9.3.4 Match Seeding Points

[SteveGPage]

Originally Posted by Lil' Lavery

Say team X is on the red alliance and team Y isn't playing. Team Y is done playing matches and has 100 seeding points. Team X has one match remaining and has 80 seeding points. In a competitive match, the red alliance might win 6-5 and get 16 seeding points (not enough for Team X to catch Team Y). In a colluded match, the red alliance might win 21-0, and Team X could pass Team Y. Or they could attempt to tie 7-7 and earn 21 seeding points for both alliances, in which case Team X passes Team Y as well.

True, but I think with X, Y, and Z playing against A, B, C the motives of the individual teams gets a little messy! The hardest part of this concept is keeping all 6 teams in the match honest with the "agreement" made, when each may have a very pressing reason to defect from the agreement.

[mathking]

The colluded shutout agreement runs some significant risk for the "winning" alliance in that if they get any penalties, they will actually come out behind the "losing" alliance in seeding points for that round. You could argue that if they two alliances cooperate they might still score more points than they would have scored if the match had been played with both alliances trying to get the most points. But I suspect that a lot of teams will be unwilling to risk what they might view as an unfair result.

One thing I think is clear is that in most unbalanced matches without any collusion, there will be a point at which the sides start trying to score for each other. If there are 30 seconds left and you are up 12-1, you have more incentive to put in balls for the opponents than for yourself. Furthermore, unless you have a reasonable chance to overtake the other side, you have no in-game incentive to try to hang from the bar if you are the losing side. All you will be doing is giving twice as many points as you earn to the winning alliance, while giving none to yourself.

Again I will say that this is a REALLY interesting game theory problem. I wish I were still teaching discrete math, because I would love to have a test question asking students to devise and justify a good strategy for the game.

[SteveGPage]

Originally Posted by mathking

Again I will say that this is a REALLY interesting game theory problem. I wish I were still teaching discrete math, because I would love to have a test question asking students to devise and justify a good strategy for the game.

So true! I think an alum at my very, very, very small college in Southwestern Virginia (John Forbes Nash, Jr) would love this game, too!

[StephLee]

Has anyone pointed out that perhaps you COULD benefit from giving your opponent more seeding points by scoring for yourself, even in a no-win situation at the end of the game?

I know in the past, we have ended up with excellent alliance partners based on our performance against them in qualification matches. Giving a likely top-8 team a run for their money is, in my experience, a good way to get them to notice you, and such a game played without nastiness is a good way to get them to notice you favorably. If the primary overall goal during the qualification matches is to seed highly yourself, the secondary should be to put on a good showing for the teams that do seed highly enough to impact your fate for the elimination rounds.

Not to mention, if you have the choice between helping your opponent at no cost to yourself or not helping your opponent also at no cost to yourself (as in, you wouldn't win either way)...well, it'd be within my personal definition of GP to help my opponent.

[SteveGPage]

Originally Posted by StephLee

I know in the past, we have ended up with excellent alliance partners based on our performance against them in qualification matches. Giving a likely top-8 team a run for their money is, in my experience, a good way to get them to notice you, ...

I remember that well ... but, trust me, our scouting had all ready noticed you that year!

This year we get to see each other's teams at both the Chesapeake and Buckeye Regionals ... maybe this year, we will get you to notice us!

[Tom Line]

Originally Posted by mathking

The colluded shutout agreement runs some significant risk for the "winning" alliance in that if they get any penalties, they will actually come out behind the "losing" alliance in seeding points for that round. You could argue that if they two alliances cooperate they might still score more points than they would have scored if the match had been played with both alliances trying to get the most points. But I suspect that a lot of teams will be unwilling to risk what they might view as an unfair result.

One thing I think is clear is that in most unbalanced matches without any collusion, there will be a point at which the sides start trying to score for each other. If there are 30 seconds left and you are up 12-1, you have more incentive to put in balls for the opponents than for yourself. Furthermore, unless you have a reasonable chance to overtake the other side, you have no in-game incentive to try to hang from the bar if you are the losing side. All you will be doing is giving twice as many points as you earn to the winning alliance, while giving none to yourself.

Again I will say that this is a REALLY interesting game theory problem. I wish I were still teaching discrete math, because I would love to have a test question asking students to devise and justify a good strategy for the game.

You may call it interesting. I call it insanity. I have to wonder that since entertainment and audience inclusion was a big part of kickoff, what part of this system makes it:

#1 Easier for the audience to understand
#2 More entertaining for the audience

I'm pretty sure that if half way through the game the teams start scoring on themselves, the audience is going to go "what the <insert word>". If then someone explains to them that the teams on the floor are artificially manipulating the scores to obtain a result rather than simply competing against one another, I'm pretty sure most of the "audience" are going to wonder exactly what type of competition their watching.

Simple it isn't. Entertaining.... I don't think so. I certainly hope they fix this quickly. Though at this point it doesn't really matter - we're all still going to design robots to score as quickly as possible.

[leafy]

Everyone seems to be missing two key factors:

1. If the two alliances are not colluding, then the best strategy for the alliance planning to score 0 is to block both goals with its robots and push the balls into the other alliance's zone.

2. Competition should lower the maximum amount of points a given alliance can get, given competency on the part of both alliances. If we both get 6 of the balls, then that's a 6 point margin that's being taken away. If one alliance plans to get 0 points, then the other alliance gets 12 points plus however many they can put back onto the field.

Some say that the cooperition bonus "is for this purpose", while shying away from the stronger statement that the cooperition bonus would compel both teams to compete. This simply isn't true; they fail to factor in the heightened maximum points you can gain from not scoring any goals.

