Let's put it this way: the LHC has on the order 2000 results so far, assuming the null hypothesis, you expect about 100 >2σ deviations and about 5 that are >3σ.

Let's put it this way: the LHC has on the order 2000 results so far, assuming the null hypothesis, you expect about 100 >2σ deviations and about 5 that are >3σ. The combined significance from ATLAS and CMS will be higher, but it's quite an involved process to get all the systematics right and get approval from both collaborations.