Velocity Arena · Day 13 fallback

Build the Equation without real match data

The Day 13 activity needs each bot's stat and win % to build a trend line. If matches haven't run, there's nothing to plug in. This sheet gives the class a ready-made Season 1 — eight bots and four match days — so the lesson runs exactly as written. The math is identical; only the source of the numbers changes.

This is stand-in data, and students should know it. Say so plainly: "We didn't get our matches in, so we're practicing the equation on a pretend season. Next week we do it again with your real bots." The skill transfers; the honesty matters.

How to run it

Open the activity and pick a statUse the same Build Your Bot's Equation → activity. Start with Speed — it's the clearest trend in this dataset (that's by design; the curriculum's win equation is Speed-based).
Give each group two bots to build their lineRead that bot's Speed and Win % off the table and enter them as the two points. Assign different pairs to different groups — that's the whole point: everyone gets a slightly different equation.
Give each group a third bot to testIn Step 4 they plug a third bot's Speed into their equation, compare the predicted win % to the actual, and read the residual. A small non-zero residual is the expected, healthy result.
Compare equations as a classEvery group reads their line aloud. They differ — because two points never capture the whole class. That disagreement is the bridge to the real scatter plot next week.

Season 1 — the class dataset

Eight bots. Each stat loadout totals 20. The four match-day columns are wins out of 5 matches that day; Win % is total wins over 20 matches. (Sorted by Speed so the trend is easy to see.)

Bot	Stat loadout (sum = 20)				Wins per match day (of 5)				Win %
Bot	Speed	End	Turn	Power	MD1	MD2	MD3	MD4	Win %
Tank	4	6	4	6	2	1	2	1	30
Pip	5	6	5	4	2	2	2	2	40
Gonzo	6	5	4	5	2	2	1	2	35
Rover	7	5	4	4	2	3	3	2	50
Dash	9	4	3	4	3	3	2	3	55
Zippy	10	3	4	3	2	3	2	3	50
Bolt	11	3	3	3	4	3	4	3	70
Comet	12	2	3	3	3	3	4	4	70

The data is internally consistent: every match day totals 20 wins across the class (20 matches a day), so a curious student who adds a column up gets a real number back.

Suggested group assignments

So groups don't collide, hand out pairs like this (build-pair → test-bot). Any two bots with different Speeds work — these just spread the class out:

Group	Build line from	Test on
A	Tank (4, 30) & Comet (12, 70)	Rover (7, 50)
B	Pip (5, 40) & Bolt (11, 70)	Dash (9, 55)
C	Gonzo (6, 35) & Dash (9, 55)	Comet (12, 70)
D	Rover (7, 50) & Zippy (10, 50)	Tank (4, 30)

Group D is a teaching gift, not a mistake. Rover and Zippy have almost the same win % at very different Speeds, so their line is nearly flat — m ≈ 0. When that group's prediction misses badly, ask the class why. Two points can lie about the trend; that's exactly why next week's full scatter plot is better.

Answer key

Group A worked example (Tank & Comet, test Rover)

Rate of change (slope): win % change ÷ Speed change = (70 − 30) ÷ (12 − 4) = 40 ÷ 8 = m = 5.

Y-intercept: b = y − m×x, using Tank (4, 30): b = 30 − (5 × 4) = 30 − 20 = b = 10.

Equation: y = 5x + 10 (predicted win % = 5 × Speed + 10).

Test on Rover (Speed 7, actual win % 50): predicted = 5×7 + 10 = 45. Residual = predicted − actual = 45 − 50 = −5. The equation under-predicted by 5 points — Rover did a little better than its Speed alone suggested. A small residual like this is the normal, healthy result.

Group B check: Pip (5, 40) & Bolt (11, 70) → m = 30÷6 = 5, b = 40 − 25 = 15, so y = 5x + 15. Notice A and B found the same slope but a different intercept — good fuel for the class discussion.

What the dataset is built to show

Speed is the strong predictor. Win % climbs about 5 points per Speed point, with real scatter around the line — so slopes land near 5–6 and residuals are small but not zero.
Endurance runs the other way. In this class the fast bots are the fragile ones, so building a line on Endurance gives a negative slope (e.g. Tank & Comet on Endurance: m = −10). A group that tries a second stat sees that a stat can be negatively linked to winning — a great compare-and-contrast if you have time.
Turning and Power barely move. Both cluster around 3–4 for every bot, so they make weak, noisy lines. If a group picks one and gets a wild slope, that's the lesson: a stat with little spread can't predict much.
Two points never tell the whole story. Different pairs give different equations from the same eight bots. That's the honest limitation the real scatter plot fixes next week.

Velocity Arena · NYC FIRST. Pairs with the Build Your Bot's Equation activity. Use this only when real match data isn't available — real bots always beat stand-in data.