Changes in the 2010 USAMO/ Announcing the 2010 USA Jr. MO

[Kent Merryfield]

[Kent Merryfield]

[unimpossible]

Can a student take both the AMC 10 and AMC 12, and then use the higher index for qualification into JMO?

[seasonal squirrel]

I agree with Kent Merryfield, all you're doing is pushing juniors and seniors out. For a more balanced representation just go with the old system of ~ 330-170.

[sophia]

[emannes]

This is an interesting idea, and I do not object to it in principle. However, the distribution of olympiad seats seems to be off.

Recall that last year, 330 seats at the USAMO were reserved for AMC 12-ers and 160 for younger students. Now, there are 250-270 for AMC 12-ers and 230 for those who take the AMC 10. This is a really, really bad distribution.

The 12th and 11th graders will continue to take the AMC 12 and try for USAMO as usual. The top 10th graders (and a large number of those who are not at the top as well) will take AMC 12s instead of the AMC 10 to try for the USAMO because there's no path for them from taking USAJMO. 9th graders are the only people with an incentive to take the USAJMO. (What's the official pronunciation, by the way? usage-mo?)

First, the change in the distribution of USAMO seats and AMC takers will lead to USAMO qualification being ridiculously hard for everyone, and perhaps raising the index to something like 240. (I don't have the data to figure this out, but the AMC does. Maybe they could estimate what the USAMO index would be with almost 50% more takers and 60-80 fewer seats.) Second, it will dilute the quality of those taking the remainder of the olympiad seats, the USAJMO-ers. I suppose this is the intention -- to supply an easier contest. This is still a problem, because it takes the top people to USAMO, and some top 9th graders and a ton of those who are not quite as good, but leaves everyone in the middle (a lot of people) out. Dozens of highly qualified people who made USAMO last year through the AMC 12, for instance, will not have a chance of making it back because there simply are not enough seats.

If the number of USAMO/USAJMO qualifiers changed to reflect the number of people taking the contest -- 400/100? 375/125? -- this experiment might work out a lot better.

[Kent Merryfield]

[sophia]

[not_trig]

First, the 270/230 split is pretty ridiculous. I would say a 350/150 split would be better. Is the goal of the USAMO to select the top students, or to make younger kids "feel better"? I didn't qualify for USAMO in 8th grade, and I didn't deserve to. The point of USAMO selection is to recognize the top students and to differentiate them even more. If the goal is to let lots of younger kids qualify for a less prestigious contest at the expense of upperclassman qualification... well then this is fine. Moreover, it is now more difficult for younger students to even qualify for the USAMO; whereas previously they could use their AMC10 index, now, they compete for fewer spots with lower AMC12 scores. So essentially you are cutting out a large majority of younger students from USAMO and sticking them into a different contest.

Second, having only #3 and #6 on the JMO be 1/4 USAMO level is somewhat silly. Would you reduce the amount of time to 3 hours if 1/2/4/5 are AIME level? Also, why would everyone take the same AIME to qualify for different contests, one of which just has more AIME level problems? I suppose this could be justified by saying "the USAMO is too hard for younger students." But is it not the whole point of USAMO to expose them to difficult problems and a new level of thinking? Now, they'll just sit at their comfort level on the JMO, instead of being challenged to constantly improve by the USAMO. Perhaps the AMC thinks that an "overly hard" contest would be "discouraging," but if you are on the level of making USAMO, wouldn't you have invested enough in math to not be discouraged, but have an incentive to improve and a goal to reach?

Third, Red MOP qualification is pretty unfortunate under this system. Would freshmen taking the JMO just work on #3 and #6? And those who could qualify without solving just 1 and 4 (I am pretty sure I know of at least 2, including the one Catalyst mentioned, who qualified by solving #3 in 2008) would definitely be hurt. But basing red MOP qualification on 2 problems, with harder problems as "tiebreakers," tends to destroy incentive to do those harder problems. Moreover, how would ties be broken when comparing between JMO and USAMO scores? If a freshman gets #2 on USAMO, is that better than solving #1 and #4 on JMO?

Sure, the current (previous?) system leaves things to be desired, but this JMO may cause problems far beyond that of the current system. Those who dislike the current system are often those who believe they should have made USAMO but did not (i.e. whining about the system as opposed to improving their own skills). Instead of constantly complaining about the system, why not spend that time to improve your skills? The practice problems are out there, and there are plenty of smarter people out there (esp. on AoPS) to help. (on a tangent: if you want help, a) use correct spelling and punctuation, b) don't use lots of ?????, c) don't put down people who try to help.) Go buy books or attend camps or something. Don't blame the system; get better.

[DataBox]

[CatalystOfNostalgia]

[Kent Merryfield]

Here's an exercise in modeling, using California data. In 2009, California had 109 USAMO qualifiers, slightly over 20% of the national total. Of those 109, 54 were 11th or 12th graders while 55 were 10th graders and younger.

Now let's take the date and make two assumptions. The first assumption is that everyone with a reasonable chance of making the USAMO would take the AMC12. The second assumption is that their AMC12 score would be 20 points lower than their AMC10 score.

