That got me curious, and I ran a few numbers. Can't get more exact without knowing the probability of us actually hitting the guy, but assuming it ain't good (the less good it is, the less extra shots we need to make the difference), and if running cuts the odds of us hitting the eye in half, then we would need about 2.11 times as many shots to get the same probability of atleast one of the shots hitting it's eye (assuming a 20% probability of hitting when not running).
Edit: no matter how bad the chance of hitting is, we need at least twice the number of shots to pull even.