Ha ha
I can see that. But like it or not that oppurtunity has been given. Now, for your average to accurately reflect the quality of the batsman, it must take all the runs scored - deserved as well as the apparently lucky ones, into account.
Now, maybe you could instead of your 'first-chance' average, divide all the runs scored by the batsman by the no. of times he's gotten out + the no. of let-offs he's had. But this average is also problematic because a batsman who get a let-off on say, 75 wouldnt bat like one starting from scratch. For example, he wouldnt be as wary of getting out as he is at the start of an innings and might take a lot more risks.
Maybe a better idea would be to take the actual average of the batsman and his first-chance average together and evaluate the batsman based on that.