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Added a "How to Cite" component to modules with DOIs. Also tweaked author formats for consistency across modules. (Last, fixed an error in a pair of worksheets for the LoL module.)
| KDA | Average kills, deaths and assists associated with each champion |
@@ -101,9 +102,10 @@ In conclusion, the analysis of Win Rates histograms in League of Legends has pro
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The continued presence of outliers highlights the importance of continuous monitoring and adjustments by game developers to ensure fair and competitive gameplay.
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### How to Cite
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If you use this module in your work, please cite it as follows:
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### Authors
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Ramler, I., Charalambous, G., & Dykstra, A. J. (2025, April 30). League of Legends. "The SCORE Network." <https://doi.org/10.17605/OSF.IO/8R3YG>
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Created by George Charalambous (St. Lawrence University), [Ivan Ramler (St. Lawrence University)](mailto:iramler@stlawu.edu), A.J. Dykstra (St. Lawrence University)
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You can include this citation directly in your references or bibliography.
description: Evaluating the predicted winning probabilities against the actual outcomes.
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Brier score originated with weather forecast research. It was designed to evaluate the predicted probabilities against the actual outcomes and is straight forward to calculate. While it is not widely used outside specific use cases, it is one of many approaches for the important step of evaluating models based on their predictions. Since the EPA model provides the predicted winning probabilities, Brier score is useful for evaluating its performance by comparing its predicted winning probabilities to the actual FRC outcomes.
| playoff | "t" for playoff match; "f" for qualifying match |
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| comp_level | "qm" for qualifying match; "sf" for semifinals match; "f" for finals match |
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| winner | winning alliance ("red" or "blue") of the match |
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| epa_win_prob | predicted winning probability for the Red Alliance by EPA model |
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</details>
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@@ -79,11 +83,9 @@ datatable(dt2023hop)
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### Brier Score
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For match $i$, let $f_i$ denote the probability forecast. In our case, it is the predicted winning probability for the Red Alliance by EPA model, i.e., the variable *epa_win_prob*. Let $o_i$ denote the match outcome: $o_i=1$ when the Red alliance won and $o_i=0$ when the Blue alliance won. The Brier score for match $i$ is calculated as $(f_i - o_i)^2$. For example, suppose it is predicted that the Red alliance will win with 80% probability, i.e., $f_i=0.8$, if the actual outcome is that the Red alliance won, the Brier score is $(0.8-1)^2=0.04$. If the actual outcome is that the Blue alliance won, the Brier score is $(0.8-0)^2=0.64$.
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For match $i$, let $f_i$ denote the probability forecast. In our case, it is the predicted winning probability for the Red Alliance by EPA model, i.e., the variable *epa_win_prob*. Let $o_i$ denote the match outcome: $o_i=1$ when the Red alliance won and $o_i=0$ when the Blue alliance won. The Brier score for match $i$ is calculated as $(f_i - o_i)^2$. For example, suppose it is predicted that the Red alliance will win with 80% probability, i.e., $f_i=0.8$, if the actual outcome is that the Red alliance won, the Brier score is $(0.8-1)^2=0.04$. If the actual outcome is that the Blue alliance won, the Brier score is $(0.8-0)^2=0.64$.
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Brier score is a quantity bounded by $0$ and $1$. Brier score of $0$ means correctly predicting the outcome with 100% certainty. 50:50 random guess would give a Brier score of $0.25$. The overall Brier score for all the matches during a competition event or season is simply the average of individual match scores:
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$$\frac{1}{N} \sum_{i=1}^N (f_i - o_i)^2$$
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The following table shows the calculation for each match.
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Brier score is a quantity bounded by $0$ and $1$. Brier score of $0$ means correctly predicting the outcome with 100% certainty. 50:50 random guess would give a Brier score of $0.25$. The overall Brier score for all the matches during a competition event or season is simply the average of individual match scores: $$\frac{1}{N} \sum_{i=1}^N (f_i - o_i)^2$$ The following table shows the calculation for each match.
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```{r}
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#| echo: false
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knitr::kable(FRC)
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```
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It is interesting to note that the predictive ability of the EPA model has improved for the past 20 years. Since the model has not changed, I believe the improvement comes from established teams becoming more consistent and predictable. Meanwhile, the pool of newer, less experienced teams has stayed healthy.
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It is interesting to note that the predictive ability of the EPA model has improved for the past 20 years. Since the model has not changed, I believe the improvement comes from established teams becoming more consistent and predictable. Meanwhile, the pool of newer, less experienced teams has stayed healthy.
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```{r}
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plot(FRC$year, FRC$Brier)
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### Author
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Created by [Jake Tan (Wissahickon High School)](https://www.jakeatan.com/). Jake is a subsystem leader at [FRC Team 341, Miss Daisy](https://www.team341.com/). Team 341 competed at FRC World Championship in the Turing Division in 2022 and Hopper Division in 2023.
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### How to Cite
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If you use this module in your work, please cite it as follows:
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Tan, J. (2025, January 15). FIRST Robotics Module. "The SCORE Network," <https://doi.org/10.17605/OSF.IO/BRG8Z>
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You can include this citation directly in your references or bibliography.
This dataprep worksheet helps students familiarize themselves with the use of basic dplyr tools to structure data in a way that is easier to analyze. In doing so, it enables to students to draw conclusions about different patterns in rowing as an Olympic sport when it comes to medaling.
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### How to Cite
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If you use this module in your work, please cite it as follows:
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Smith, A., Lock, R., & Ramler, I. (2025, June 12). Olympic Rowing - Data Wrangling. "The SCORE Network." <https://doi.org/10.17605/OSF.IO/XRYTQ>
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You can include this citation directly in your references or bibliography.
This Olympic rowing medals worksheet builds students' understanding of data distribution through histograms, summary statistics, and outliers. It also strengthens students' ability to critically evaluate confounding variables and devising relationships amongst variables through looking at barplots. Additionally, it provides an interesting opportunity for students to look at patterns in medals for Olympic rowing.
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### How to Cite
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If you use this module in your work, please cite it as follows:
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Smith, A., Ramler, I., & Lock, R. (2025, June 12). Olympic Rowing - Summary Statistics. "The SCORE Network." <https://doi.org/10.17605/OSF.IO/6YGJV>
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You can include this citation directly in your references or bibliography.
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