The uniqueness of behavioural biometrics (e.g., voice or keystroke patterns) has been challenged by recent works.  Statistical attacks have been proposed that infer general population statistics and target behavioural biometrics against a particular victim.  We show that despite their success, these approaches require several attempts for successful attacks against different biometrics due to the different nature of overlap in users' behaviour for these biometrics.  Furthermore, no mechanism has been proposed to date that detects statistical attacks. In this work, we propose a new hypervolumes-based statistical attack and show that unlike existing methods it: 1) is successful against a variety of biometrics; 2) is successful against more users; and 3) requires fewest attempts for successful attacks.  More specifically, across five diverse biometrics, for the first attempt, on average our attack is 18 percentage points more successful than the second best (37% vs. 19%).  Similarly, for the fifth attack attempt, on average our attack is 18 percentage points more successful than the second best (67% vs. 49%).  We propose and evaluate a mechanism that can detect the more devastating statistical attacks.  False rejects in biometric systems are common and by distinguishing statistical attacks from false rejects, our defence improves usability and security.  The evaluation of the proposed detection mechanism shows its ability to detect on average 94% of the tested statistical attacks with an average probability of 3% to detect false rejects as a statistical attack.  Given the serious threat posed by statistical attacks to biometrics that are used today (e.g., voice), our work highlights the need for defending against these attacks.