Brawler Stat Slides Brawl Math Arena • Day 1
Operations & Rate Labs
Brawler Stat Showdown
Decode health pools, burst damage, and reload rates using arithmetic power to dominate the arena.
Burst Damage
Multi-bullet arithmetic
Reload Cycles
Rates per second
Effective HP
Survival margins
Anatomy of a Brawler Stat Card
Mission Intel
Health (HP)
6,400 HP
The total amount of damage a Brawler can absorb before being knocked out.
Attack Burst
6 × 520 dmg
Colt shoots 6 bullets per attack. Total damage = \(6 \times 520 = 3,120\).
Ammo Slots
3 Full Bars
Full ammo burst deals \(3 \times 3,120 = 9,360\) maximum potential burst damage.
Key Rule: Multiply bullet count by single-bullet damage before computing multi-ammo combos.
Damage Per Second (DPS) Formula
Core Equation
Sustained DPS Rate
\[ \text{DPS} = \frac{\text{Damage per Shot}}{\text{Reload Time in Seconds}} \]
High single-hit damage means nothing if your reload speed is too slow during an active fight!
Example: Shelly's Buckshot
2,100 Damage / 1.5 Seconds
\( 2,100 \div 1.5 = 1,400 \text{ DPS} \)
Example: El Primo's Fists
1,920 Damage / 0.8 Seconds
\( 1,920 \div 0.8 = 2,400 \text{ DPS} \)
Primo reloads in almost half the time, giving him significantly higher continuous DPS. +1,000 DPS Advantage
Clash Simulation: Bull vs. Frank
Battle Scenario
Bull (Shotgunner) HP: 8,000
• Point-blank blast: 2,400 dmg
• Ammo available: 3 ammo bars
Total Burst = \(3 \times 2,400 = 7,200\)
Leaves Frank with: \(10,000 - 7,200 = 2,800\) HP
Frank (Heavy Tank) HP: 10,000
• Hammer swing: 2,000 dmg
• Hits required to KO Bull: \(8,000 \div 2,000 = 4\) hits
Can Bull fire a 4th shot before Frank hits 4 times?
Math decides the victor before the battle even starts!
Solve how many seconds Bull takes to reload his 4th blast on your worksheet. Step-by-step challenge
Gem Grab Arena Challenge
Field Worksheet
Grab your Gem Grab Math Worksheet and calculate team health thresholds, countdown timers, and reload rates.
Section 1
Mine Spawn Rates
Calculate gems generated per minute.
Section 2
Burst & DPS Tables
Find total damage from multiple brawler attacks.
Section 3
Countdown Defense
Multi-step word problems under pressure.
Show all your calculations neatly in the workspace provided. Ready for battle!
Gem Grab Worksheet Gem Grab Combat Math
Brawl Math Arena • Day 1 Student Mission
Name:
Date:
Mission Objective: Calculate gem spawn rates, multi-bullet damage totals, and reload requirements to win the Gem Grab showdown. Show All Work
Part 1: Gem Mine Production Rates
The center mine spawns exactly 1 purple gem every 7 seconds once activated.
1. Gems in 42 Seconds
How many total gems spawn in 42 seconds of match play?
Answer:
2. Time to 10 Gems
How many total seconds must pass before 10 gems appear?
Answer:
3. Maximum Gems (2 Mins)
In a 2-minute (120 sec) match, how many complete gems spawn?
Answer:
Part 2: Brawler Attack Burst Matrix
Complete the data table below to calculate burst damage across multiple ammunition clips.
Brawler Projectiles per Shot Damage per Projectile Single Attack Damage Full Ammo Burst (3 Attacks) Colt 6 bullets 540 dmg
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| Shelly | 5 pellets | 420 dmg |
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| Spike | 6 spikes | 800 dmg |
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| Brock | 1 rocket | 1,960 dmg |
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4. Burst Comparison: Which brawler deals the highest total burst damage in 3 attacks? How much more damage do they deal compared to Shelly?
Brawl Math Arena • Lesson 1 Document Page 1 of 2
Gem Grab Tactical Scenarios
Multi-Step Operations & Defense Problems
Part 3 & Part 4
Part 3: The 15-Second Countdown
5. El Primo carries 10 gems and activates the 15-second victory countdown. He has 8,400 HP. An enemy Colt attacks him, dealing 2,700 damage every 2 seconds. Will Colt knock out Primo before the 15 seconds expire?
4 Pts
Calculate how much damage Colt inflicts in 15 seconds and Primo's remaining HP:
Final Conclusion (Survives or Knocked Out):
6. Poco's Super heal restores 2,900 HP to every teammate within his musical wave. If his team of 3 brawlers (Poco, Nita, and Bull) each take 2,400 damage, does a single Super heal completely restore the damage taken by all 3 players?
