Introduction
It began with an unexpected email from a reader—someone going by the alias Master Yoda. They suggested that the formula I had been puzzling over in my Kredit optimization article for EVE Galaxy Conquest resembled something straight out of biochemistry: the Michaelis-Menten equation.
That caught me off guard. As someone with years in game design, I knew better than to use a piecewise formula for something as simple as seasonal reward scaling. It would be a nightmare to maintain—and devs hate that kind of complexity. So I decided to put the theory to the test. What followed was a full-on data mining journey.
Table of Contents
What Is Data Mining in Video Games?
Data mining comes in many forms and is widely used in big data applications. However, what I often do is a manual, targeted form of data mining, specifically aimed at extracting hidden mathematical rules from datasets within video games. Other methods include scripted data collection or inspecting game’s asset files. While the approach may vary, the process typically follows these key steps:
Step 1: Raw Data Collection
This involves gathering information from transaction logs, player behavior records, drop rates, or system outputs. The data can be captured in various forms—videos, screenshots, or even simple handwritten notes. Key elements to track might include the number of attempts, time measurements, or a combination of both.
Step 2: Pattern Discovery & Hypothesis Testing
At this stage, raw data is refined, cleaned, and transformed into a structured format—such as transferring handwritten notes or screenshot data into an Excel table. Outliers are removed, and initial hypotheses are formulated. This step resembles exploratory data analysis (EDA) in traditional data mining, where different statistical distributions are tested to uncover potential relationships.
Step 3: Model Fitting & Optimization
Here, predictive modeling comes into play. Depending on the complexity of the data, this step may involve regression analysis, curve fitting, or even machine learning techniques to train models based on historical data. The goal is to find a formula that accurately represents (fits) the underlying system.
Step 4: Interpreting the Model
Once a suitable model is found, it’s crucial to analyze whether the formula aligns with well-known mathematical relationships. This is a form of pattern recognition, where we determine if the extracted rule follows existing statistical or physics-based laws. Recognizing these structures helps validate the integrity of the results.
Step 5: Refinement & Validation
Finally, the model is refined based on new insights. This might involve Excel-based validation, addressing rounding issues, or considering limitations in a game system. In formal data mining, this corresponds to model validation, ensuring that the results generalize well across different scenarios.
From Raw Numbers to Guidelines
This entire process is a fascinating journey of discovery, which I like to call DIKW transformation—a concept derived from Data, Information, Knowledge, and Wisdom.
- Data – the raw numbers, logs, and observations collected.
- Information – processed data that is refined, structured, and digestible for my analytical tools.
- Knowledge – insights gained from analyzing the information, leading to a deeper understanding.
- Wisdom – the ability to apply knowledge effectively, integrating it with prior experiences.
The final step? Turning wisdom into actionable guidance—a game guide that distills all findings into something useful for the community. This is how my research journey unfolds, from analyzing in-game data to crafting a comprehensive guide on KekBur.net.
Reverse-Engineering Game Mechanics
This process is an example of reverse-engineering game mechanics—understanding how a game functions to develop better strategies, optimize gameplay, or even uncover emergent properties (unexpected behaviors arising from complex systems).
I find immense joy in discovering these mechanics and then designing ways to share them with others. Whether it’s through articles, guides, or discussions, the goal is always the same: to make knowledge accessible to fellow players who enjoy diving deep into game systems as much as I do.
Now Onto the Real Data!
Since I have multiple characters in Eve Galaxy Conquest (I call them data agents, not alts!), I started by manually recording conquest points and estimated Kredit values in a notepad. I incrementally increased the values and logged new data. After a few days of data collection, I had compiled an Excel dataset with 80 records, ranging from 0 to 17 million in score. With multiple confirmations of the same values and a full range of data, I was confident enough to proceed to the next step.
Visualizing the Saturation Effect
To better understand the progression, I plotted the data on a log-scale graph to highlight the saturation effect. This revealed a rapid Conquest Kredit increase at lower scores, which then gradually leveled off—a classic saturation behavior.
Picture 1: Log-scale plot of Kredits vs. Score with Michaelis-Menten fit attempt.
Michaelis-Menten Model Fit
The Michaelis-Menten equation provided a strong fit to my dataset, with an R² value of 0.9985, indicating an excellent correlation. The estimated Vmax (the maximum asymptotic value of Kredits) was approximately 2117.08.
However, despite the high R², I noticed two problematic zones in the fit:
- 150-700 Kredit range: The model overshoots significantly, predicting higher values than observed.
- Near the upper limit (1950+ Kredits): The Michaelis-Menten curve climbs faster than expected, suggesting it does not correctly capture the hard cap behavior.
