Statistical Analysis of Trophy Progression in Brawl Stars
Abstract
This study explores 3v3 trophy progression in Brawl Stars, a popular mobile game, using computer simulations to analyze how players with varying skill levels (win rates) progress in the game’s trophy system. Our simulations show that players with an average skill level (50% win rate) can make limited progress, requiring significant playtime to achieve meaningful milestones. In contrast, players with higher skill levels (above 60% win rate) progress much faster, leading to a naturally stratified player base. We explore how win streak bonuses impact 3v3 trophy progression, providing faster advancement for skilled players, and examine the distribution of trophies across the player population. Our findings suggest that the 3v3 trophy system strikes a balance between accessibility for slightly-above-average players and rewarding higher-skilled players.
1. Introduction
Competitive games need reliable systems to rank players and create fair matches. Brawl Stars uses trophies, where players gain trophies for wins and lose them for defeats. The amount gained or lost depends on the player’s current trophy count, creating a system that aims to reflect skill level.
This paper examines:
- Whether players with a 50% win rate can make meaningful progress in the 3v3 trophy system. While the trophy system allows progress, players with an average win rate (50%) face significant barriers to achieving higher milestones, requiring substantial playtime to do so.
- How quickly players with different win rates reach trophy milestones
- The mathematical relationship between win rate and final trophy count
- How trophies are distributed across the player population
- How win streaks affect trophy progression and distribution
Understanding these patterns helps explain player experiences and tests whether the trophy system effectively balances accessibility for average players with rewards for skilled ones.
2. Methodology
2.1 Trophy System Model
Brawl Stars uses a tiered structure where rewards and penalties change based on current Brawler trophy count. Table 1 shows the complete model used in our simulation.
Table 1: Trophy Gain/Loss Structure
| Trophy Range | Win Reward | Loss Penalty |
|---|---|---|
| 0-49 | +8 | 0 |
| 50-199 | +8 | -1 |
| 200-399 | +8 | -2 |
| 400-599 | +8 | -3 |
| 600-699 | +8 | -4 |
| 700-799 | +8 | -5 |
| 800-899 | +8 | -6 |
| 900-999 | +8 | -7 |
| 1000-1099 | +8 | -8 |
| 1100-1199 | +7 | -11 |
| 1200-1299 | +6 | -13 |
| 1300-1399 | +5 | -16 |
| 1400-1499 | +4 | -19 |
| 1500-1599 | +3 | -22 |
| 1600-1699 | +2 | -25 |
| 1700-1799 | +1 | -28 |
| 1800-1899 | +1 | -31 |
| 1900-1999 | +1 | -34 |
| 2000+ | +1 | -50 |
2.2 Win Streak Bonus System
Win streaks provide additional trophies as players consecutively win matches, rewarding players with higher skill level and dedication.
Table 2: Win Streak Bonuses
| Win Streak | Extra Trophies Awarded |
|---|---|
| 2 consecutive wins | +1 Trophy |
| 3 consecutive wins | +2 Trophies |
| 4 consecutive wins | +3 Trophies |
| 5 consecutive wins | +4 Trophies |
| 6+ consecutive wins | +5 Trophies |
2.3 Simulation Approach
We ran several simulations using Python to track trophy growth under different conditions:
- Average player viability: Simulating 1,000 players with 50% win rate over 500 matches to determine if average players can make progress
- Milestone comparison: Tracking how quickly 1,000 players with win rates from 40% to 80% reach various trophy milestones
- Win rate-trophy relationship: Analyzing 1,000 players with randomized win rates to model the mathematical relationship between win rate and final trophy count
- Trophy distribution: Examining how trophies are distributed across a population of 100,000 players with normally distributed win rates
- Win streak impact: Including win streak bonuses in all simulations to assess their effect on progression
3. Results
3.1 Average Player Progression
Figure 1 shows the average trophy progression for 1,000 players with a 50% win rate over 500 matches, starting at 0 trophies.