4 Pts
Calculate individual health status after healing and total net team health change:
Gem Grab Solutions Guide Gem Grab Solutions & Scoring Guide
Brawl Math Arena • Lesson 1 Teacher Key
Total Score: 25 Points
Part 1: Gem Mine Production Rates (6 Pts - 2 Pts Each)
1. 42 Seconds
Answer: 6 gems
\(42 \div 7 = 6\). Exactly 6 gems spawn.
2. Time to 10 Gems
Answer: 70 seconds
\(10 \times 7 = 70\) seconds (or 1 min 10 s).
3. 2-Minute Match
Answer: 17 gems
\(120 \div 7 = 17\) R1. 17 whole gems.
Part 2: Brawler Damage Matrix (8 Pts) & Comparison (2 Pts)
Brawler Calculation Single Attack Full Burst (×3)
Colt \(6 \times 540\) 3,240 dmg 9,720 dmg
Shelly \(5 \times 420\) 2,100 dmg 6,300 dmg
Spike \(6 \times 800\) 4,800 dmg 14,400 dmg
Brock \(1 \times 1,960\) 1,960 dmg 5,880 dmg
4. Comparison Solution:
Spike has the highest burst (\(14,400\) dmg). Difference from Shelly: \(14,400 - 6,300 = 8,100\) more damage.
Part 3 & 4: Word Problem Solutions & Step-by-Step Scoring (9 Pts)
5. El Primo Survival (4 Pts)
Conclusion: Knocked Out
Attack cycles in 15s: \(15 \div 2 = 7.5\) cycles (7 full attacks). Total damage = \(7 \times 2,700 = 18,900\). Primo has 8,400 HP. \(8,400 \div 2,700 \approx 3.11\) attacks (approx 6.2s). Primo is defeated well before 15s.
6. Poco Super Heal (4 Pts)
Conclusion: Yes, Completely
Each brawler receives +2,900 HP and lost 2,400 HP. Net gain = \(+500\) HP per brawler (full recovery). Team total: \(3 \times 2,900 = 8,700\) healed vs. \(3 \times 2,400 = 7,200\) taken.
7. Boss Robot Battle (5 Pts)
Answer: 30 Seconds
Step 1: Cycles needed = \(45,000 \div 4,500 = 10\) cycles. Step 2: Time = \(10 \times 3\text{ seconds} = 30\) seconds total.
Teacher Facilitation Notes & Common Misconceptions
• Rate Remainder Confusion: In Q3, students may divide \(120 \div 7 = 17.14\) and mistakenly round up to 18 gems. Emphasize that the 18th gem has not yet spawned at 120 seconds.
• Cycle vs. Direct Multiplication: In Q5, remind students that attacks occur in discrete discrete 2-second intervals, not as continuous fractions.
Brawl Math Arena • Lesson 1 Teacher Key 1 Page Complete
Trophy Analytics Slides Brawl Math Arena • Day 2
Probability & Ratio Analysis
Trophy Road Tactics
Master win-rate percentages, net trophy progression, and calculate the exact odds of unlocking Legendary Starr Drops.
Win Percentages
Ratio of victories to total
Net Trophy Rate
Points gained minus lost
Starr Drop Odds
Fractions & probabilities
Win Rate & Net Trophy Progression
Data Analytics
The Win Rate Formula
\[ \text{Win Rate} = \frac{\text{Matches Won}}{\text{Total Matches Played}} \times 100\% \]
Example: 18 wins out of 25 matches played:
\( \frac{18}{25} = 0.72 = 72\% \text{ Win Rate} \)
Net Trophy Balance
• Win: +8 Trophies
• Loss: -5 Trophies
In 10 games (7 Wins, 3 Losses):
\( (7 \times 8) - (3 \times 5) = 56 - 15 = +41 \text{ Trophies} \)
What minimum win rate is needed so you don't lose trophies? Break-Even Threshold
Official Starr Drop Probabilities
Probability Table
Rare
50%
\( \frac{50}{100} = \frac{1}{2} \)
Coins / Power pts
Super Rare
28%
\( \frac{28}{100} = \frac{7}{25} \)
Credits / Sprays
Epic
15%
\( \frac{15}{100} = \frac{3}{20} \)
Pins / Rare Brawlers
Mythic
5%
\( \frac{5}{100} = \frac{1}{20} \)
Mythic Brawler / Skins
Legendary
2%
\( \frac{2}{100} = \frac{1}{50} \)
Hypercharge / Hero
Sum of all outcomes: \( 50\% + 28\% + 15\% + 5\% + 2\% = 100\% \) 1 in 50 drops is Legendary
Daily Starr Drop Projections
Simulation
The 3 Daily Drops
Every active player earns 3 Starr Drops daily by securing 1, 4, and 8 match victories.
