10 point goal versus 1 point goal

[DjScribbles]

Originally Posted by jlmcmchl

The simplest way to confirm the effectiveness of the one point goal, at this stage of competition was the Southfield district. 7th seed went for the 3-assist one point goal and made it all the way to the finals. Props to 862 1250 and 2474 for working together so well.

Thanks! I expected the 1-pt goal would make be a viable scoring option this season, but I was a bit surprised how well it worked. Our robot is capable of scoring the high goal, but under heavy defense it simply wasn't viable to do so unless you could fire on the run; and with 2/3 of the opposing alliance on defense, I think we'll see a lot more teams favoring the 1pt goal in elims.

[Bongle]

We ran the math on this, and the math comes to the same conclusion.

Variables:

• BallBase - Value of the ball. A fresh ball is 0pts, single-assist is 10pt, double-assist is 30pt, etc.
• ShooterP - High goal probability. Probability of getting a shot into the high goal. Value between 0 (never) and 1 (always)
• HighWaste - How many seconds you waste recovering a missed high goal shot
• LowWaste - How many seconds you waste repositioning after a failed low goal shot
• LowGoalP - Low goal probability. How probable each attempt at the low goal will go in.
• LowGoalTime - Time it takes to do a low goal attempt.
• HighGoalTime - Time it takes to do a high goal attempt.
• PointsPerSecond - How many points a wasted second is worth. I usually use 1pt/second, assuming 140pt alliance scores.

Concept: Expected value. The expected value of some event is the probability of the event occurring multiplied by the value of that event. So if you have ShooterP=0.5 and a 0pt ball, then E(highgoal) = 0.5*(0pt + 10pt) = 5pts.

Now, the expected value of a high-goal attempt:
E(highgoal) = (BallBase+10 - HighGoalTime*PointsPerSecond)*ShooterP - (HighWaste*PointsPerSecond)*(1-ShooterP)

Let's go through that:
"BallBase+10": Adding the 10pt high goal bonus
"- HighGoalTime*PointsPerSecond" - Subtracting the point value of the time it takes to make a high goal attempt
"*ShooterP" - Finds the expected value of a successful high goal attempt by multiplying the big term in brackets by high likely that it will occur
"- (HighWaste*PointsPerSecond)" - subtracts the cost of missing multiplied by the probability of missing (1-ShooterP)

Likewise, we have the low goal equation:
E(LowGoal) = (BallBase+1 - LowGoalTime*PointsPerSecond)*LowGoalP - (LowWaste*PointsPerSecond)*(1-LowGoalP)

Ideally, you'd want your expected value of a high goal shot to be positive. However, for many teams with unreliable shooters, it won't be.

But having a positive high goal expected value isn't sufficient. What you need is for the expected value of a high goal shot to EXCEED the expected value of a low goal shot.

Thus, you need:
E(HighGoal) > E(LowGoal)

Let's solve for how good your shooter needs to be (ShooterP) to be worth going for the high goal...

• (BallBase+10 - HighGoalTime*PointsPerSecond)*ShooterP - (HighWaste*PointsPerSecond)*(1-ShooterP) > (BallBase+1 - LowGoalTime*PointsPerSecond)*LowGoalP - (LowWaste*PointsPerSecond)*(1-LowGoalP)
• multiply shooterPs (and call ShooterP SP for shortening)
• SP*BallBase + 10SP - SP*HighGoalTime*PointsPerSecond - HighWaste*PointsPerSecond + SP*HighWaste*PointsPerSecond > ...
• SP(BallBase + 10 - HighGoalTime*PointsPerSecond + HighWaste*PointsperSecond) - HighWaste*PointsPerSecond > ...
• SP(BallBase + 10 - HighGoalTime*PointsPerSecond + HighWaste*PointsperSecond) > (BallBase+1 - LowGoalTime*PointsPerSecond)*LowGoalP - (LowWaste*PointsPerSecond)*(1-LowGoalP) + HighWaste*PointsPerSecond
• SP > ((BallBase+1 - LowGoalTime*PointsPerSecond)*LowGoalP - (LowWaste*PointsPerSecond)*(1-LowGoalP) + HighWaste*PointsPerSecond) / (BallBase + 10 - HighGoalTime*PointsPerSecond + HighWaste*PointsperSecond)

So if you plug in your BallBase, LowGoalTime, PointsPerSecond, LowGoalP, LowWaste, HighWaste, HighGoalTime assumptions into that equation, it'll tell you how good your shooter needs to be in order to make it worth taking a high shot over a low shot.

For example, let's say:
BallBase = 30 (double-assist ball)
HighWaste = 20 (20 seconds to recover a bounced ball)
PointsPerSecond = 1 (assuming a 140pt match)
LowGoalP = 0.85 (low goal is easy)
LowWaste = 5 (repositioning after a low goal miss is quick)
HighGoalTime = 2 (quick shooter)
LowGoalTime = 5 (positioning again)

Then:
SP > ((30+1 - 5*1)*0.85 - (5*1)*(1-0.85) + 20*1) / (30 + 10 - 2*1 + 20*1)
SP > (26*0.85 - 0.75 + 20) / (40 - 2 + 20)
SP > 41.35 / 58
SP > 0.71

So in that scenario (and given this equation), you should be sure you have a shooter accuracy of more than 71% before trying for the high goal, as the expected value of a low goal attempt is greater.

[B2E175]

I feel the teams that can acurately score in the 10 pt goal are going to to be the teams that we see winning later in the season. Now it seems like the one point goal is a good option but once 10 point shooters are fine tuned and drivers get experience i feel they will dominate over 1 pointers

[pabeekm]

Originally Posted by B2E175

I feel the teams that can acurately score in the 10 pt goal are going to to be the teams that we see winning later in the season. Now it seems like the one point goal is a good option but once 10 point shooters are fine tuned and drivers get experience i feel they will dominate over 1 pointers

One problem with that though is that as drivers improve the defense will also get much better, and from what I've seen it's a whole lot harder to do the high goal under defense than the low goal.

[billylo]

We played in GTR-W in week 1. During qualifications, we typically go for high goal because defence is not as intense.

In elimination, it's very difficult to get a shot off, unless a reliable running shot is an option (e.g. the shot after the block attempt here. http://www.justin.tv/watchfirstnow2/b/507662405?t=2231) We find it hard to do this reliably though.

Low goal is our friend and we primarily rely on 2 assists, truss and low goal (31pt cycles.)