Investigating the Effectiveness of the Expected Goals (xG) Model in Evaluating Harry Kane's Performance in the 2023/2024 UEFA Champions LeagueSL
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4
Official IB Result
11/20
General feedback
11/20
0
10
20
No overall summary is available for this report.
5.1·Weakness
Page 7
The logistic regression explanation is repeated in several nearby places, which weakens conciseness. The student should define the model once, then refer back to that definition when applying it, rather than reintroducing the same idea multiple times.
5.2·Suggestion
Page 8
The student should return to the RMSE idea in the conclusion and explain what its value would imply about model quality. That would turn a definition into a genuine evaluation of outcomes and implications.
5.3·Weakness
Page 9
The “Main body” heading suggests the start of analysis, but the section mostly restates what the investigation plans to do. The student should distinguish more clearly between planned method and actual findings so the structure feels more purposeful.
5.4·Suggestion
Page 13
The comparison section would read more cleanly if it followed a consistent pattern: total goals, total shots, then model comparison. A tighter structure here would reduce repetition and make the final analysis easier to track.
5.5·Weakness
Page 13
The comparison table is a useful idea, but the presented values do not yet support a full evaluation of model effectiveness. The student should calculate and compare actual vs expected outcomes more systematically, rather than only stating the rows.
5.6·Weakness
Page 14
The overperformance discussion is based on a few selected examples rather than a full analysis of the dataset. The student should justify why these shots are representative, or else explain the overall pattern using all cases.
5.7·Weakness
Page 14
The reflection remains descriptive rather than evaluative. The student states that Kane shows both overperformance and underperformance, but does not probe why the model may be producing mixed results or what the limitations of the data might be.
5.8·Strength
Page 14
The student does begin to interpret patterns in the results rather than simply listing them. That is a useful starting point for reflection because it shows an attempt to think about what the data suggests beyond the raw calculations.
5.9·Weakness
Page 15
The evaluation does not critically examine whether the “high xG” and “low xG” categories are meaningful enough to support the conclusions. The student should question whether the thresholds used are justified and whether they align with the model’s assumptions.
5.10·Weakness
Page 15
The concluding claim that Kane’s shot geography “translates low xG shots into goals” is not weighed against counterexamples in the table. Reflection would be stronger if the student acknowledged where the pattern breaks down as well as where it holds.
5.11·Weakness
Page 16
The “SWOT Analysis and Industry Trends” section adds extra material that does not clearly advance the mathematical argument. Trimming or tightly connecting this section to the xG investigation would improve relevance and conciseness.
5.12·Question
Page 16
If the model were applied to a larger set of Kane’s shots, would the same pattern still appear, or might the current conclusion be driven by a small sample? Considering sample size would deepen the reflection on reliability.
Criteria A: Presentation
3/4
0
2
4
Criteria Strands
A.1Coherence and logical development
Good
A.2Organization and structure
Good
A.3Conciseness and relevance
Moderate
Criteria Feedback
- Your exploration is clearly sectioned and easy to follow from introduction through to conclusion.
- You keep the reader oriented with a logical sequence of ideas and signposted methodology.
- Most of the material stays focused on the football context and the modelling aim.
- Some parts of the argument are not fully consistent with the calculations shown.
- A few sections repeat ideas or add material that does not contribute much to the main analysis.
- The work would be stronger if every stated step was actually carried through in the final analysis.
1.1·Strength
Page 2
The table of contents and clear sectioning help the reader follow the exploration’s progression from introduction to conclusion. This supports the overall coherence and makes the investigation easy to navigate.
1.2·Strength
Page 6
The methodology is signposted in a logical sequence, which helps the reader understand the intended process before the calculations begin. This is a strong organisational choice because it frames the investigation as a planned analysis rather than a set of disconnected steps.
Criteria B: Mathematical Communication
2/4
0
2
4
Criteria Strands
B.1Mathematical language and notation
Moderate
B.2Multiple representations
Moderate
B.3Logical structure and clarity
Moderate
Criteria Feedback
- You use relevant mathematical language such as logistic regression, coefficients, probability, and xG.
- You include more than one form of representation, especially formulas and tables.
- Your working is usually laid out in a way that shows the intended sequence of the calculation.
- Some notation and formulas are not written consistently, which makes parts of the mathematics harder to trust.
- You rely mostly on formulas and tables, with limited visual or graphical representation.
- There are places where the communication becomes unclear because the values or totals do not match the table shown.
2.1·Strength
Page 6
The student uses the correct logistic form here, which shows a solid understanding of the expected goals framework. Writing the probability model explicitly is effective because it connects the football context to the mathematics in a transparent way.
2.2·Strength
Page 7
The definition of as a linear combination of features is clear and mathematically appropriate. This helps the reader see how shot variables such as distance and angle are intended to influence scoring probability.
2.3·Suggestion
Page 8
Since RMSE is introduced as a validation measure, the student should actually compute it using the shot data that has been tabulated. Doing so would make the mathematical communication more complete because the evaluation metric would move from definition to application.
2.4·Weakness
Page 12
The calculation also appears to substitute a value of that does not match the previous line, where was found but the next step uses . The student should carry forward the same value consistently so the calculation is trustworthy.
