  We investigate a two-level model with a large number of open decay channels
in order to describe avoided level crossing statistics in open chaotic
billiards. This model allows us to describe the fundamental changes of the
probability distribution of the avoided level crossings compared with the
closed case. Explicit expressions are derived for systems with preserved and
broken Time Reversal Symmetry (TRS). We find that the decay process induces a
modification at small spacings of the probability distribution of the avoided
level crossings due to an attraction of the resonances. The theoretical
predictions are in complete agreement with the recent experimental results of
Dietz \textit{et al.} (Phys. Rev. E {\bf 73} (2006) 035201).
