Day 13 — Build Your Bot's Equation

Step 1 of 5

Pick a stat. Select two class bots.

You'll build a trend line from class data. Pick one stat to analyze, then enter two bots with different values for that stat. The line will describe a trend across the whole class.

1

Which stat do you want to track?

Pick the stat you want to investigate.

Speed

How fast your bot moves

Endurance

How long your bot lasts

Turning

How well your bot steers

Power

How strong your bot is

💡 What is a data point?

A data point = one bot's result. It has two numbers: that bot's stat and its win %.

Example: a bot had a Speed of 8 and a win rate of 60%.
That data point is written as (8, 60).
The stat goes first. Win % goes second.

1

Bot 1

Stat value

Win % (0–100)

Your Point 1: ( — , — )

2

Bot 2

Stat value

Win % (0–100)

Your Point 2: ( — , — )

📊 Two class bots on a graph

Bot 1

Bot 2

⚠ Your two stat values are the same. You need two different values to build a line. Change one of them.

Fill in all four numbers first.

Step 2 of 5

How much does win % change?

For every 1 point of stat you add, how much does win % change? That number is the rate of change.

📊 Your match data

Point 1

Point 2

📈 What is rate of change?

Rate of change = how much your win % goes up for each stat point you add.

Formula: rate of change = win % change ÷ stat change

Math calls this the slope. We use the letter m.

1

Calculate the rate of change

Step A — Find the win % change

Win % changed from ? to ?

Change = ? − ? = ?

Step B — Find the stat change

Stat changed from ? to ?

Change = ? − ? = ?

Step C — Divide: win % change ÷ stat change

Rate of change (m) = ? ?

m =

📺 What is the y-intercept (b)?

The y-intercept (b) is where the line starts.

It predicts win % when the stat equals 0.
Even if no real bot has a stat of 0, the line still needs a starting point on the graph.

We calculate it with: b = y − m × x
Use your Point 1 numbers.

2

Calculate the y-intercept (b)

Plug Point 1 into the formula: b = y − (m × x)

b = ? − ( ? × ? ) = ? − ?

b =

Confirm both answers before moving on.

Step 3 of 5

This line models the two bots you selected.

It passes through both bots you chose. Choosing different bots produces a different line — two points alone don't capture the full class picture.

Note: Any two points define exactly one line. This equation fits your two bots exactly — but different bot pairs give different equations. Test on a third bot in Step 4 to see how well it holds.

📊 Your two-bot model as a line

Point 1

Point 2

Model line

Your Two-Bot Model

y = —x + —

y = Win %

m = —

x = Stat

b = starting value

What each piece means

y

Win % — the percentage you want to predict.

m

Rate of change — how much win % changes per 1 stat point. Your value: —

x

Stat — the number you plug in to make a prediction.

b

y-intercept (b) — sets the line's starting value when the stat is 0. Your value: —

What your rate of change means

"For every 1 point I add to stat, my predicted win % changes by m percentage points."

Interpreting your slope:
↑ A positive slope means increasing this stat was linked to higher win % in your data.
↓ A negative slope means increasing this stat was linked to lower win % in your data.
↔ A slope near 0 means win % changed little between these two bots for this stat.

Important: This equation describes a pattern in the class data. It does not prove that one stat alone caused winning.

✓ Substitution check: plug in Point 1

Substitute Point 1 into your equation. It will come out exactly right — because Point 1 was used to build the equation. This confirms your arithmetic, not whether the model is good.

y = —

Step 4 of 5

How accurate is your equation?

Use a third class bot — one you didn't use to build your line. This tests whether the class trend holds for unseen data.

What is a residual?

Residual = predicted win % − actual win %

If the actual point is above the line, predicted − actual is negative.
If the actual point is below the line, it is positive.

• Residual = 0: exact match for this bot.
• Positive residual: equation over-predicted (actual win % was lower than predicted).
• Negative residual: equation under-predicted (actual win % was higher than predicted).

Most real-world equations are not exact. A small residual is normal.

Your equation

y = —

1

Pick a third class bot. Enter that bot's numbers.

Stat value

Actual win % (0–100)

Enter the test bot's numbers before continuing.

Step 5 of 5

Share with the class.

Read your report card out loud. Different bot pairs produce different lines.

🏆 Your Group's Report Card

Your Equation

—

Rate of Change (Slope)

—

y-Intercept

—

Test Residual

—

Listen for these things when other teams share

Which group has the steepest slope? Their two selected bots produced the steepest rise in win % per stat point.

Which group has the smallest residual size? Their two-bot model predicted Bot 3 most accurately. (Use absolute value — −8 is larger than +2.)

Did two groups use the same stat but get different slopes? Which bots they chose changes the line.