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Velocity Arena · Day 11 · Phase 1

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 proposal: if you argue for raising a stat cap, you need to know which formula it feeds into. Raising a Speed cap is proportional — predictable. Raising a Power cap is not — the effect grows faster than the stat.
Apply it
The Commissioner is proposing raising the Power cap by 2 points above your current stat. Using your numbers, calculate what that would do to your Charge Speed. Then write one sentence telling the Commissioner whether you support the change and why.
Next — Phase 2 (25 min)

Commissioner Proposal Prep

Use your Phase 1 numbers as data evidence. Your proposal needs one specific rule change, two numbers from your Season 1 dashboard, and a statement on how the change affects the last-place team.

A rule may cap a stat or set a floor (e.g., "no team may have Speed above 10")
A rule may not force a specific value (e.g., "all teams must set Power to 5")
A rule may not change the formulas or the budget constraint