Multiplier Powerup Study

Time to put some of my applied stats skills to work here.

Multiplier Study: Assuming you hit every single multiplier ball and no multiplier powerup is used, each one will roll out at the following times (in-game time, not the timer on the top-left). Note the timer may run out before you even get to multiplier 9, hence some of the later values's time results are skewed a bit.

Games tested: 29 - Leaping Lava
    Range           Median           #     Time
x2: 4.35 - 9.55s   (median:  7.10s)  (29)  0:07
x3: 13.0 - 27.6s   (median: 19.85s)  (29)  0:20
x4: 21.3 - 45.25s  (median: 32.00s)  (29)  0:32
x5: 31.7 - 64.75s  (median: 48.85s)  (29)  0:49
x6: 45.2 - 83.65s  (median: 65.30s)  (29)  1:05
x7: 58.5 - 100.95s (median: 81.00s)  (25)  1:21
x8: 72.9 - 106.15s (median: 89.83s)  (12)  1:29
x9: 91.5 - 101.35s (median: 97.75s)  (3)   1:38
xe: Not enough data  (0)
xe: Not enough data  (0)

Where 'xe' is other multiplier balls that pop up if you didn't hit other ones. 

Conclusion:

• In a 60 second game if you didn't collect timer powerups, best case = can get up to a x7 multiplier, worst case, up to x5.
• Typically, five multiplier balls will show up on a regular no-power game, but there was one instance where eight showed up in a 1m40s game.
• The first multiplier ball comes out within 4-10 seconds.
• The higher the multiplier, the longer it takes on average before another multiplier comes out. (an x9 takes 20% longer than an x2)
• Multipliers love to spawn near ball starting points.
• On average, it takes 15 seconds between multiplier balls coming out and another. You can get lucky and wait around 5 seconds before another one comes out, or bad luck waiting around a half a minute. Theoretically, you can reach your x9 within 30 seconds with multi-multiplier, but the pseudorandom number generator that determines how long it takes for another ball to appear will make it very unlikely for that to happen.

Note: Something for me to think about via randomness of powerup appearances.