Here is a firsthand example for an officer thats been there, done that:
A home in-progress burglary had been reported to the police. this occured in a county adjacent mine. being a burglary detective for 13 years, i recognized the description of the get a way car and the location it parks in my county. i immediately went to the interstate exit, i felt the burglars would exit. in approx. 6 minutes, i was correct. here came the burglary suspect vehicle. i followed the vehicle into a projects area. the vehicle was occupied by one person. his car stopped beside a dumpster in the projects. i ordered the suspect out of the vehicle. he ran. i ran. suspect finally stopped at the top of a grassy area in the projects and pointed a pistol at me. i raised my 12 guage shotgun at him, ready to fire. i knew the suspect and called him by name to drop his weapon. he pulled the hammer back on his pistol. i was about to shoot the suspect, when a child walked up behind him. i shouted, “james, there is a child behind you, drop your weapon”. he did not look, but instead ran off into a wooded area and was later apprehended.
Split second decisions, common sense, a cool head and sometimes raw bravery can make or break a situation in a “shoot or no shoot” situation.
I was blessed that day and i know it. my police training had taught me to wait just one more second before firing my weapon. in this case, i am thankful for the training and that no one was injured.