The Michaelis-Menten function assumes an asymptotic increase toward a maximum value (Vmax), meaning it approaches but never quite reaches a limit. However, in my dataset, the Kredit count appears to hard cap at 2000 (plausible), rather than approaching it indefinitely. This suggests that a strict upper bound is in place—something the standard Michaelis-Menten model does not account for.
Moreover, the rate of increase in Kredits flattens more sharply than expected, hinting that a logistic function might be a better fit.
Modifying the Michaelis-Menten Model
To test this hypothesis, I attempted to artificially cap the function at 2000 and observed how the upper end behaved. Despite an improved R² = 0.9989, the modified Michaelis-Menten fit suggested an effective cap of 1952 Kredits, reaching a plateau much earlier than I anticipated. Notably, I also had a verified data point at 1983 Kredits, further indicating that the standard Michaelis-Menten function was inadequate.
Picture 2: Modified Michaelis-Menten fit
Why Michaelis-Menten Fails in This Case
- Monotonic Growth Assumption. The model assumes a smooth, continuous increase, but my data exhibits irregular jumps and fall-offs.
- Hard Cap Issue. The Kredits distribution appears to have a strict upper bound (~2000), which Michaelis-Menten does not inherently support.
- Non-Smooth Plateau. Instead of a gradual approach to a limit, the plateau flattens abruptly, suggesting an alternative function is needed.
- Mid-Range Fluctuations (150-700 Kredits). The Michaelis-Menten model fails to account for anomalies and deviations in this range, indicating additional game mechanics or hidden constraints at play.
Time to Move On and Try Something Else!
After identifying the limitations of the Michaelis-Menten model, I tested several alternative approaches, including a logistic (sigmoid) model, power-law function, and exponential decay with saturation. While all provided a reasonable fit, they were partially off in critical areas. But I wasn’t just looking for the best fit—I needed to decode the exact function behind the in-game calculations.
Picture 3: Alternative model comparisons
Modified Exponential Decay Model – Almost There!
After a few more iterations, I developed a modified exponential decay model with flexible saturation, which provided a solid fit for both lower and mid-range values. However, it completely failed on the upper end beyond 1650 Kredits.
Picture 4: Modified Exponential Decay Fit, highlighting upper-end failure
Despite an R² of 0.9979, which is nearly perfect, the model was still not quite right. This was frustrating—it was so close, yet still off in key areas.
Remembering the Hill Equation
While experimenting with curve adjustments and saturation caps, I suddenly remembered the Hill equation—a widely used model in biochemistry and… game design!
The Hill function is a rational function, meaning it consists of a polynomial divided by another polynomial. Crucially, it includes the Hill coefficient, which controls the steepness of the curve, making it an excellent candidate for modeling nonlinear saturation behavior (our case!).
Picture 5: Hill equation fit test
The Rational Function – A Perfect Fit!
The final model that provided the best fit was a generalized rational function. And just like that—it clicked! This function fit across all regions, naturally adjusting in both early and late score scenarios. Moreover, it was easy to implement, avoiding complex exponentials or iterative calculations for a game engine.
Picture 6: All Models fit test
The final R² score was 0.999969, making it the most accurate model tested.
Model Performance Ranking (Worst to Best):
- Power Law – 0.897550 (worst)
- Logistic Growth – 0.968710
- Generalized Logistic – 0.983725
- Michaelis-Menten – 0.998051
- Rational Function – 0.999969 (best)
Picture 7: Model ranking comparison
Why R² ≠ 1?
The only reason the R² score isn’t exactly 1.0000 and why the formula includes long decimal values is due to the imprecision of the original dataset. The in-game UI rounds heavily, often displaying values like 1.2M instead of 1,249,393. This rounding introduces a margin of error, preventing a perfect correlation.
Final Formula
The final equation for Conquest Kredits estimation in Eve Galaxy Conquest in Excel function format:
=(1.86762771E-4 * A1^1.23316719) / (1 + (8.87074213E-8 * A1^1.23637373))
The Results
With these findings, I can now update my EVE Galaxy Conquest seasonal guide and provide you with a calculator. This tool will let you input your desired Conquest Kredit value and instantly see the exact score required to achieve it.
For now, I’ve hard-capped the calculator at 17 million score (or 1970 Kredits) due to insufficient data beyond this range, but I’ll update it as more data becomes available.
Update: The game developers have implemented a hard cap of 1 million Conquest Score from Station Escorts.
And that concludes our deep dive into the numbers! I hope you found this exploration as fascinating as I did. If you enjoyed it, let me know in the comments—I’d be happy to share more behind-the-scenes posts like this in the future.
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