Most people who say that their maximum is 1,600 watts won’t put out 1,600. My maximum is 1,580, and that is a lot.
Quoted like that, the 1580watt number will be for 1 second most likely.
1 second is the typical recording rate of the SRM PowerControl units (same with the Garmin Edge). So unless a duration is specified, "maximum" will refer to the highest recorded sample in the file
(the PowerControl can record faster than 1 sample/second, but the higher rates are typically only used for analysing events like standing starts in track racing, not for 200km road-race stages, where 0.25 second resolution is excessive)
This article on "The profile of a sprint" gives some specific numbers:
The sprint peak power output was 1248±122 W (range: 989-1443 W), and the average power was 1020±77 W (865-1140 W) for a duration of 13±2 s (9.0-17.0 s). These data fall within the range of previously published data where, for example, a peak power of 1097 W and 1370±51 W were reported for won sprints. The peak speed reached during the sprints was 66.1±3.4 (57.1-70.6), slightly lower than the expected; however, the speed data were in agreement with previously published data (J Martin 2007, Menaspa 2013)
The whole article is worth reading, and it backs up the quote from your question "It’s not watts, and it’s not just my frontal area in a sprint",
We know that the highest sprint power is not always the race winner, because there is no correlation at all between the two outcomes
In practical terms, such a reduction in CdA (~10%) can result in more than three metres advantage over a 14 seconds sprint. Based solely on these data, it becomes obvious why there were no correlations between absolute power (Watts) and race results
Tactical variables may be as important as, or even more important than, power alone. A recent case study showed that a good position in the bunch and team support are important factors for road sprint performances (Menaspa 2013)