Why do some of my distance run splits show a fastest pace as being a slower time than my average pace? That's a mathematical impossibility!

I see this all the time with shorter laps.

Although some will disagree with me, I think the reason is that average pace (for activity or lap) is calculated/measured separately from instant pace. (Max pace for an activity/lap is obviously the fastest recorded instant pace for the activity/lap).

- Average pace (for activity or lap) isn't even recorded in the activity FIT file (at least not for the older devices like Forerunner 955). It's calculated after the fact in Connect as time / distance. This is despite the fact that average lap/activity pace fields are available during the activity, on the watch. It does seem to me that average pace fields on the watch and in Connect are calculated in exactly the same way (time / distance). Sometimes the average pace in Connect may differ from the average pace on the watch by 1 second or so (maybe due to rounding?)

Notably, average pace is not calculated as some sort of average of all the instant paces/speeds.

I have developed Connect IQ apps in the past, and I def noticed that if you try to calculate lap/activity average pace as the average of all the instant paces/speeds, you will not get an answer that agrees with the built-in lap/activity average pace. If you calculate average pace as time / distance, then your answer will line up with built-in average pace.

You can verify at least this part of what I'm saying by looking at activity/lap time and distance on your watch and in Connect and noting that they *always* line up with average activity/lap pace. 

- Instant pace is measured based on a combination of GPS speed and accelerometer, and recorded to the FIT file (once per second). Since average pace is not an average of instant pace, and since both GPS and accelerometer are imperfect (it's well known that GPS is not reliable over very small distances), this explains why average pace doesn't always line up with instant/max pace. 

Some ways to see that instant pace is not based on solely on GPS speed:

- Export the FiT file and open it in fitfileviewer.com. You will see there is a separate table for GPS Metadata which contains GPS speed (and position), once per second. The Session table contains the instant speed values that are actually used for the activity (in the instant pace field on the watch and in Connect), and you will see that the session speed values and GPS speed values are not necessarily the same

- Use a 3rd-party tool like runalyze.com which syncs with Connect and shows your max speed/pace for fixed sub-segments of time/distance, including 1 second. When I look my fastest 1 second pace in runalyze for an activity, it's often much faster than the max pace reported by Connect, because runalyze is solely using the GPS position/distance in the file to determine pace over any given distance/time. This shows that Garmin instant pace isn't based solely on GPS position/distance/speed