Reefscape Game Analysis

Scoring

Here, the goal is to compute the expected value¹ of accomplishing each task.

Ideally this will make few assumptions, and support each assumption with evidence.

Barge

Barge scoring is the simplest to evaluate. With either the Shallow Climb or the Deep Climb, you need to drive over the Barge first, so parking forms a baseline score that all the other methods have to beat.

Excepting a buddy climb (which is a very high technical bar), these points are exclusive. If you aren’t climbing, your partner isn’t climbing for you.

Endgame	Points	Value	Volume	Notes
Park	2	2	1/robot, exclusive	Baseline
Shallow Climb	6	4	1/robot, exclusive	Value accounts for parking baseline
Deep Climb	12	10	1/robot, exclusive	Value accounts for parking baseline

Coral

Levels

“Initial slots” refers to the number of slots that start the match unblocked by algae.

“Max slots” refers to the number of total slots on the reef, assuming all the algae are removed.

Level	Points	Auto Bonus	Initial Slots (scoring cap)	Max Slots (scoring cap)
L1	2	1	Uncapped	Uncapped
L2	3	1	6 (18 + 1/auto)	12 (36 + 1/auto)
L3	4	2	0 (0)	12 (48 + 2/auto)
L4	5	2	12 (60 + 2/auto)	12 (60 + 2/auto)

Auto

L3 and L4 provide a +2 bonus in auto, while L1 and L2 provide a +1 bonus in auto. This makes L3 and L4 more attractive in auto. L3 offers a likely more reliable placement, but requires you to clear algae.

Algae

Algae scores the same in auto and teleop, but the expected value of algae changes based on the number of algae that are already scored in the net. When there are few algae in the net, it’s easier to score. When there are some algae in the net (around 5) you start to see diminishing returns from the net because balls can bounce out. When there is a lot of algae in the net, the expected value of shooting into the net approaches 0.

Net

Lined up end-to-end, 9 algae fit in the net almost exactly. If you can arrange them perfectly you could fit many more in there, but gravity will generally pull the balls towards the center of the barge, and they will tend towards a maximum volume of 9 balls.

\[ E[net] = 4(robot \; \%) \]

The expected value of a shot into the net (either by a human or a robot) decreases as net fills, because you run the risk of the thrown algae bouncing out when it hits a algae already in there.

Takeaway: The Net has diminishing returns.

Processor

Assumption: We assume that most HPs will throw the algae into the net rather than throw them across the field so their alliance gets another algae for the processor.²

Then, scoring in the processor has a value of the 6 points it scores minus giving your opponent an algae.

\[E[processor] = 6 - 4(shot\;\%)\] Since the shot percentage decreases as the number of algae increases, the expected value of scoring an algae in the processor increases (from an initial value near 2 towards the limit of 6) as the net fills.

Takeaway: The processor has accumulating returns.

Relative value

This matrix describes the value of each scoring action in terms of the other scoring actions - a more useful metric to keep in mind than the point numbers when making tradeoff decisions.

The “net shot %” is the assumed long-term average of shots in the net.

Ranking System

Tiebreakers

Since there are 3 bonus RPs this year, there are more degrees of freedom in the ranking score, and ties are less likely. The value of co-op as a ranking tiebreaker is low. Teams that are explicitly looking to rank high should look to earn it, but it isn’t super critical.

Barge RP

There are two cases that earn the Barge RP: a deep climb plus anything, or 2 shallow climbs plus anything.

Assumption: A park is essentially “free”; any robot can get it.

Evidence: Unless your partner no-shows, even if they are disabled you can push them into the zone for a park.

A Deep Climb gets you the RP almost every time; the main limiting factor is the success rate of the climb.

\[ Deep \; Path = (deep \; \%)P[\geq 1 \; park] \]

A Shallow Climb is much less reliable for the RP, primarily because you need another partner to Shallow Climb. Another facet of this is that for the shallow + shallow + park/shallow path, you cannot have any members of the alliance outside the barge zone at the end of the match.

\[ Shallow \; Path = (shallow \; \%)(partner \; shallow \; \%)P[no \; dead \; partners] \]

Auto RP

• Does A-stopping your robot count as disabling it for the purposes for the ranking point? (Current read of the rules: no)
• Notably, you can push your partners off the line and earn the RP for them.
• LEAVE is evaluated at the end of auto, not anytime during auto.
• The auto RP requires

In 2018, the “Auto Quest” RP also required scoring one game object and all three robots to get mobility points.

Reef RP

You score the Reef RP either by scoring 5 pieces of coral on each level of the reef, or by earning co-op (both alliances score 2 algae in the processor) AND scoring 5 pieces of coral of 3 of the 4 levels of the reef.

Game Flow

The field is rotationally symmetric; your processor is always on your right, and your cages are always on your left. There isn’t a big red/blue difference in this game.

Segmented Field

• Scoring locations and pickup locations are on the same side; offensive play will primarily happen on your side of the field.
• There is a penalty (6pts + Barge RP) for touching your opponents’ cages at any point in the match. The main takeaway here is that you can only use your own Barge zone to travel to the opponent’s side of the field.
• The cages provide a physical obstacle to crossing to the other side. Not a huge deal, but slows you down in passing through and could damage poorly designed robots.

Game Piece Supply

Manual Fig 6-2

• Coral supply is effectively infinite - you get 60 pieces on your side of the field. The limiting factor is the number of slots you have to score it.
• Of the 18 algae on the field, each alliance clearly has an advantage in controlling 9 of them due to the segmented field. Opponents run the risk of penalties by trying to steal algae from your side of the field.
• Algae is the only “zero-sum” scoring resource.

