  Vision and language models (VL) are known to exploit unrobust indicators in
individual modalities (e.g., introduced by distributional biases) instead of
focusing on relevant information in each modality. That a unimodal model
achieves similar accuracy on a VL task to a multimodal one, indicates that
so-called unimodal collapse occurred. However, accuracy-based tests fail to
detect e.g., when the model prediction is wrong, while the model used relevant
information from a modality. Instead, we propose MM-SHAP, a
performance-agnostic multimodality score based on Shapley values that reliably
quantifies in which proportions a multimodal model uses individual modalities.
We apply MM-SHAP in two ways: (1) to compare models for their average degree of
multimodality, and (2) to measure for individual models the contribution of
individual modalities for different tasks and datasets. Experiments with six VL
models -- LXMERT, CLIP and four ALBEF variants -- on four VL tasks highlight
that unimodal collapse can occur to different degrees and in different
directions, contradicting the wide-spread assumption that unimodal collapse is
one-sided. Based on our results, we recommend MM-SHAP for analysing multimodal
tasks, to diagnose and guide progress towards multimodal integration. Code
available at \url{https://github.com/Heidelberg-NLP/MM-SHAP}.