The graph shows that players with an average 50% win rate can barely make any progress, only reaching 400 trophies just after finishing 100 matches (4-5 hours of play time). They would need to spend 400+ matches (20+ hours of play time) just to reach 1,000 trophies on a Brawler.
3.2 Comparing Trophy Milestone Achievement
Figure 2 compares how quickly players with different win rates (50% to 80%) reach trophy milestones over 500 matches.
The differences in progression rates are substantial:
- Players with 40-50% win rates make slow but steady progress
- Players with 60% win rates reach trophy milestones approximately twice as fast
- Players with 70%+ win rates hit early trophy thresholds significantly faster and have huge gaps in later growth
For example, reaching 1,000 trophies takes approximately:
- Virtually impossible at <50% win rate
- 442 matches at 50% win rate (as shown in Figure 1)
- 245 matches at 60% win rate
- 172 matches at 70% win rate
- 129 matches at 80% win rate
(For reference: reaching 1,000 trophies at a perfect win streak takes about 79 matches, which is just around 3 hours)
3.3 Win Rate-Trophy Relationship
Figure 3 shows the relationship between win rate and final trophy count for 1,000 players after 200 matches, where the win/loss outcomes are probabilistically determined based on the player’s win rate.
The data shows a linear relationship between win rate and final trophy count, which can be modeled using a linear regression. The linear fit is:
- Linear Regression: y = 1718.97x + 121.28
- R² = 0.7024
This means that as the win rate increases, the final trophy count increases in a relatively consistent manner. The model suggests that players with a higher win rate progress more quickly in terms of trophies, but the relationship is not perfectly linear, with a moderate R² value indicating some variability in the trophy count even for players with similar win rates.
3.4 Trophy Distribution
Figure 4 presents the distribution of trophies across 100,000 simulated players after 200 matches.
The distribution is right-skewed, indicating that only a small percentage of players have significantly more trophies than the average. Analysis of trophy percentiles reveals:
Table 3: Trophy Percentiles
| Percentile | Trophy Count |
|---|---|
| 50th (top 50%) | 665+ |
| 75th (top 25%) | 810+ |
| 90th (top 10%) | 958+ |
| 95th (top 5%) | 1059+ |
| 99th (top 1%) | 1227+ |
| 99.9th (top 0.1%) | 1418+ |
These results demonstrate substantial stratification, with the top 1% of players having approximately 2 times more trophies than the median player.
3.5 Win Streak Impact
Win streaks significantly boost progression, especially for players with win rates above 55%. With a 60% win rate, approximately 13% of matches are part of a streak of 3+ wins, providing substantial bonus trophies over time.
The win streak system particularly benefits players during “hot streaks,” allowing them to climb more quickly through higher trophy ranges that might otherwise be significantly harder to reach.
4. Discussion
The results of this study show that Brawl Stars’ trophy system effectively separates players based on their skill level. Players with higher win rates tend to progress faster, while those with lower win rates take much longer to move forward. The linear relationship between win rate and trophy count, with an R² value of 0.7024, indicates that while win rate is a key factor in determining progression, other factors, like strategy or adaptability, also play a role.
The analysis also highlights how much faster players with win rates above 60% reach trophy milestones compared to those with lower win rates. Players with less than 50% win rate struggle to progress, while players with higher win rates, especially those who maintain win streaks, advance way more quickly. The win streak bonuses give a further advantage to players who can consistently perform well, speeding up their trophy progression.
The trophy distribution shows a right-skewed pattern, meaning that most players have similar, lower trophy counts, while only a few players have much higher counts. This reflects the competitive nature of the game, where the top players stand out. However, even players with lower win rates can make slow but steady progress, which keeps them engaged in the game.
References
- Supercell. (n.d.). Win Streaks. Retrieved from https://support.supercell.com/brawl-stars/en/articles/win-streak-3.html
- Brawl Stars Wiki. (n.d.). Trophies. Retrieved from https://brawlstars.fandom.com/wiki/Trophies#3v3/5v5_Modes
Note: All simulation code used in this analysis is publicly available at this link.