[FRC Blog] "Standard District Points System for 2015"

[Zebra_Fact_Man]

First takeaway: Why was the QS capped at 22 pts instead of the previous 24? Also, why is the minimum 4 instead of 0?

Not that it matters, but it does strike me as odd.


So max pts this year is now 83 w/ Chairman's, 73 w/out at District events, instead of 85/75.

[artK]

Originally Posted by Zebra_Fact_Man

First takeaway: Why was the QS capped at 22 pts instead of the previous 24? Also, why is the minimum 4 instead of 0?

The answer to the first question is because, even in a WLT system, perfect 24s are pretty rare. In MAR, according to this, 23's have only been done twice, and in theory a 24 should have only happened once at this point. (Though it would be interesting to see what a difference a WLT would have on this game on the rankings). More matches per team make it harder to score a perfect record.

And regardless of the reason for the upper cap, the lower cap probably exists to keep the average score at 12. If the average score from qualifying becomes less than 12, teams that win judged awards, eliminations, or are a new to gain a slightly greater advantage in their 5 or 10 points, and re-adjusting the point values in that respect would make the system even more complicated.

[Ty Tremblay]

Here's a spreadsheet that uses an approximation method of InvERF(). It's not 100%, kind of a hack actually, so let me know if you have any improvements.

[Rachel Lim]

This Wolfram Alpha Widget: http://www.wolframalpha.com/widgets/...2fb3bb85e071b4 should calculate it if I put in all the equations properly (I'm not sure if I completely understand how the district ranking works, so there may be errors). It doesn't require any other programs to run (I know some students who don't have Excel so I decided not to try and figure out the equations in it). Please let me know if you catch any problems in it and I'll try to fix them.

[MasterMentor]

Originally Posted by Ty Tremblay

Here's a spreadsheet that uses an approximation method of InvERF(). It's not 100%, kind of a hack actually, so let me know if you have any improvements.

Originally Posted by Rachel Lim

Please let me know if you catch any problems in it and I'll try to fix them.

You both forgot the Ceiling Function.

[Thad House]

So I just did this for us, but it seems like this would be a small net increase for the teams at the top of the rankings. We went 11-1-0, and 10-2-0, and 10-2-0, with a 1 seed, 1 seed, and 3 seed. So we got 22, 20, and 60, for a total 102. With this structure, we would have gotten 22, 22, and 63, for a total of 107. So if you were constantly at the top seeds, this most likely will be a net increase in points, especially at tougher events, where the 1 seed might only have had 10 wins. However, the top teams are not usually the ones where 5 points makes a difference, so it most likely would not have much of an actual effect on the top.

[MikeE]

Originally Posted by Thad House

However, the top teams are not usually the ones where 5 points makes a difference, so it most likely would not have much of an actual effect on the top.

This is the key point (pun intended) in the discussion^*
The small difference in points for teams at the top and bottom of the distribution make little impact on progression through the season. For example, in New England last year every team with a record of better than 10-2-0 at either of their scored events ranked in the top 10 teams going into the District Championship.

However running the 2015 rank-based points model on 2014 New England results shows that there would have been only 1 change to the teams invited to the District Championship. So it doesn't seem to make much difference in the middle of the pack either.

One small effect of the change is that teams are no longer penalized directly for disqualification or not being inspected in time for the qualifications matches. The indirect penalty of a reduction in average score may be larger.

Finally the use of the ceiling function means smaller events have a slightly higher expected points total per team, but this is minuscule in comparison to the huge seeding/playoff points advantage at smaller events.

^*although I personally enjoy any work incorporating a statistical model, so props to Danny!

[Rachel Lim]

Originally Posted by MasterMentor

You both forgot the Ceiling Function.

Thanks for the catch--I believe it's fixed now, but I don't know what the results should look like, so I can't really check. Please let me know if you catch anything else.

The same link should work: http://www.wolframalpha.com/widgets/...2fb3bb85e071b4

[AGPapa]

Originally Posted by artK

The answer to the first question is because, even in a WLT system, perfect 24s are pretty rare. In MAR, according to this, 22's have only been done twice, and in theory a 24 should have only happened once at this point. (Though it would be interesting to see what a difference a WLT would have on this game on the rankings). More matches per team make it harder to score a perfect record.

To clarify, 23's have only been done twice. 22's are a little more common.


Oh, and I made a spreadsheet showing how the QS points will be distributed by rank for every MAR event. The MAR events are all similar in size this year, so it doesn't change much event by event.

[MasterMentor]

Originally Posted by Zebra_Fact_Man

First takeaway: Why was the QS capped at 22 pts instead of the previous 24?

In the GameSense interview, Frank mentioned that only 0.6% of all teams scored 24 points last year. I guess it would have been nice to have a perfect comparison to last year, but ignoring the 0.6% doesn't seem devastating to me.

Originally Posted by Zebra_Fact_Man

Also, why is the minimum 4 instead of 0?

In the summary document, it says "typically-sized district events" would have a minimum of 4 points. Though, in the explanation document the tables show that at about an event size of 55 the minimum goes from 4 to 3. Using Rachel Lim's district points widget, it looks like 3 is the minimum going all the way up to a tournament size of 1,000. If you look at the explanation document, the range scale in the formula is 10, but the gain factor at the end is 12; that says to me the formula is built to never go below 2 points, and because of the nature of the Inverse Error Function (going to infinity at the limits and all) and the use of the Ceiling function, you will never go below 3 points period.

Though, I must admit, it would be a crushing blow for a team to show up at an event and get no points whatsoever. Even if they don't have aspirations of making it to the District Championships, getting a goose-egg is deflating.

[Ian Curtis]

I think a one sentence version of Danny's white paper should really ought to go into the manual with a graph (and a link to the white paper!). This function is going to be needed to be explained several thousand times this season and teams/volunteers/the public seeing math as a scary black box is good for no one.

Something along the lines of "This function assumes teams are approximately normally distributed, and awards points based on rank. The #1 seed will receive 22 points, the middle of the pack ~12, and the lowest ranked teams ~4.

Then a plot for a 40 team event, with rank on the x axis and points awarded on the y.

[MasterMentor]

Originally Posted by Ian Curtis

This function is going to be needed to be explained several thousand times this season and teams/volunteers/the public...

Really? You think Volunteers and the Public care about the District Points System beyond what can be found in a, "Rank/Points" chart?

I'm glad FIRST didn't just publish a "bunch of tables" and actually showed us what's behind the scenes. It gives more credibility to the data in my opinion.