# Launcher Accuracy Graph

This is a theory I thought up and decided to get some opinions on. The topic is on launcher accuracy for shooting games in FRC and how that relates to strategy.
The attached graph demonstrates the concept. Please note that it’s just a quick representation that I drew up and the plot is not based on any empirical data.
This theory assumes that you have a finite load of gamepieces, you go to a specific point on the field to shoot every time, and that you can make alignment adjustments after each shot to increase your accuracy. The graph will change shape depending on the gamepiece used, the goal being targeted, the location the shots are taken from, and the characteristics of the particular launcher.
The theory is as follows:
You line your robot up to shoot and take your first shot. This shot has the lowest chance of going into the goal in relation to all subsequent shots. You continue firing gamepieces at the goal making alignment adjustments after each shot. Each shot you take will increase in it’s potential to enter the goal (because of the alignment corrections). This can be observed on the graph using the shot numbers starting at “1” on the left side of the x-axis of the graph. Each shot is plotted verses it’s accuracy on the y-axis. Eventually the slope of the graph will level off indicating that you have achieved your robot’s “sweet spot” and that the accuracy has become completely dependent on launcher variables (not robot alignment). This will create a horizontal asymptote in the graph indicating the maximum possible average accuracy for your robot. The location of this asymptote is governed solely by the mechanical characteristics of your launcher.
It is also possible to calculate the average accuracy of your robot based on how many shots you take (represented by the grey curve).
One important thing to note is that as soon as you have exhausted your load of gamepieces, and you drive the robot away to collect more, the graph will reset and you’ll start from the left side of the graph again on your next trip.
Now how does this relate to strategy and design?
The goal of the mechanical design of your shooter mechanism should simply be to make the maximum accuracy asymptote as high on the graph as possible (as close to 100% accuracy) by controlling or entirely removing the variables in the launching mechanism and gamepiece management systems.
The application to strategy is a bit more complicated. There are two types of shooting games: finite storage and infinite storage. Finite storage is like 2012 or 2013 where there is a predefined limit to the number of gamepieces you are allowed to carry at one time. Infinite storage is like 2006 or 2009 where you are allowed to carry as many gamepieces as you can build a robot to hold. In the former case the limit to gamepiece possession is often so low that you will never approach the asymptote. This means your accuracy depends primarily on your alignment system (driver skill, camera tracking, photon cannon, etc.) and your launching hardware.
However in the latter case this graph is more useful. You can choose to make many trips of a few gamepieces each in the match or make only a few trips with a large number of gamepieces. You can use this concept to balance the number of trips you take with the number of gamepieces to hold. Should you spend half the match picking up 50 gamepieces and then spend 30+ seconds launching them? You will achieve the highest average accuracy possible this way, but what about the 30 seconds at the end of the match? That is wasted time considering it’s not enough time to make another huge load of gamepieces. A defender might also be able to cut you off until the end of the match and prevent you from scoring any points at all. Would it be more efficient to make 3 or 4 trips of 30 balls each with a lower average accuracy per trip? This might make you more versatile and unpredictable for defenders. Also decreasing you hopper size (and capacity) may add additional functionality in the way of endgame and collection methods.
These are the type of questions I hope to be answer with this theory in future shooter-based games.

I would appreciate feedback! Have you used something like this graph? Is this helpful or is it so obvious that it’s a waste of time discussing it? Are there any provisions, exceptions, or modifications that need to be made to make it more accurate?

That sounds about right. I guess you could determine empirically whether you would gain more points from a given improvement in precision or alignment.

But this seems like a very narrowly applicable result. Normally, you don’t know how much better you would make one of them without doing it. I guess this would be useful if you already had two different mechanisms built and you were just trying to choose between them.

Yea, this all depends on mechanism to mechanism. In a game applicable to this scenario, you need to see if you can justify many small loads or one big load with your specific mechanism in mind.

For example, in 2009, some teams chose to “vomit” all the rocks in large quantities, while other teams chose to specifically target the limited amount they had. Both strategies worked well, but both depended on reliable mechanisms.

I think the biggest dependency would be more on allignment method, as proven last year. Many robots that pushed up against the lower bar of the pyramid had nearly 100% accuracy on the first shot. With that accuracy level. It was too costly to adjust. The best method was for them to machine gun their full load of Frisbees into the goal as fast as possible so you could go back for as many more as possible.

They had hard allignment points that were easily determined.

My second thought is that access to the practice ranges was critical. This is due to object aging / wear (and launcher component aging / wear). The more used, the less accurate. But if you get to make adjustments on the range, you can come up with a new constant. At home you pre-age loads of objects. On the tournament field, you practice from the appropriate load. Again adjustment on the game field may not be necessary.

Neal

When using such a graph for strategy discussions, don’t forget to identify areas where robots can shoot without real impediment, and take them into account in your discussions. Examples: Zone near wall in 2011, Key in 2012, touching pyramid and loading zone in 2013. I don’t know of any similar zones in previous years.

Another factor is the variability from piece to piece. The balls in 2012 were highly susceptible to wear; the discs in 2013 were remarkably durable, consistent and predictable. The variations from piece to piece will affect how valuable such adjustments will be.

Not really true. While I 100% agree that accuracy was probably in the 80-90th percentile off the first shot for frisbees (at least from under the pyramid), it was definitively not best to just shoot your whole load of frisbees, especially if you missed the first one. That would be true if you had only one or two more frisbees to shoot, or if gathering them took essentially the same amount of time as realigning to shoot would, but neither was true for this game.

You couldn’t really add an extra cycle by shooting your discs faster. On the other hand, you could probably score 30-60% more points by just seeing where the first disc went then carefully realigning the robot. If you didn’t realign, you essentially just threw away all that time you used to gather those extra discs. If you do realign, sure, you might have burned an extra five seconds, but you’ll still get six or nine more points.

Going slow to go fast is one of the major things I work with my drivers on as coach. With something that’s in limited supply, like frisbees, you’re much better off getting a partial success by going slow than a complete failure by rushing.