I have seen as part of this discussion that the USAMO qualifying index might be 210. (Note that it was actually 201 for the AMC12 in 2009). Let's use 210 as that index. That would give us 77 USAMO qualifiers: 42 in the 11th and 12th grades, 35 that are younger.

Note that 42 is 12 fewer than 54; we have already pushed 12 11th/12th graders out of USAMO qualification - almost a quarter of the total. Yes, there were that many 11th/12th graders in the 201-209 range.

But there's another problem lurking here, which is that 77 USAMO qualifiers is too many. Cutting down from the current 500+ to 270 should give us no more than 60, and probably fewer. So we need to cut down the total by another 15 or 20 to match it to 270 qualifiers nationwide. Well, let's look at the 35 10th grade and younger students that this model shows as qualifying for the USAMO. Perhaps some of them would continue to take only the AMC10, thus removing them from the USAMO pool and presumably putting them in the USAJMO. But how many? Of this group, only 6 of the 35 took only the AMC10 in the first place. (Quite a few of them took one AMC10 and one AMC12.) Would they all have continued to take only the AMC10? The three I know personally would have very likely have changed their behavior and taken at least one AMC12. (And one of those falls into the AIME category anyway.) My best guess is the 5 out of the 6 would have shifted to the AMC12, with the result that we're still dealing with 76 USAMO qualifiers when we need 60 or fewer.

So the index would have to go up.

Let's say that we set the index to 215.5. With that, we would get 60 USAMO qualifiers (a little high, but maybe California is like that). Of those 60, 35 would be 11th and 12th graders and 25 would be younger. And I'm even more convinced that all of those in the younger category would switch to the AMC12 and stay in the USAMO pool.

So it looks like the system would go from this:

54 upper class USAMO qualifiers, 55 younger USAMO qualifiers

to this:

35 upper class USAMO qualifiers, 25 younger USAMO qualifiers, 50 USAJMO qualifiers.

Perhaps California is dramatically different than the rest of the country, but I don't really think so. I see plenty of young grades on USAMO lists from other states as well.

The new system is OK, but the numbers aren't OK. If there are going to be 500 USAMO + USAJMO participants, then 270 is far too few for the USAMO and 230 is far too many for the USAJMO.

That fact that this is that dramatic a change in numbers might be a good thing anyway, but I don't personally agree with that. The AMC has a certain amount of resources to invest. Should they redirect a significant fraction of those resources towards younger students? That feels to me like a baseball general manager using most of his draft picks on high school pitchers. You will find some major stars that way, but you'll also get a very large number of those who put in some time in the "minor leagues" (the USAJMO) and never really develop from there so that you never hear from them again. What about those were slower to develop in the first place and never really got it going until the second half of high school? I'm sure that if you scour IMO rosters past, you'll find some students who answer to that description as well. Of course, those older students will still have opportunities, and 270 is still larger than the number of students in the entire USAMO not very long ago. But I do wonder about directing so much in the younger direction.

[Sly Si]

I don't think the new process is unfair to anyone. It's essentially returning the USAMO numbers to where they were five-ish years ago. And having the AMC12 as the only route to USAMO solves a lot of problems, while the USAJMO does a nice job of providing a destination for AMC10 takers to aim for. Dr. Merryfield has a good question about whether this is the best use of AMC resources, and I think that bears some consideration by CAMC if it hasn't received such already. I'm also unclear on the selection process for Red MOP, but I trust it will be taken care of in some reasonable way, even if the standard is not 100% objective.

Mr. Dunbar, I'd like to suggest a slight modification to the selection procedure: I believe AMC12 takers in grades 10 and below who do not qualify for the USAMO should remain eligible for the USAJMO, with their AMC12 score used to compute their index. Otherwise, a situation could arise in which the cutoff score for USAJMO is lower than the USAMO cutoff (though I don't know how likely this is). In that situation, AMC12 takers would be in effect "punished" for taking the harder test, under the very reasonable assumption that their AMC10 score would have been equal to or higher than their AMC12 score. I see this change as akin to the last-minute change made in 2002, in which the floor cutoff was changed to apply to all students in grades 10 and below (instead of just AMC10 takers as the rule originally stated), for a similar reason.

[sophia]

[Quickster94]

Just a question for the AMC Director, how "concrete" is this accepted proposal? Is this exactly what will be happening next year, or is there room for change after feedback from here and other places?

[hurdler]

[MellowMelon]

[AMCDirector]

As of this writing, there are now 50 posts in this thread filled with conjecture, speculation, questions, opinions and counter-opinions. This is too many, too diverse, and too cacophonous to respond to intelligently in this thread.

If you have a question about either a fact or a procedure related to the 2010 USAMO or the 2010 USA Junior Math Olympiad, please begin a new thread and ask your question in that new thread. (One question per thread for simplicity and clarity, please). Either I or AMCFinance (E. Claassen) will answer your question in that thread for all to see. Thank you.


Steve Dunbar
MAA Director, American Mathematics Competitions

[worthawholebean]

I'm about to do some splitting on this thread.

[benzi455]