01:09 AM: Message edited by: GreenAsJade ]

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I think the Push to Maleme battle actually was one of the few battles that allowed a reasonable amount of troops AND tactical options and that was why it could go either way. As such I would consider it as close to perfect as I have come across.

As the Axis I actually stripped out a platoon for an ambush and for the sake of perhaps one more turn I could have got many more points. Conversely it could have gone horribly wrong if my opponent had taken a more risky untraditional attacking posture. Either way we both had options to take - and unusually for the defence - enough room and troops to think outside the box.

[being as VIB's are cheap the plane was realistic and probably!!! not a game breaker]

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Originally posted by Walpurgis Nacht:

I'm not sure I understand who's been wronged here to inspire this thread? I've heard my game with BigDog (Maleme) mentioned repeatedly with little mention of anyone else save a few.

I started using that game as an example to crunch numbers on, because it looked like a good case.

If you followed my posts, you'll see that I eventually concluded that luck of draw gave you no advantage in total potential points.

The total potential nabla score and possible imbalances due to which sides a player was assigned was what got the discussion started, not the idea that anyone who won shouldn't have. This has always been a discussion about "fine tuning".

The topic has now shifted a bit to how to tweak the tourney so that the results are more reflective of overall performance and therefore more useful to the vast majority of players who don't win, but like to see how they measure up to some tough competition.

I certainly wasn't complaining about the current system, since it gave me a section win!

PS I'm still bitter about Luga Breakthrough 2. smile.gif

[edited for smileys, so you know I'm not really bitter. That much.]

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Originally posted by Cpl Carrot:

Try this .

It should be the results after the nabla formula has been applied, along with the tournament score (ie the total divided by 5)

Robert

That doesn't seem right Cpl. Carrot. If you take my group for example (Group 5), I managed to achieve the equal top score for the axis side in Wet Triangle yet Jon L. in the same group who achieved the second best score for the Allies in that scenario obtained an adjusted score more than twice that of mine. Also Sripe in group 8 for the same scenario managed a huge Nabla adjusted score which pretty much achieves what was trying to be avoided where the one big win can get you through to the finals. Comparing Malakovski's battles with Sripe in that group you can see that Malakovski actually did better than the median (i.e won) all 5 scenarios yet isn't within a bulls roar of Malakovski's final adjusted score.

I think the original Nabla formula may not be applied properly based on just these two observations.

Regards

Jim R.

[ June 16, 2005, 07:25 AM: Message edited by: Kanonier Reichmann ]

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I've managed to put together the huge input file for the original Nabla DOS program. I've run the entire tourney through the program. No group winners changed!

There were only a handful of ranking changes below the winners. However, the final Nabla scores correlate much better with actual tourney performances IMO. I can post the results if the handful of non-winners who dropped a notch can take the pain gracefully. :D

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