pic: Alliance Scores Over the 2011 FRC Season

[IKE]

Originally Posted by Ian Curtis

Since I assume 33 has pretty decent points per robot per match data, have you ever matched up the OPR with the actual points a robot is worth per match? Can you make any comments as to how good that fit is?

We do a comparison at the events we are at to see how good of an indicator OPR is. We don't run stats on it, but mostly do visual checks to see if we are missing something or to look for trends. This probably would be a good thing to run stats on though...

Like Joe Ross said, 2008 correlated incredilby well. Especially if you used the top 2 offensive teams OPR. Unfortunately, negative OPRs also correlated well that year.*

2009 didn't work well at all. Over 50% of moonrocks were scored by humans, and many teams rotated the human player position.
2010 was pretty good. With good teams though, 2+2+2 =8 at MSC, the scores inflated drastically as teams could do zone play because there were good teams that could pick up the slack. 2010 also had some unique strategies that would underpredict certain teams. 67, 254, and 1114 were so good that even though OPR had them at 8-10, they would frequnetly score that many points, plus attempt a couple of points for the other teams! In reality, in a close match, those guys could do 10-12. OPR would often underpredict good alliances that year. Our qualifying match against 254 had an OPR predictor of I believe 16 to 12. The actual match turned out to be 20 to 18 (still one of my favorite FRC qualifying matches even though we lost).

2011 was interesting. OPR ws a reasonable predictor, but due to digressive scoring, it had the opposite effect as 2010 had. In 2011, 50+60+45 = 120-130 was not uncommon. There wasn't enough room for 3 good robots to put up a good score, and there were only 2 minibot poles.

************************************************** *****

*One partner in 2008 had a 6WD with omnis on the corners. Every lap the driver would inadvertently spin the wrong way when changes direction while doing a lap and would spin back over the line and get a penalty. I convinced a the team to zip-tie grip-mat to their omni wheels for a our match, and they only got 1 penalty that match.

Examples like this are where scouting can pay dividends. Often a team with a negative OPR is either breaking a rule or driving poorly. If you can observe their issue, and point it out to them, you can frequently get a few more points, ah er, not loose a few points that you likely would have without the comments. I was suprised that there were not more DQs in 2011 with all the red-card opportunities the GDC had in the rules.

[Jim Zondag]

Same data graphed by Percentage lets you see the trends a little better:
You can see how the population center moves to the right as experience increases
A little bit about the data set and this method. I have a database which has all the OPRs for all the team at each event they play, spanning many years. I take all of the OPRs and group them into catagories, this year it is in segments of 5 points per segement. I have used the "20 slices" method since 2006 to allow me to overlay data from several years worth of competition onto the same chart for analysis of multi year trends even though the games often have very different scoring systems.
Included in the 2011 data set:
Teams who played at least one event = 2053
Teams who played at least two events = 800
Teams who played at least 3 events = 244
Teams who played at least 4 events = 45
Beyond this, the popluations are too small to be relevant.

You can see from the chart some of the things IKE mentions: At 4 events, the teams are clearly limiting one anothers' total performance as indicated by the big peak at 40-45. With multiple robots of this caliber, the per team score actually goes down.

[Racer26]

Observation in the first graph. from about 6400 to 6600 on the x axis looks like MSC.

The peaks from the 6 competition weeks, then MSC at a much higher caliber (quals nearly as good as week 6 elims), followed by CMP with CMP quals at MSC elims level.

[BHS_STopping]

Originally Posted by IKE

Anyone care to do an alysis on how many teams would have to average net 0 pts. in order for 20% of alliances have a resultant score of 0 pts.?

for example, with dice, if I have 3 dice, the probility of at least 1 of them being a 1 during a roll would be 3*1/6 or 50%. the prob of 2 being 1s would be 3/2*1/36 or 4.5%. The probablility of 3 1s would be 0.5%. At a district event with 80 matches, there would be 160 alliances, and thus I would expect 1,1,1 0.8 times or 80% of events, there would be at least 1 alliance that got 1, 1, 1.

If 0 is assumed as the lower limit, then a 0,0,0 should be difficult to get. If FRC was on 2 vs 2, and 50% of the field could score 1 (or more), and 50% of the field could score 0. I believe you would expect on 25% of alliances to have a score of 0.

For 3 vs. 3, it should (in theory) be significantly more difficult... in theory. I guess my argument is that if "average" robot might correspond with your values, but the "median robot" may perform significantly lower...

Just wanting to correct you slightly on your math here.

If you throw three dice, the probability of at least one of them coming up with a 1 is not simply 3 * 1/6. Using this logic we could then assume that if we throw 6 dice then the number 1 is going to appear every single time (which is false, the actual probability in this case is about 66.5%). When throwing three dice, the probability of throwing at least one 1 is equal to 1 - (5/6)^3. This number turns out to be about 42.1%.

The probability of throwing exactly two 1's is a little bit trickier, but it's not too difficult. There are 216 possible dice rolls for three dice, and 15 of those rolls have exactly two 1's in them. 15/216 is roughly 6.9%. If we include the 1, 1, 1 case (that is, all situations where at least two 1's come up) then our probability is 16/216, or 7.4%.

The probability that all three dice show 1's is 1/216, or .46%, so you were right about that one.

[Racer26]

Originally Posted by BHS_STopping

Just wanting to correct you slightly on your math here.

If you throw three dice, the probability of at least one of them coming up with a 1 is not simply 3 * 1/6. Using this logic we could then assume that if we throw 6 dice then the number 1 is going to appear every single time (which is false, the actual probability in this case is about 66.5%). When throwing three dice, the probability of throwing at least one 1 is equal to 1 - (5/6)^3. This number turns out to be about 42.1%.

The probability of throwing exactly two 1's is a little bit trickier, but it's not too difficult. There are 216 possible dice rolls for three dice, and 15 of those rolls have exactly two 1's in them. 15/216 is roughly 6.9%. If we include the 1, 1, 1 case (that is, all situations where at least two 1's come up) then our probability is 16/216, or 7.4%.

The probability that all three dice show 1's is 1/216, or .46%, so you were right about that one.

And this is where the house edge on the casino game of Sic Bo comes from. Yay math.