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Velocity Arena · Season 2 · Reallocation

Proportional Scaling

Does scaling a stat by 50% scale the bot output by 50%? Find out.

Motor Power = Speed × 5
Charge Speed = Power²
Budget = 20 − S − E − T − P
Key terms — match all four to continue
0 / 4
Click a term on the left, then click its definition on the right.
Term
Scale × 1.5
Proportional
Quadratic
% Change
Definition
Output grows much faster than input because P² = P × P
(new − old) ÷ old × 100
Multiply by 1.5 — 50% more than before. e.g. 6 × 1.5 = 9
Input grows 50% → Output grows 50%. Same rate.
✓ All matched — enter your stats below to start calculating.
Step 0 — Enter your Season 1 stats
Speed (S)
Power (P)
Part A — Speed · Motor Power
Formula: Motor Power = Speed × 5
Multiply
Motor Power = ? × 5
Calculate your original motor power using your Season 1 Speed.
Scale up 50%
Scaled Speed = ? × 1.5 = ?
Scale Speed up by 50%. What is the new Speed value?
50% more = multiply by 1.5
Original
× 1.5
+50%
Multiply
New Motor Power = ? × 5
Calculate new motor power using the scaled Speed.
Find % Change
% change = (new − old) ÷ old × 100
What is the percent change in motor power? Fill in the scaffold, then enter your answer.
Place your numbers — then calculate in your head or on paper
(
New MP
−
Original MP
) ÷
—
Original MP
× 100 =
?%
Your answer ↓
Fill in your values above, work out the answer, then type it in the box below.
%
Speed Results
Stat increase—
Output increase—
✓ Proportional — input and output scaled by the same factor.
Part B — Power · Charge Speed
Formula: Charge Speed = Power²
Multiply (P × P)
Charge Speed = ?²
Calculate your original charge speed using your Season 1 Power.
Scale up 50%
Scaled Power = ? × 1.5 = ?
Scale Power up by 50%. What is the new Power value?
50% more = multiply by 1.5
Original
× 1.5
+50%
Why squaring multiplies twice
Original
P × P = P²
→
After scaling P by 1.5
(1.5P) × (1.5P)
= 1.5 × 1.5 × P × P
= 2.25 × P²
The 1.5 multiplied itself. You scaled P by 1.5, but squaring means that 1.5 appears twice — once for each P. So the output grows by 1.5 × 1.5 = 2.25×, not 1.5×. That's why quadratic formulas are much more sensitive to stat changes than linear ones.
Multiply (P × P)
New Charge Speed = ?²
Calculate new charge speed using the scaled Power. Remember: Power squared = Power × Power.
Find % Change
% change = (new − old) ÷ old × 100
What is the percent change in charge speed? Use the same formula as before.
Place your numbers — then calculate in your head or on paper
(
New CS
−
Original CS
) ÷
—
Original CS
× 100 =
?%
Your answer ↓
Fill in your values above, work out the answer, then type it in the box below.
%
Power Results
Stat increase—
Output increase—
✗ Not proportional — the output grew by more than the input.
Before you see the comparison
You've seen both numbers. Which stat is more dangerous to raise in this system — Speed or Power?
Reverse check
If charge speed doubled (100% increase), did Power increase by 50%?
Here's the difference
Speed scaled proportionally. Power did not. When you increased Speed by 50%, motor power went up by exactly 50%. When you increased Power by 50%, charge speed went up by 125% — not 50%. That's because charge speed = P², a quadratic formula. The same input scaling produces a much larger output jump.
Speed → Motor Power
Stat ↑
+50%
Output ↑
+50%
Same growth rate = Proportional
Power → Charge Speed
Stat ↑
+50%
Output ↑
+125%
Much bigger growth = NOT Proportional

Why this matters for your reallocation: when you move a point into a stat, you need to know which formula it feeds. A point into Speed is proportional — a steady, predictable gain. A point into Power is not — the effect grows faster than the stat, so the same point can be worth more.
Apply it
You're about to reallocate for Season 2. Using your numbers, decide which stat you'll raise and by how much — then write one sentence on what the math says that change does to your output, and why it's worth the point.
Next — Season 2 Reallocation

Reallocate your stats

Season 2 is open: you may now move points between Speed, Power, Turning, and Endurance. Your total still adds to 20 — every point you add to one stat comes out of another. Use what you just found to spend each point where it does the most work.

A point into a proportional stat (Speed → Motor Power) gives a steady, predictable gain.
A point into a squared stat (Power → Charge Speed) grows the output faster — for the same one point.
Stay legal: S + P + T + E = 20, and no stat below 1.

Take your numbers to the My New Build worksheet: pick your changes, predict the effect, test them in solo practice, then commit your new loadout in the dashboard.