IB Mathematics Analysis and Approaches (AA) SL Internal Assessment Exemplar: How effectively can XG and XGA be used to predict the results of matches in the Premier League?

The introduction concisely frames the topic but risks overgeneralization about fan understanding. Consider tightening the focus on statistical aspects to improve relevance and avoid broad claims without evidence.

The research question is clearly stated but could be made more precise by specifying the time frame (e.g. 2024/25 season) to anchor scope and improve coherence.

This rationale section effectively situates the investigation in a broader context but could link more explicitly to the mathematical methods to strengthen logical development.

When introducing per-90 metrics, briefly explain why normalizing by game time (per 90) yields more meaningful comparisons between teams.

The axes on the correlation graph lack units and explicit labels for clarity. Add “Goals Scored” (x) and “XG” (y) with units per 90 matches.

Combining goal difference and XG–XGA is a strong step towards synthesis; an explanatory sentence on why these two align conceptually would solidify clarity.

The excerpt table for match-by-match analysis is insightful, but column headings like “Match/No Match” need clearer definition to guide the reader.

The table showing expected standings introduces coloured superscripts effectively, but the notation ^+3.62 needs a legend explaining the meaning of positive and negative values.

The probability table is informative but would benefit from shading or bolding predicted outcomes to enhance readability.

The label “Gools Scored per 90” contains a typo. Correct to “Goals Scored per 90” and ensure consistency in notation to maintain clarity.

Figure labels (e.g., Table 1.2) are clear, and the scatter plot effectively represents the XG vs. goals relationship.

The presentation of multiple regression lines demonstrates effective use of representation but could be enhanced by a residual plot to assess model fit.

The linear model y = 1.03x –5.16×10⁻³ is well calculated, showing strong correlation. Consider discussing the significance of the tiny intercept term.

The worked example P(X=1)=0.335 is clear and mathematically sound. Good use of LaTeX formatting for presentation.

The rationale reflects a clear personal interest in football analytics, demonstrating genuine engagement with the topic.

Correlation between expected and actual positions is discussed well; however, mentioning outliers explicitly (e.g. Spurs, Bournemouth) would deepen critical analysis.

The surprise results analysis shows thoughtful reflection on model limitations, acknowledging tactical/systemic factors beyond XG modelling.

The conclusion summarises findings well but remains descriptive. To strengthen reflection, propose a concrete follow-up study or refined methodology.

The methods list is clear, but the choice of Poisson distribution would benefit from a brief justification of its assumptions and limitations in this context.

The calculation of the t–statistic references n=20, but the sample is 18 teams. Adjust degrees of freedom and n accordingly to ensure accuracy.

The regression equation intercept lacks interpretation. Discuss what an intercept of –1.78 means in the context of goals conceded vs. XGA.

The Poisson distribution formula is correctly presented but lacks a brief comment on why it suits football goal modeling (rare discrete events).

Calculating probabilities only for k≤2 simplifies computation but omits tail events. Consider summing probabilities to k=3 or 4 to capture lower-frequency outcomes.