Rumble sprinkle calculations

=How to calculate the size of a sprinkle attack=

The exact calculations behind the size of a sprinkle attack have not been published by the developers or any individual (although Boothook claims to know the answer; see the 1 Million PoE Rumble Research Event!).

The basic formula below represents the results of experiments and guesswork by the community and is a work in progress. See Rumble sprinkle data for examples of situations where the formula does and does not work correctly. However, in many cases and as a starting point, there is a simple way to calculate the size of a sprinkle attack:

Take the number of popped balls (including the breaker ball) and divide that number by two, discarding any fractional part. Since you must pop 3 or more balls, this number will be 1 or more. If you have dropoff (loose balls that fall down after popping the balls), take the number of dropoff balls and divide by three, again discarding any fractional part. This gives you the number of sprinkles created by your attack.

Example 1:


 * Popping five balls and having seven dropoff (which can be notated as 5d7) has the following effect:
 * Sprinkles from popping: 5/2 = 2.5 -> 2
 * Sprinkles from dropping: 7/3 = 2.33 -> 2
 * Total # of sprinkles: 2 + 2 = 4

The Sprinkle Queue
However, small sprinkle attacks are not sent immediately; if there are less than a full row of sprinkles (9 balls) created, they will be stored up in the "sprinkle queue" until a full row or more are created, at which point they will all be sent at once.

Example 2:


 * Popping eight separate groups of three balls will produce 3/2 = 1.5 -> 1 sprinkle for each group, for a total of 8 sprinkles. You can wait as long as you want and your opponent will never receive these sprinkles. If you then pop a group of six, this will add another 6/2 = 3 sprinkles and bring the total up to 8 + 3 = 11. Your opponent will shortly receive 11 sprinkles.

Multi-row sprinkles
If you hover over your bludgeon pattern in your booty panel, the bottom two rows you see are the sprinkle pattern. The top one is called the single row pattern, and the bottom row is called the multi-row pattern. On some bludgeons like the fish the two rows are identical, whereas for other bludgeons such as the fists, the multi-row is significantly harder to clear because it contains an additional color.

If you only make a single row of sprinkles, it will always send the single row pattern. But if you create more than a single row as in the last example, the extra balls can use the multi-row pattern. In Example 2 above, we created 11 sprinkles; the opponent would receive the full first row (9 balls) and then the remaining two balls using the multi-row pattern.

Example 3:


 * Popping a group of 3 and dropping 30 off will produce 1 sprinkle from the pop, and 30/3 = 10 sprinkles from the drop, for a total of 11 sprinkles (9 single row, 2 multi-row).

Example 4:


 * Popping three separate groups of 3 followed by a fourth group of 3 and dropping 22 off will produce 4 sprinkles from the 4 pops, and 22/3 = 7.33 -> 7 sprinkles from the drops for a total of 11 sprinkles again (same as above).

An important thing to remember is that it can be impossible to tell whether you've received multi-row sprinkles or two single rows of sprinkles, depending on which sprinkle locations were chosen for the multi-row. The locations appear to be random, but there is certainly room for someone to demonstrate a pattern. (Strike locations in swordfighting were at one point thought to be random, but actually follow a well-defined pattern.)

Squishing
One other effect that occurs is that if the number of sprinkles in your sprinkle queue ever exceeds two full rows, it will be "squished" down to a single row. This is why a single gigantic pop will not bury your opponent in row after row of sprinkles.

Example 5:


 * Popping five separate groups of three produces one sprinkle for each attack, for a total of five sprinkles in the queue.


 * If you then continue with a huge attack, for example pop 7 and dropping 42 that will add 17 sprinkles to the queue, for a total of 22 sprinkles. This is greater than two full rows, so the attack will be squished and your opponent receives a measly 9 sprinkles.

Sprinkle Scaling
Sprinkle scaling is a little-known game mechanic. BootHook described it in this post on the forums. He said "In the beginning of the game, you need to pop 18 balls to send one row of sprinkles. (...) If both players send a sprinkle attack, then the sprinkle scaling goes away. This mean that you only need to pop 9 balls to send one row of sprinkles.". This information dates from 2006, therefore it is not known whether this effect is still in the game. This effect may help to explain BootHook's 2nd and 3rd hint videos; the left player is playing by our basic formula, but the right player clearly is not.

Current Research
The above formula works for a large number of cases, and yet it is not completely correct. In some cases the actual result is off by +1 or -1 balls, and in other cases completely different effects happen! Check out Boothook's Rumble Challenge Hint videos for some interesting cases. If you can come up with a theory that explains all of these cases, you could win a million PoE!

Challenge Hint Analysis

Boothook's hint videos are annotated here for your convenience and experimental uses. A plain number such as 3 or 8 denotes that many balls being popped, and a number prefixed with a d such as d6 indicates number of balls being dropped.

Video 1

Attacker sends:

3 3 3 4d22

Defender receives:

12 sprinkles (3 multi-row)

Notes: This one works as expected using the above calculations.

Video 2

Both players attack during this video.

Right attacker sends:

4d1 3 4 3 3 3 3 3 5 3 6 4 3d4 4 3 3 5d4 3d9 3 3d10 3 3d7

Left defender receives:

9 9 9 9

Notes: This one works as well.

Left attacker sends:

16 8

Right defender receives:

9

Notes: These large pops are one place where the formula breaks down; we would expect 12 sprinkles and only got 9.


 * One suggestion regarding this are that there is a limit to how many sprinkles a single pop can create; if we assume that at most 5 sprinkles can be created per popped group, this will work.


 * Another suggestion is that extraballs adds a "bonus" to the original sprinkle volume and therefore the 16 balls group itself sends the 9 balls (single row) sprinkle attack and the 8 balls group form another queue to a new attack. Tests have shown that breaking one single group of at least 15 balls (including the breaker!) in the beggining of the game will send an attack of 9 balls to the oponnent. So probably the extraballs "bonus" is around 1/3 of the total extraballs in the group.

Video 3

Again, both players attack during this video.

Left attacker sends:

6 4 3 3 3 5d13 4 3 5d12 7d11 4d12 5d3 3 3 3d2 3 3 4d2 7d5

Right defender receives:

14 9 12 10

Notes: The formula works perfectly on this long string of attacks, which is a success in itself.

Right attacker sends:

3 10 17d3 14d5 7 5d1 3d3 6d10 4d1 3 3d2 5d6

Left defender receives:

9 9 9

Notes: The formula fails miserably on this side, predicting 44 sprinkles total when only 27 are actually sent. This is a prime case where modifications are needed.

Tips for Rumble Research

 * Use an alt account, or a friend on a separate computer to test your theories. You can open two clients at once and rumble yourself to see what your attacks are doing.
 * Record everything! There are many programs such as Desktop Activity Recorder, Camstudio, and Hypercam that allow you to record video of your screen for later analysis. It makes it much easier to study your results, and provides evidence should anyone question your data.
 * Post on the Rumble Research thread; more eyes on your theory will help to improve it and you could win huge PoE.
 * Have fun!

=Link to different theories= If you have a different theory you can create a page for it and put the link here.

Giobb's Rumble Sprinkle Calculations Theory