If a HP could roll the coral from the HP station towards the reef, you might be able to cut out some time from coral cycles. (After testing, we reject this idea - the coral doesn’t roll reliably, and the distance between the reef and the coral stations is small so the potential benefit is small.)

Visibility

The field is mostly wide open and scoring locations are generally quite visible, with a few exceptions.

• It isn’t easy to see the back side of the reef from any driver station.
• From DS3 (the rightmost) it’s difficult to see the cages
• All the way to the opponent’s side of the field.

Alliance Interaction & Defense

Rules:

• Zone protection for the Reef and Barge zones is strong. If any part of your robot is in your zones, contact by an opposing robot is a Major (6pts), regardless of initiation. Note that an extension from your robot qualifies for this protection.
• Only one robot from your alliance can be on your opponent’s side of the field at any given time.
• 3-second pin count; pinning every cycle is less valuable.

Note: The coral stations are not protected!

Strategies:

• Zone denial defense near the coral stations seems viable. However, if you deny your opponents one of the two coral stations, they still have the other one to use, and if you chase them around the field you run a higher risk of zone penalties.
• Stealing your opponents’ algae at the beginning of the match seems valuable if you’re all-in on the processor and daring your opponents to get a lot of algae in their net.

Triangle Cycles

“Triangle Cycles” take advantage of the fact that the scoring location for coral also serves as a pickup location for algae to save one leg of travel time every other cycle.

This fits most naturally with net scoring on the left hand side and processor scoring on the right hand side.

Split the Field

One very natural way to play the game is for two coral robots to split their side of the field in half and cycle coral. The third robot can contribute either by also feeding from a coral station (slightly crowded), handling algae, or disrupting the opposing alliance.

Value of Ground Intake

For algae, it is high - one third of the “natural” algae you have access to start essentially on the ground. Furthermore, missed algae shots on the net become ground intake opportunities.

For coral, ground intake has limited value because of the short distance between the stations and the reef, and the nearly-infinite access to coral.

Value of holding both game pieces

There really isn’t a pathing that can repeatedly take advantage of holding both a coral and a ball, because the algae and coral are acquired from different places and scored in different places.

Sidebars

Considering L1

L1 is the lowest-value scoring available, but it does have a high cap. Does that high cap matter? That is, how much scoring would an alliance have to do before L1 scoring becomes efficient?

• Assumption: You have access to 9 algae
  • (i.e. you aren’t stealing from your opponents’ side)
• Assumption: All members of the alliance can score somewhere other than L1
  • (so we can average out scoring between 3 teams)

You would need to score all 9 algae (either net or processor), plus 12 coral for each of L2, L3, and L4. That’s 45 game pieces scored, for an average of 15 per alliance member.

The match has 150 seconds (auto included), so to fill all scoring locations other than L1, your alliance needs to average 10 second cycles.

Takeaway: Reorienting coral is a waste of time. Designing your robot to both be able to score “wide” for L1 and “long” for L2-L4 adds more complexity than it is worth. Just pick one between L1 and L2-L4, depending on your capacity.³

Net vs Processor

We can set the EV of Net and Processor scoring equal to each other to retrieve the (robot/human) net shot % required to equalize EV. This essentially tells us: given a certain human player shot %, what does the robot shot % need to reach to equalize the expected value?

Assumption: Processor scoring is 100% reliable.

Assumption: HPs attempt to score every time they have the ball, instead of feeding.

Let \(r\) be the robot’s net scoring percentage, as a proportion. Let \(h\) be the same for the oppponent’s human player.

\[ \begin{aligned} E[net] = 4(r) \\ E[processor] = 6 - 4(h) \\ E[net] = E[processor] \\ \implies 6 - 4h = 4r \\ \implies \frac{3}{2} - h = r \\ \implies r = \frac{3}{2} - h \end{aligned} \]

Algae Stealing

Algae does not score additional points in autonomous, but it is the “zero-sum resource”, since both alliances effectively have infinite coral access (and climbs can’t be interfered with, mostly.) This means that in matches where both alliances expect to be filling L4 and L3, the number of algae your alliance has access to is a critical tiebreaker for efficient scoring.

Takeaway In high level play, keeping control of the 9 algae on your side of the field, and possibly stealing algae from your opponent, is a key difference maker.

Algae Specialization

Since scoring in the net has decreasing efficiency and scoring in the processor has increasing efficiency, you are incentivized to score all your algae in the same place.

This doesn’t account for what your opponents are doing (for example, if they score a lot of algae in their net very early, maybe processor scoring is a good choice for your alliance.)

Takeaway In general, be all-in on either the net or the processor (ignoring co-op considerations, and ignoring what your opponents are doing.)

Algae Feeding

The HP does not have to shoot algae into the Net. They could choose to use those algae to feed their own robots. This doesn’t make much sense if the robots would then score them in the net - but it could make sense if your alliance scored in the processor. The idea being to fill up your opponents’ net and make each processor score nearly EV = 6.

Generally, taking the time of a robot in the match to execute this strategy is unlikely to be worthwhile. But if you expect to score all the algae on your side of the field (and will put them in the processor), this gives you more algae to work with.

Footnotes

1. not just the number of points scored - the additional points relative to a baseline

2. A HP could throw the Algae to the other side of the field so their alliance can score it in their processor, rather than taking the \(E[net] \approx 3.5\) shot.

3. If an alliance is unable to clear the algae from the reef, being able to fit more coral into L1 does raise the number of available scoring locations. However, clearing the algae from the reef is very easy - probably easier than coral reorientation. If you really need to fit more L1 coral on there, you can just have an upgraded kitbot specialist do it.