  Incentive compatibility is usually considered a binary concept in the
academic literature. Our paper aims to present a method for quantifying the
violation of strategy-proofness in the case of sports tournaments, in
particular, through the example of the European Qualifiers for the 2022 FIFA
World Cup. Even though that competition is known to be vulnerable to
manipulation since certain teams might be interested in the success of other
teams, the extent of the problem has remained unexplored until now. Based on
computer simulations, the strategic behaviour of the contestants is found to
have non-negligible sporting effects. While strategy-proofness cannot be
guaranteed without fundamentally changing the tournament design, we can
substantially mitigate this threat by adding a carefully chosen set of draw
restrictions, which offers a justifiable and transparent solution to improve
fairness. Sports governing bodies are encouraged to take our findings into
account.
