9.3.4 Match Seeding Points

[leafy]

Originally Posted by mathking

This game does not really have a Nash equilibrium. With the "n to 0" strategy the side with the n points has an incentive to unilaterally change strategies to score for the opponent. This incentive increases if they have received (or think they received) any penalties. If the sides are playing for an "n to n" tie they both have an incentive to score n+1 and end up with 3n +1 points instead of 2n points. I would guess that the game designers looked at all this when they designed the game.

If the score is 0 to n, they have 1 seeding points to gain for every point they score on themselves, whereas if they score on the opponent, they have 2 seeding points to score for themselves. This is true.

However, the 0-alliance is allowed to have 2 robots blocking their own goals. They can also forcibly score on the other alliance's goals, which the winning alliance has no incentive to block.

Originally Posted by Daniel_LaFleur

I believe you are incorrect here.

Both alliances benefit better in a high scoring tie (the reason for this, over your 'x to 0' strategy is that coopertition points are the tiebreaker ... therefore teams would wish to maximize them), so early on in the competitions they are well motivated to do just that (high scoring ties).

But as the competition goes along and rounds will score differently, teams will become more motivated to change that strategy so that they will move up in the seeding.

Applying the Nash Equilibrium to game strategy will mean that teams will change their strategy towards scoring based upon their seeding position as the regional goes on, and therefore the Nash Equilibrium must be re-evaluated each match.

... it's going to be a fun year

Both alliances don't benefit in a high-scoring tie. Only one does. If an alliance score is n-u with p penalties on the team with n, with u<n, the n-alliance gains 2u + (n - p) seeding points, larger than n seeding points that the losing team gets.

If u is 0, then the winning alliance gets n-p seeding points, and the losing team gets n seeding points. I don't see how the losing team has any benefit to scoring higher in a tie; only the winning alliance does. You could say it increases their chance of winning, but that's not what we're talking about.

Originally Posted by Jonathan Norris

In my interpretation the Coopertition bonus is totally separate from the seeding points, it says nothing about adding the Coopertition bonus to seeding score in the rules. This is where I think I may be wrong, someone please correct me if so.

It's not; the coopertition bonus is added to their running total seeding score. See 9.3.5:

9.3.5 CoopertitionTM Bonus
All teams on the winning ALLIANCE will receive a coopertition bonus: a number of seeding points equal to twice the un-penalized score (the score without any assessed penalties) of the losing ALLIANCE.
In the case of a tie, all participating teams will receive a coopertition bonus of a number of seeding points equal to twice their ALLIANCE score (with any assessed penalties).

Originally Posted by Jonathan Norris

To me with my interpretation I dont see a situation where teams would actually want to compete against one another... I'm not even going to get into the situation where the loosing teams actually receives more seeding points due to penalties on the winning team.

They want to compete to win for the Coopertition bonus. If they win, they get it. We can't go assuming what the score will be, then postdict the team's behavior.

I never got to get my post back; I don't know why - it said the post was moderated and it never showed up. Here's the gist of what I was saying:

Some would say that this will encourage a lot of colluding. But who do they think will be colluding - two alliances? Hardly. The only collusion that will happen if this strategy is employed is between the teams on one alliance planning to score 0. What is the incentive for the other alliance (the alliance who stands to win the Coopertition bonus) to collude with the losing alliance? If they don't, then they get the Coopertition bonus. Intuitively, though I may think otherwise, it seems that most players view this strategy as counter to GP or the spirit of the rules / FIRST. This would be an additional disincentive to use this strategy.

Originally Posted by kirtar

Here's another proposition with respect to your third one.
Say that that the score is 8-8
Each alliance gets 8+8*2=24, which is 50% more. In every scenario in which there is an even numbered total score, it is always more beneficial to both teams to split the score evenly.

This is actually false. Even with the example you gave, it's false. If alliance W gets 8 points, and alliance L gets 8 points, then it's a tie. As per 9.3.4, they get seeding points (it says ranking points, but probably means seeding points) equal to their own alliance's score. In this case, each alliance gets 8 points, plus twice their alliance score (as per 9.3.5). This results in a net gain of 24 points.

Only in a tie, though. That's an edge case. And it still doesn't apply retroactively to this strategy.

If alliance L gets 0 points, then alliance W gets 8 points for their seeding score. Alliance L also gets 8 points. Primia facie, this seems to be a loss relative to other teams that are playing other matches. However, the previous case is only in the case of a tie. If the previous scenario had a much more likely difference in score, then the points become unbalanced:

Say alliance L gets 6 points, and alliance W gets 8 points. W wins, netting 11 seeding points. L gains 8 seeding points.

This is much more likely than 8-8; consider last year's game. FIRST data shows that at an average regional (picked one at random: New York City Regional 2009) there was only 1 tie. That's hardly enough to offset the median or mean ranking score with this new system. Even when counting for the fact that the range and standard deviation were both higher, the number of ties will still be significantly low enough.

Another important fact is being glossed over: the number of balls is doubled when one team is playing to score 0. If they are constantly fighting for each ball, then of course they'd only get 8. That means that 4 balls total were recycled. This number would be quite higher - perhaps 12 or more (speculative) - increasing the total ball count. This would, I think, overcome the incentive to work for a coopertition bonus.