• In 30 days of active play: \( 30 \times 3 = 90 \) Starr Drops
• Expected Rare drops: \( 50\% \text{ of } 90 = 45 \) drops
• Expected Super Rare drops: \( 28\% \text{ of } 90 \approx 25 \) drops
Legendary Odds in 100 Drops
With a \( 2\% \) probability (\( \frac{1}{50} \)), how many Legendaries are statistically expected in 100 drops?
Starr Drop Worksheet Trophy Road & Starr Drop Analytics
Brawl Math Arena • Day 2 Student Mission
Name:
Date:
Mission Objective: Calculate player win rates, balance net trophy equations, and analyze Starr Drop probability distributions. Show Work
Part 1: Brawler Win Rate Analysis
Convert each player's match record into a simplified fraction, decimal, and final win percentage.
Player Tag Wins / Played Simplified Fraction Decimal (Hundredths) Win Percentage LeonMain_99 15 / 20
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| StarPower_Kai | 18 / 25 |
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| BrawlBot_07 | 14 / 50 |
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| PiperSnipe_X | 32 / 40 |
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Part 2: Net Trophy Push Calculations
In 3v3 mode, each Victory earns +8 trophies ; each Defeat loses -6 trophies .
1. Net Trophy Balance (12 Wins, 8 Losses)
Calculate total trophies gained and lost, then find the net change.
Net Trophy Change:
2. Target Milestone Push
A player needs +70 trophies to reach Gold League. If they win 11 matches, how many matches can they lose and still reach 70 trophies?
Max Losses Allowed:
Brawl Math Arena • Lesson 2 Document Page 1 of 2
Starr Drop Probability Matrix
Theoretical Probability & Expected Value
Part 3 & Part 4
Part 3: Starr Drop Rarity Table
Complete the table below showing the official probability distributions for Starr Drops.
Rarity Tier Probability (%) Simplified Fraction Decimal Value Expected in 200 Drops Rare 50%
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| Super Rare | 28% |
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| Epic | 15% |
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| Mythic | 5% |
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| Legendary | 2% |
Starr Drop Solutions Guide Starr Drop Solutions & Scoring Guide
Brawl Math Arena • Lesson 2 Teacher Key
Total Score: 25 Points
Part 1: Win Rate Conversion Solutions (8 Pts)
Player Wins / Matches Fraction Decimal Percentage
LeonMain_99 15 / 20 3/4 0.75 75%
StarPower_Kai 18 / 25 18/25 0.72 72%
BrawlBot_07 14 / 50 7/25 0.28 28%
PiperSnipe_X 32 / 40 4/5 0.80 80%
Part 2: Net Trophy Balance Solutions (5 Pts)
1. Net Balance (12W, 8L)
Answer: +48 Trophies (2.5 Pts)
Gained: \(12 \times 8 = 96\). Lost: \(8 \times 6 = 48\). Net: \(96 - 48 = +48\) trophies.
2. Milestone Push
Answer: Max 3 Losses (2.5 Pts)
11 wins give \(11 \times 8 = 88\) trophies. \(88 - 70 = 18\) buffer. \(18 \div 6 = 3\) maximum allowable losses.
Part 3: Starr Drop Rarity & Expected Value Solutions (8 Pts)
Tier Percent Fraction Decimal In 200 Drops
Rare 50% 1/2 0.50 100 drops
Super Rare 28% 7/25 0.28 56 drops
Epic 15% 3/20 0.15 30 drops
Mythic 5% 1/20 0.05 10 drops
Legendary 2% 1/50 0.02 4 drops
Part 4: Real-World Probability Solutions (4 Pts)
3. Combined Tier (Epic+)
Answer: 22% or 11/50 (2 Pts)
\(15\% + 5\% + 2\% = 22\%\). As simplified fraction: \(\frac{22}{100} = \frac{11}{50}\).
4. Seasonal 180 Drops
Answer: 140 or 140.4 Drops (2 Pts)
Combined Rare + Super Rare = \(50\% + 28\% = 78\%\). Expected = \(180 \times 0.78 = 140.4\) drops (accept 140 or 140.4).
Common Pitfalls to Address During Debrief
• Theoretical vs Experimental: Clarify that having a \(2\%\) chance does not promise a Legendary on the 50th drop. Each Starr Drop event is mathematically independent.
Brawl Math Arena • Lesson 2 Teacher Key 1 Page Complete
