The math of the cans...

[asid61]

So after discussing with some of my team members about whether we should make our step can grabbers faster (Yes!) I decided to run some numbers on whether it would be worth it in elims to grab, say, 2 cans, faster than anybody else. Or 4 cans but remove something major from our bot.
Or literally have a bot made of can grabbers that grabs all 4 cans in a fraction of a second, using superior firepower (all the cims + as many motors and pneumatics as you can fit in that 120lb-limit), plus our drivetrain for shoving noodles or totes.

I am not counting the value of noodles due the unknown factor in how long it takes to put them in cans or how many can fly to the other end of the field.

Most of this is calculated with a 3-stack assumption for really good teams. This is lowballing IMO, but you can see at the end that more stacks/ team means a more effective can grabber.

With 2 cans to each alliance, then it's evenly matched points-wise per alliance. If, in one match, an alliance can score 5 full stacks of totes + can (not counting noodles here) and one non-can stack that's
36 points/stack * 5 stacks + 12 points for non-can stack = 192 points.
A high number, to be sure, but doable depending on where you are (thankfully, my team is not attending Dallas lol). With no cans, only the 3 you begin with, then you run a point total of
36*3 + 12*3 (tote-only 6-stack) = 152 points.
Okay, that's not too bad, your average still remains relatively good, especially if against other teams you can match taking 2 cans off the step. Plus, you can still score totes instead of picking up cans once you run out to lessen the impact. The other team still gets only 192, which could be beatable overall with other elims scores.

TL;DR: If a really good robot this year can score 2 canned stacks (as in, that's the effective maximum for even the really good teams) then the can grabbing bot is somewhat ineffective in elims. Very situation-specific as to its other capabilities.

But...

If two alliance members can stack 3 fully loaded stacks, and the can grabber can only grab 4 cans, then that's a total capacity of
6*36 = 216 points.
with canned stacks. By contrast, if you can only get 2 cans off the step and a decent stacker (2 loaded stacks) with the two good stackers that's
5*36 + 3 * 12 = 216 points.
TL;DR: At any level of competition, two demon-stackers and a decent stacker w/ two-can grabber would do as well as an alliance containing a bot that grabs 4 cans and flops over with two demon-stackers. If the can-grabbing-flopper can cap 6-tote stacks with cans or load cans with noodles or something, then it has the upper hand.

If an alliance with the capability to get 4 cans the fastest makes it to semis, then it gets very interesting. Because each team plays 2 matches, and there's only 4 teams playing, a lowered score due to loss of the cans could impact the score enough to outweigh the fewer points that a specialty can-grabbing bot would make compared to a fast stacker.
Using the 3-stack/bot model,
4-Can grabber alliance:
6*36 = 216 points.
Other alliance:
3*36 + 6*12 = 180 points.
In matches without facing the 4-can grabber, but still obtaining two cans:
5*36 + 4*12 = 228 points.

Cutting it pretty close there at 228 vs. 216. But, at 6 matches worth 228, and 2 matches worth 180, the average is only 216 points! What an interesting coincidence.
So if you have that 4-can flopper, pushing some noodles around could possibly win you semis.
TL;DR: A 4-can bot that does nothing else can tie with an alliance made of really good stackers if it has stackers of similar level oiance in semis. It can beat the opposing alliance if it can push stuff around or do anything other than flop over.

On Einstein, the 4-can-and-flop is an almost guaranteed win. If every robot there can make, say, 3 loaded stacks over the course of the match, this is the flopper's alliance:
6*36 = 216 points.
This is the other alliance:
3*36 + 6*12 = 180 points.
In order to beat the flopper's alliance, the opposing alliance has to score an additional 18 totes. That's 3 extra stacks, or essentially one entire extra stack per robot on an alliance. And everyone's on Einstein here. 3 stacks is a lot of upper hand.

I'll have to wait until Dallas to see what the metagame is- how many stacks can the best of the best get? 3? 4? 5? The more stacks they can make, the more effective the can-grabber-flopper bot becomes (assuming the alliance is made up of good robots), as it becomes increasingly likely that they can score all 7 canned stacks every single match, and the opponent's average score drops even lower.

Take Einstein again. The opposing alliance has to make do with 3 cans. With only two functioning robots on the flopper's alliance after auton, at a capacity of 4 stacks per non-can bot, the flopper alliance makes
7*36 + 1*12 = 264 points.
Compared to
3*36 + 9*12 = 216 points for the no-canners.
AKA 24 extra totes to score to catch up. I'm not doing the math for semis, but I think it's still going to be pretty close for a can grabber vs. everybody else with higher points totals, although the can grabber would have a better upper hand.

So to summarize:
-On Einstein, cans are important. It could all be decided in the literally the first second.
-In elims, cans are important, but not as much. A can grabber has to still carry its weight, at least a bit.
-If a really good robot can stack 3 canned stacks per match, then a 4-can grabber is about equal to a 2-can grabber with 2 canned stackes in a match.
-If the metagame is 3 stacks/bot, then the 4-can-grabber is pretty good. As the metagame gets better, to 4 or even 5 stacks per robot, the value of the can grabber becomes much higher to the point of being overpowered.
-If a very high-seed team with 2-can grabber picks the next fastest 2-can grabber, it stands poised to win if it can pass through quarterfinals.



Personally I wouldn't want to build just a 4-can grabber as the robot unless we spent all season getting the code and mechanism perfect to the point where it was a guaranteed grab of all 4 in 1/10th of a second, and I knew it was impossible to be faster than us.
Which is totally possible.

Thoughts and errors in my concepts? Assuming all tote stackers are created equal is a fallacy, but it doesn't look like there will be a massive fissure between the fantastic teams and the good teams this year. Still, the 4-can flopper has to do something else other than grab the cans...