For instance, take the numbers that have been thrown around. Say the score is 8-8. That means that 4 balls have been re-entered into the field. A total of 16 balls. The winning team in kirtar's scenario is 8-8, or 8-7, or something close to a tie. The winning alliance gets 12 seeding points minus penalties, while the losing team gets 8 points.

Compare this to the strategy of scoring 0: using the same number of active balls, one alliance scores 16 and the other 0. The final seeding points distributed is 16 points to each team. 4 points higher for the winning alliance, and double the losing alliance's potential score. It is simply not the case that it is always beneficial to tie a game.

In fact, the original scenario assumes that 8-8 is the score, assuming that the number of active balls is 16. The two teams fight for the 16 balls, making sure that they are not efficiently delivering goals and re-entering balls into the play field. If they did, by teaming up to score the most points, they could increase the number of balls higher, thus making their score even higher.

Why does everyone think this strategy is counter to the spirit of FIRST? It's not counter to the spirit of the rules, since Dean Kamen himself foresaw this use of the rules in his patent. Second, it effects an environment in which both teams work together in order to maximize their benefits. Is this not more close to gracious professionalism than competing to make sure you beat the other team just hard enough to get the win, but just soft enough to get the most cooperition bonus? Surely once you have established the win, it's almost manipulative to behave this way. If you are at 1 minute left with your alliance at 8 points and the other alliance at 4, a team looking for seeding points (and who isn't?) would wait for the other alliance to score up to 3 points to gain that extra 6 seeding points. The losing team knows this. They know it, and they know that they're going to lose and any attempts to win would just increase the other alliance's seeding points at the end of the match. What hopelessness. Scoring for yourself actually drags you lower relative to the mean seeding points.

I'm not advocating this as a main strategy; when I presented it to my team our mentors repeatedly said that it would probably be changed, it might be entirely eliminated, and that we shouldn't use it as our main strategy. The strategy we could use, if this isn't changed, is determine whether we're going to lose or not beforehand. If we are, then convince our alliance partners to not score. If they won't be convinced, score like mad. If they will be convinced, don't score and block the goals, helping the other team while preventing them from lowering our score relative to them.

Again, most teams will likely examine this strategy and find it too risky. What if the other team scores on us - then we actually lose points. I'm just pointing out that this is a legal, effective strategy, and worthy of discussion, even as a matter of pure game theory. Questions of fairness or fidelity to our foundations are tangential at best.

[Enigma's puzzle]

I believe that these seeding rules were actually implemented to encourage offensive teams that tried to accomplish scoring instead of just going for the defensive approach. And actually i think that this will do a more accurate job of calculating the most potent scoring robots, and actually in an effort to raise the score of the match many teams will not put someone on the "defensive" end to encourage scoring and quick ball recycling. This strategy would benefit both sides because hopefully the score by both teams will increase.

[PhilBot]

Originally Posted by mathking

One thing I think is clear is that in most unbalanced matches without any collusion, there will be a point at which the sides start trying to score for each other.

Yes, this seemed like the "missing" conclusion to me too.

At some point of imballance BOTH teams are better off scoring on each other.

Of course, at that point, the whole "This 1020 game is easier for the crowd to understand." concept goes out the door.... Will it make sense to anyone not on this forum that the red is now scoring for blue and that blue is now scoring for red?

It will be interesting if the term "Tipping Point" starte getting applied to matches.....

Annoucer..... "Looks like we've hit the tipping point. Teams are starting to score in each other's goals."

You read it here first

Phil.

[Daniel_LaFleur]

Originally Posted by SteveGPage

So true! I think an alum at my very, very, very small college in Southwestern Virginia (John Forbes Nash, Jr) would love this game, too!

You're right.

This is a great example of 'Nash equilibrium', which is why I don't believe we'll see as much collusion (but we will see some) as is being posted here.

Each team will work to their own benefit ... which will mean that they will be very motivated to break their 'agreements' when the crucial time comes.

[leafy]

Originally Posted by Daniel_LaFleur

You're right.

This is a great example of 'Nash equilibrium', which is why I don't believe we'll see as much collusion (but we will see some) as is being posted here.

Each team will work to their own benefit ... which will mean that they will be very motivated to break their 'agreements' when the crucial time comes.

The nash equilibrium refers to a strategy which, when all players are aware of it, is the optimum strategy while accounting for any changes other teams may make in their strategy. No player has any reason to change, since the strategy they have is optimal, and any change would lead in a decrease in benefits.

The nash equilibrium of this game is not every team working to break agreements; An alliance has much more to gain if they score 0 than if they work hard, given that the other alliance is at least somewhat similar in scoring ability.

I made a long post that never appeared; expect this post to be edited ~6:30pm EST.

[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.

[Koko Ed]

FIRST really wanted to make sure that we're all winners this year.

[waialua359]

The way I see it, seeding points is just like W-L, except in the way you can position yourself higher/lower than another team.
In the W-L method, the only way you can overcome a team with a better record, is if they start losing matches, and often times is out of your control.
In the seeding system, you have more control to a certain extent, of positioning yourself with higher seeding points vs. other teams.
Penalties in the past sometimes was the difference to a W-L. The same situation this year would be a loss of coopertition bonus points. That's pretty substantial in a high scoring close match, where the penalties were a difference maker.

[Daniel_LaFleur]

Originally Posted by leafy

The nash equilibrium refers to a strategy which, when all players are aware of it, is the optimum strategy while accounting for any changes other teams may make in their strategy. No player has any reason to change, since the strategy they have is optimal, and any change would lead in a decrease in benefits.

The nash equilibrium of this game is not every team working to break agreements; An alliance has much more to gain if they score 0 than if they work hard, given that the other alliance is at least somewhat similar in scoring ability.

I made a long post that never appeared; expect this post to be edited ~6:30pm EST.

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