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Even if we start the scenario from the time the weapon is picked up, the time scale is simply different - unless I missed something, we do not know that he pursued them into the alley, just that this is where the woman died. Was she shot on the way out of the house? Did he have a line of sight from his original position into the alley? He could potentially have done everything (with a gun) in a few seconds without even getting up off the floor. </p>
<p>Conversely, the bat scenario assumes that he gets up off the floor and pursues into the alley - that is the time issue I am talking about. Perhaps he did get up off the floor, and chase them into the alley… but I have not seen any evidence of such, nor do I see any reason to presume that a battered old man could move fast enough in that time frame to even have a shot at the slower assailant.</p>