What is the ideal number of teeth on those "toothed circles" you speak of?

My answer will betray my mechanical disinclination, but ...

Most of us are riding 39x53 up front.

As for cassettes in the back, none of us is likely to need an 11, so 12x23 is pretty standard. Myself, I use a 12x25 because I like to do hilly races and I'm too lazy to swap out my cassettes. I've found 12x25 to be plenty versatile enough for me, and it often means I can get over small climbs without having to go small.

I will second Luke's comments and add a bit more. The cassette in the back also depends on whether you have 9 or 10 speed. The one "magical" cog to have for a crit is the 16. It is the one I use the most and since I have 9 speed, 12x23 is what I have used most. I did get an 11x21 this year and have started using it for all flat crits or downhill finishing races. I have found that I can increase my max speed by a 1 or 2 mph with the 11 if the conditions are right where I can even use it.

If you have a 10 speed, a 12x25 will give you a 16, so that will work well also.

One should also not rule out the compact crank set. This has a 50/34 combo in the front. They are relatively new and have a stigma as being reserved for women and old farts who have tender knees. However anyone can do well with them.

I bought a new bike recently that was listed as having a 53/39. I rode it for about two weeks and did the four-man TTT (1:39:59) with it before I noticed a few days later that it was compact set!

Take home message? Either one can be fine as you will find similar gear ratios . . .sorry, let me translate into easy speak! Either is fine because you will likely find a comfortable gear, and with an 11 on the back of the 50 you can still haul some serious butt down the finishing straight. So there is no shame at all in having a 50/34!

I think the compact crankset is great. I have a compact crankset and use an 11x23 cassette, and it's works perfect for flat races and a race like fox river grove with the steep climb. That's the main reason the compact came about. It has more useable gear ratios.

I ride a normal 53x39 up front and have recently switched to the SRAM 11x26 ten-speed cassette in the back. For an all-arounder who still wants to be competitive in fast elite men's sprints, I do believe there are times when you need a 53x11 (depending on wind, terrain, etc.). So I think that should rule out compact cranks for Cat 1, 2, and 3 men for crit riding in the midwest.

On the other hand, I dig the versatility of SRAM's 11x26 so you can just stay in the big ring for stuff like the aforementioned Fox River Grove. (FYI: I won the Cat 3 version of the race back in June and went up the climb in the 53x25 each time, except 53x21 when attacking.) I used a 27 for the Tour of Ohio, which got used a lot, but I know a 26 would have done the trick as well. So I think SRAM's 11x26 is the best way to go for elite men out there, and that's probably cheaper than a whole new crankset too.