ntpd: consistently incorrect time on mid-2013 MacBook Air

I'm using ICMP time stamping on my mid-2013 MacBook Air, and I need my clock to have an accuracy of no worse than 1ms. I see that ntpd is running, with the default settings, and /etc/ntp.conf contains just one line, server time.apple.com, without even any comments. However, if I run ntpdate -d time.apple.com (or ntpdate -d ntp1.yycix.ca, which produces the same offset reading for any given time as time.apple.com farm does), always as a non-root user, I'm often getting the reading that my clock is offset by as much as 6ms, or, most often around 4ms (sometimes 0ms, but very rarely). Why is this happening? I'm not even rebooting my MacBook, it runs 24/7, plugged in, why is its ntpd not keeping the time correctly? Syslog has the following: % syslog | fgrep ntp | fgrep -v sudo | tail Nov 19 12:59:30 mba.cnst ntpd : proto: precision = 1.000 usec Last I checked, 1.000 usec is no worse than 1 us, which is 0.001ms, or 0.000001s; why does it claim that precision is 0.001ms, when in reality the clock is offset by as much as 6ms?