Kendall, Olddude et al:

New York City police statistics show that simply hitting a target, let alone hitting it in a specific spot, is a difficult challenge. In 2006, in cases where police officers intentionally fired a gun at a person, they discharged 364 bullets and hit their target 103 times, for a hit rate of 28.3 percent, according to the department's Firearms Discharge Report. The police shot and killed 13 people last year.

In 2005, officers fired 472 times in the same circumstances, hitting their mark 82 times, for a 17.4 percent hit rate. They shot and killed nine people that year.

In all shootings — including those against people, animals and in suicides and other situations — New York City officers achieved a 34 percent accuracy rate (182 out of 540), and a 43 percent accuracy rate when the target ranged from zero to six feet away. Nearly half the shots they fired last year were within that distance. In Los Angeles, where there are far fewer shots discharged, the police fired 67 times in 2006 and had 27 hits, a 40 percent hit rate, which, while better than New York's, still shows that they miss targets more often they hit them.

Bad marksmanship? Police officials and law enforcement experts say no, contending that the number of misses underscores the tense and unpredictable nature of these situations. For example, a 43 percent hit rate for shots fired from zero to six feet might seem low, but at that range it is very likely that something has already gone wrong: perhaps an officer got surprised, or had no cover, or was wrestling with the suspect.

"When you factor in all of the other elements that are involved in shooting at an adversary, that's a high hit rate," said Raymond W. Kelly, the New York police commissioner. "The adrenaline flow, the movement of the target, the movement of the shooter, the officer, the lighting conditions, the weather ... I think it is a high rate when you consider all of the variables."
(N.Y. Times)

And these are trained officers who are required to requalify periodically. I can't see that retired cops, who are older, slower, and are not required to demonstrate proficiency on a regular basis, would do any better.