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Quantitatively Evaluating the Regionals
Now that all of the regional and district events are finished for 2011, does anybody have a favorite way of evaluating which ones were the toughest to win?
This is a fairly complicated question, despite an obvious answer (Michigan State Champs) and some conceptually simple possible methods (ex: total average points per match).
I'm toying with this problem for fun, and initially I'm looking at ways to compare the OPR data from regional to regional. For example, one can reason that the high scoring teams have the biggest impact on regional difficulty, and thus calculate OPR minus some threshold for each team, sum that up for the whole event, and in this way determine how much big scoring is present at a given event.
I am also interested in the impact of having different numbers of super strong and fairly strong teams present. For example, having just one super powerhouse doesn't make an event really hard to win, because then you can win by getting picked. Having two of those super teams makes it really hard for everyone else, but fairly easy, relatively speaking, for those two teams, even moreso than if there was only one super team. That's assuming they aren't opposed to being allied together.
But there are other things going on as well. If it's a big regional with lots of teams, then it's slightly harder for the two super teams to win, because a third team might go undefeated (not facing either super team) and have a higher qualification score, then go onto prevent the super partnership. Also, a regional with exactly 2 super teams, 21 solid teams, and 30 really weak teams might be a bit harder for the super teams since they'd have a weaker 3rd robot than opposing alliances and would have to fight through 3 stacked alliances to win.
Another angle to consider this from is that the percentage chance of winning a given event is going to depend on your team's robot ability, represented by OPR or some other measure. Obviously a higher OPR will give you a better chance to win any event... or would it? In the event with two super teams, you might be better off with a medium OPR than a higher OPR, because you'd have a better chance of landing on the top alliance with pick #16. Also, I can envision a pair of events where a higher OPR team would be more likely to win event A than event B, while a medium OPR team would be more likely to win event B than event A. For example, let's say two events already have 3 super strong teams registered, but one has a really deep pool of solid robots in its second tier, while the other only has a couple of solid tier 2 bots. I think the medium OPR team is better off with the deep pool in hopes of either being a 3rd pick or getting on a stacked alliance; in the other event, the medium team is more likely to end up as an alliance captain without any really strong teams to pick as partners. The super team, on the other hand, is probably more likely to win the event with 3 strong robots and a sharp dropoff after that. They can expect to end up on one of two strong alliances and get their chance to duke it out in the finals with the other strong alliance.
Anyway, given that difficulty depends on your team's OPR, I think it would be cool to have an algorithm that could output the percentage chance of winning for a mystery team with a given OPR that joins at the last minute.
I know that I'm missing a lot of important considerations here. I just think this is an interesting problem to examine. It must be because I'm a baseball stat nerd.
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I think we all should strive to be better than what is expected of us. :) - Madison [more] 
12-04-2011, 19:38
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