Multicollinearity in Football Models: When Different Statistics Carry the Same Information

Multicollinearity occurs when the explanatory variables in a statistical model contain strongly overlapping information. In football, several measures of attacking activity can rise together, making their separate contributions difficult to estimate. A table consulted on RubiScore may describe each measure correctly while leaving this modelling problem entirely unresolved.

Football records at https://rubiscore.com provide context for the questions readers ask of statistics. Turning those observations into a regression introduces another question: does the available evidence distinguish the inputs, or does it mostly show them moving together? More columns do not necessarily provide more independent information.

Why does overlapping information cause trouble?

Imagine an illustrative analysis of attacking performance. The analyst includes shots, shots on target and expected goals. These are different concepts, but the observations may contain many matches in which all three rise or fall together. The model sees a shared pattern before it can assign a separate contribution to each column.

The difficulty is attribution. If the sample rarely contains more shots without a corresponding change in the other inputs, it offers limited evidence about what changing shots alone would mean. A fitted coefficient can therefore depend heavily on the few observations that separate those patterns.

NIST describes multicollinearity as interdependence among a model's input columns and warns that small changes to those inputs can cause substantial changes in estimated coefficients. This concerns the fitted relationship, even when the source measurements are accurate. NIST: regression diagnostics.

The football interpretation should remain modest. A statistical difficulty separating attacking measures does not establish that one of the underlying actions is unimportant.

Is this the same as entering a statistic twice?

An exact duplicate is an especially clear case, but the problem can be less obvious. A model may contain a total alongside the components that sum to that total. It then asks the data to distinguish quantities that are linked by construction.

For example, if a dataset defines total passes as completed passes plus incomplete passes, entering all three in an ordinary regression creates an exact dependency. Changing the total while holding both components fixed is not an available possibility within that definition.

Other relationships are approximate. Attacking touches and passes into advanced areas need not be identical, but a particular sample might offer little independent variation between them. Their separation becomes a matter of degree rather than a simple duplicate check.

Reading the metric definitions is therefore part of model design. A spreadsheet can look varied because the labels differ while its columns repeat the same underlying counts, totals or denominators. Removing duplicated meaning is more useful than merely removing duplicated column names.

What does a coefficient actually describe?

In a multiple regression, an input's coefficient describes its fitted association with the outcome while the other included inputs are held fixed. That qualification matters. It is not simply the relationship visible in a chart of that input against the outcome.

Suppose shots generally increase alongside expected goals. A coefficient on shots while expected goals is held fixed concerns a different comparison: changing shot volume without changing the model's total chance-quality measure. That can imply a change in the average quality of the attempts.

A surprising sign can therefore have several explanations. The conditional question may differ from the reader's intuitive question, the inputs may be difficult to separate, or the model may be poorly specified. A negative sign alone does not prove that shooting harms a team.

Write the question in football language before interpreting the coefficient. If holding all the other inputs fixed describes an unrealistic or scarcely observed combination, the apparent precision of the output should not hide that limitation.

How should an analyst investigate the problem?

Begin with definitions and simple plots, then use diagnostics appropriate to the fitted model. A correlation matrix can reveal pairs of inputs that move closely together, but it does not detect every dependency involving several variables.

NIST identifies the variance inflation factor, or VIF, as a diagnostic for this wider problem. It assesses how strongly an input is explained by the remaining inputs. Its documentation also distinguishes that assessment from looking only at pairwise correlations. NIST: variance inflation factors.

A useful review asks:

• Are any columns totals or transformations of other included columns?
• Do several measures share a strong dependence on minutes or possession?
• Does removing one input substantially change the remaining coefficients?
• Are those changes accompanied by meaningful changes in held-out predictions?
• Does the interpretation survive a different but relevant sample of matches?

No single diagnostic answers every question. The point is to locate the dependence, understand why it exists and decide whether it prevents the intended use of the model.

Can predictions remain useful when coefficients are unstable?

They can, especially for observations similar to those used to fit the model. Different allocations of weight across correlated inputs may produce similar combined predictions because the inputs continue to move together.

Consider two illustrative fitted models. One puts more weight on shot volume; the other puts more on a related attacking measure. When both measures rise together in the evaluation sample, their predictions may stay close even though their explanations sound very different.

That distinction is crucial when a model is presented as evidence about coaching priorities. A system that predicts reasonably well has not necessarily established which action should be changed to improve performance. Prediction, explanation and intervention are separate ambitions.

It also creates a boundary around the model's usefulness. If a new team produces combinations absent from the training sample, the apparent agreement may disappear. A model that handled familiar attacking patterns may be unreliable for a substantially different style of play.

Does adding more matches solve it?

More observations can help when they introduce the missing variation. Matches with different styles, roles or tactical conditions might provide evidence that separates inputs which previously moved together. The relevant gain is variety connected to the modelling question.

Simply repeating the same relationship across a larger sample does less. If a total is exactly determined by its components, collecting more rows will not remove that identity. If the inputs remain closely linked, a bigger dataset may still leave individual contributions difficult to distinguish.

RubiScore can help readers keep team, competition and match context attached to the football observations they review. The model builder must separately judge whether expanding the sample introduces comparable evidence or combines fundamentally different environments.

This is why a larger sample should not automatically be described as a cleaner sample. Including another competition might improve variation while changing the meaning of the relationship. Both effects deserve examination before the revised coefficients are interpreted.

Should one of the overlapping variables be removed?

Sometimes, but the choice should follow the purpose. If two columns encode essentially the same quantity, retaining the clearer or better measured version may make the model easier to interpret. If each represents a meaningful mechanism, removing one can change the question being answered.

Combining related variables is another possibility, provided the combined measure has an intelligible definition. A composite attacking measure may be suitable for prediction while being less useful for explaining a particular player's responsibility.

Regularisation can stabilise estimation by constraining fitted coefficients. It does not turn observational associations into causal effects, nor does it discover a uniquely correct division of credit between overlapping football concepts. Its settings become part of the model's assumptions.

A sensible report should explain the treatment in ordinary language: which inputs overlapped, what was changed and what happened to predictions and interpretation. Quietly deleting a troublesome variable until the coefficients look plausible is much harder to defend.

What should readers take from a model's explanation?

Ask whether the conclusion concerns a combined prediction or an individual contribution. Then ask how the analyst checked that contribution when related inputs were included, removed or redefined. The stability of the answer matters more than the confidence of its presentation.

Avoid turning a coefficient table into a league table of football importance. A small or unstable coefficient can reflect information already captured elsewhere. It does not mean the underlying skill has little value on the pitch.

The most useful explanation identifies the evidence the model can distinguish and the evidence it cannot. When several attacking statistics travel together, the combined signal may be informative even though assigning separate credit remains uncertain. Recognising that boundary makes the analysis more precise, without discarding useful football data.