2.5·Weakness
Page 12
The substitution for xG is not written consistently with the correct sigmoid form. The denominator should be , so the student needs to check that the formula used in the worked example matches the model stated earlier.
2.6·Weakness
Page 12
The table is useful, but several entries are difficult to interpret because the numerical values are compressed together. The student should make sure each column is clearly labelled and that the outcome and xG values are unambiguous so the mathematics can be checked easily.
2.7·Strength
Page 14
The discussion links numerical xG values to football meaning, which strengthens communication by translating abstract probabilities into performance language. This is effective because it helps the reader understand why the numbers matter.
2.8·Weakness
Page 15
The conversion rate formula is correct, but the stated result of “8 goals out of 8 shots” is inconsistent with the earlier shot table, which includes misses. The student should recalculate the conversion rate from the actual total shots shown in the analysis.
Criteria C: Personal Engagement
1/3
0
2
3
Criteria Strands
C.1Independent thinking
Poor
C.2Personal approach
Good
C.3Creativity and initiative
Poor
Criteria Feedback
- You chose a topical and personally relevant context that clearly interests you.
- You show some initiative by trying to connect football performance with a statistical model.
- You make an effort to interpret the numbers in relation to finishing quality and shot location.
- Your modelling choices are mostly presented rather than independently developed.
- Some promising ideas are mentioned but not fully carried out.
- The exploration would feel more original if you justified key assumptions more clearly.
3.1·Strength
Page 3
The student shows a clear personal connection to the topic by linking football interest with data evaluation. This helps justify the investigation’s focus and gives the exploration a genuine personal rationale rather than a generic statistical case study.
3.2·Suggestion
Page 5
The aim would be stronger if it were narrowed into a more precise research question, such as whether the model accurately predicts Kane’s shot outcomes or whether his finishing differs by shot location. A sharper question would make the subsequent mathematics easier to evaluate.
3.3·Weakness
Page 11
The coefficients are introduced as “for the purposes of this example,” which limits independent thinking because they are assumed rather than justified. The student should explain how these values were obtained, or use fitted coefficients from a dataset, so the modelling choices feel original and defensible.
3.4·Question
Page 11
What would change in the interpretation if the coefficients were estimated from Kane’s own shot data instead of being assumed? Considering that would help the student show more initiative and make the model more personally developed.
3.5·Strength
Page 15
The student attempts to draw a football-specific insight from the calculations by linking lower xG chances to finishing quality and shot geography. This shows some initiative in moving beyond calculation toward interpretation.
3.6·Weakness
Page 16
The “SWOT Analysis and Industry Trends” section feels only loosely connected to the mathematical investigation. If included, it should feed directly into the xG analysis; otherwise, the student should remove or integrate it more tightly to keep the work focused.
Criteria D: Reflection
1/3
0
2
3
Criteria Strands
D.1Depth of reflection
Poor
D.2Critical analysis
Poor
D.3Evaluation of outcomes
Poor
Criteria Feedback
- You do make some effort to interpret what the results suggest about performance.
- You identify both stronger and weaker shot situations rather than treating every result the same.
- You include some evaluative comments about what the numbers imply in context.
- Your reflection stays mostly descriptive instead of deeply analytical.
- There is limited discussion of the quality or reliability of the model itself.
- The conclusions would be stronger if they were more tightly supported by the calculations shown.
Criteria E: Use of Mathematics
4/6
0
3
6
Criteria Strands
E.1Relevance of mathematics
Moderate
E.2Level appropriateness
Moderate
E.3Understanding and accuracy
Poor
Criteria Feedback
- You use mathematics that is clearly relevant to the question, especially logistic regression and xG.
- Your model setup shows a good understanding of how shot variables can be linked to probability.
- You work at a level that is appropriate for the course and keep the mathematics connected to the football context.
- You show some correct use of exponential and probability ideas in the worked examples.
- Some formulas and substitutions are written incorrectly or inconsistently.
- The coefficients are not justified from data, so the model is more illustrative than fully evidenced.
- There are reliability issues because some totals and claims do not match the shot table shown.
4.1·Strength
Page 6
The student selects mathematics that is genuinely relevant to the topic: logistic regression, xG probabilities, and a validation metric. This is an appropriate modelling framework for evaluating shot outcomes in football.
4.2·Suggestion
Page 8
A graph comparing xG and actual outcomes would make the model’s performance much easier to judge visually. Including one would also help show whether the predictions cluster near the line of best fit or deviate systematically.
4.3·Weakness
Page 11
The chosen coefficients are not justified by data or modelling procedure, so the mathematics is applied more as an illustration than as an evidence-based model. The student should either explain the fitting process or clearly frame this as a simplified demonstration.
4.4·Strength
Page 11
Defining in terms of distance, angle, and shot type shows that the model is using variables that make sense in context. That is a strong choice because it connects the mathematics to realistic features of shooting chances.
4.5·Weakness
Page 13
The claim that Kane scored 8 goals in the competition is not consistent with the shot-by-shot table shown earlier. This weakens the mathematical reliability of the exploration because the overall totals and the detailed evidence do not agree.