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profile.Profile.calibrate can only produces a bias for the default timer. If you've specified a different timer, it will not be used when calibrating.
Additionally, setting profile.Profile.bias will affect the computed bias. It will produce a bias that must be added to profile.Profile.bias and cannot be used independently, which is surprising.
The fix is to change
 p = Profile()
to 
 p = Profile(timer=self.timer, bias=0)
in _calibrate_inner().
The attached patch makes that change and additionally removes some code that temporarily resets self.bias in calibrate(), as it had no effect. Perhaps Profile.bias was meant instead. At any rate, _calibrate_inner() no longer needs to exist, but is left for backwards compatibility.
This will demonstrate the problem with calibrating after setting profile.Profile.bias:
import profile
profile.Profile.bias = profile.Profile().calibrate(100000); 
print '%+.9f' % profile.Profile.bias
profile.Profile.bias = profile.Profile().calibrate(100000); 
print '%+.9f' % profile.Profile.bias

@Adam sorry about the delay in getting back to you.
@Georg can you comment on the patch please.