First, I am concerned about costs rising again next year. The bus we are using this year costs about 50% more than the bus we used from the same company two years ago, and I expect fuel prices to continue to rise. I am holding out hope that the $275 we are charging students this year will be sufficient to cover our costs, but I am seriously worried that even $300 may not be enough next year. Given that, I think it might be a good idea to start looking into sustainable fundraising opportunities for the future..

Next, the transportation situation is always tight on the bus. The bus we have this year can accommodate three full teams of 15 students and a full coaching staff, and the only way we have been able to accommodate more than that the last three years is because some parents have volunteered to fly with their students in order to open up additional space on the bus for more team members. We obviously can't rely on this as a long-term solution, but I do think we can continue to count on there being sufficient interest from the Bay Area to field three full teams as long as costs do not increase substantially. As such, it might be worth looking into a system where we can implement a fair and objective method of selecting 45 students to represent the Bay Area at ARML each year..

This leads right into the issue of team selection. In addition to having to choose which 45 students can go to ARML, we will be faced next year with the issue we have every year, namely that of selecting which students go on which team. We have been administering team selection tests at our Sunday practices, but this method ends up taking up more than half our time at each practice, when I feel we should be spending more time on content and team building. In addition, because we have only four of these tests and take each student's top three scores, a student who has more than one conflict with our practices is in trouble. On top of this is the fact that team selection is occurring so late in the year we won't have our rosters finalized until less than two weeks before ARML..

We also run a risk in the future of being unable to provide fresh tests this late in the year. We obviously can't use old ARML tests for team selection, as those are all accessible to students who search for them. This year we have been using tests from mathleague.org, NYSML, and TRML, all of which are similar enough to ARML that it makes sense to use their individual rounds even if they are easier than ARML tests to varying extents. While the mathleague.org tests have been given out the same weekend they are officially released, we had a three or four week lag between the date the NYSML tests were released and when we administered them; the TRML lag is several months. This strategy worked fine for this year, but NYSML and TRML will dry up as problem sources once students realize we are using them and that they can get their hands on copies in advance. All this suggests a need for some sort of team selection mechanism that is independent of our team practices, that concludes earlier in the year, that offers students more opportunities to participate, and that can ensure fresh tests..

With that in mind, I propose that the SFBA team employ a team selection mechanism that ranks students based on their performance at various math contests throughout the year. I have no problem incorporating a mandatory AIME score into this mix, because the importance of the AMC contests is such that no ARML student should miss out on that contest. I hesitate to include AMC 10/12 scores for two reasons: first, I have yet to see a valid metric that allows scores from those two tests to be compared; second, I find it unreasonable that any student accepted onto our ARML teams would not have qualified for the AIME, so in that sense an appropriately weighted AIME score should serve as an even more reliable proxy for a student's AMC index..

As for other contests, it makes sense to allow students to attend a number of contests and to take the top three or four performances. The biggest problem here is that my students only reported about three or four contests that currently exist in the Bay Area, and to require students to attend all of these does nothing to alleviate the schedule conflict problem I identified above. So to implement my proposal we will need to increase significantly the number of contests in the Bay Area. The other big problem is that it will be difficult to assign some sort of composite score to students given the diverse nature of the contests that currently exist, unless we can find some way to normalize the scores or to impose some sort of standardization on the contests..

As things stand, mathleague.org is currently equipped to solve both of these problems by supplying tests for as many as eight additional contests per year in a consistent format that will allow scores from one contest to be compared to scores from all the other contests. Eight of these contests will provide students ample opportunity to register three or four valid scores for team selection. Furthermore, while some of these contests could be hosted by schools or colleges, the ARML team could host contests on any of the unclaimed dates and operate these contests as fundraisers for the team. I estimate that for $10 per student we could host contests that would provide nice awards and lunch for the students while still raising a significant amount of funds for the ARML team. In addition, we could sweeten the deal by offering students who are accepted onto the team a $10 rebate off their ARML fees for each contest they attended. This would create a situation where students on the team would incur no net cost to participate in these contests while realizing the benefit of a further discount based on the revenue generated by the contests..

I do think it is important to be able to include results from other contests as well, so I would like to start a dialogue with the extant contests in the Bay Area to see if we could find a way to incorporate them into the team selection process, either by using mathleague.org contests or by coming up with an approprite way to scale the results from the contests in their current format..

The biggest problem I anticipate with this setup will be what to do about students who claim to find out about this process too late in the year (realistically, in March) to participate in the team selection process. I would plan to advertise heavily at other contests, on AoPS, over the team mailing list, and through a direct mailing to schools across the region. However, there is still a chance a student could slip through the cracks. To be fair, even this year I have had some students claim that they found out about ARML too late to attend the first few practices, but this issue will become more acute as we move to an earlier process. I'll have to give some thought to how to deal with this fairly; any suggestions are certainly welcome..