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Why do Wikipedia and other sites claim that the 1st and 2nd-placed runners at the 2000 Boston Marathon set identical times?

The above video shows that the winner won by a full second. Why do these sources claim they set the same time?

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    For reference: crossing the finish line happens at 1:27:07 in the video
    – ImClarky
    Aug 5 at 22:34

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Generally speaking, marathon times have not included fractions of seconds. The times are rounded up to the next second. Based on the video the second place finished within a second of the first, so it's reasonable to see the top 2 spots awarded the same time for this race.

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The identical times are reasonable. The clock time above the runners is not 100% accurate - while the elite runners are "gun time" not "chip time", the official clock can be a small amount off of the display clock. I'll trust the ARRS, which is as close as official as you can get for race time statistics; the BAA page also confirms this time.

As to whether the second place runner was within less than a second, they clearly are; by my calculation he finishes 2 to 2.5 strides behind, maybe 5 meters behind at most. The runners are running just under 300 second miles on average, and as elite marathoners they're pretty consistent - plus the adrenaline of being at the end suggests they're at least at their average for the last few paces. 300 second miles means those 2.5-ish steps (or 5 meters) take 0.9 seconds or thereabouts - so plausible they are "in" the same second (and it may be more like 0.7 if it's 2 strides, or 4 meters). Of course, the second could tick during that 0.7-0.9 seconds; but it's also possible it doesn't.

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