During an interview with Michael Kay in May of 2010, Brett said that he had never run Track and Field in his life and has never been timed in a race. Brett (jokingly) said that he probably couldn't run that far (100 meters).
On May 15, 2009, Brett hit an inside the park home run. From the time his bat hit the ball to his hand touching home plate, about 14.5 seconds had expired. Brett ran 360 feet in 14.5 seconds or 24.83 feet per second.
There are about 328 feet in 100 meters. There are 360 feet in about 109.728 meters. Brett was running 7.57 meters per second during his inside the park home run.
So for a 100 meter dash time trial:
You divide 100 meters by 7.57 meters per second, you get 13.21 for a 100m dash time. This obviously is quite unrealistic as we all know that Brett is much faster than that.
On April 17, 2010, Brett had 3 infield singles in one game. It took Brett about 4.2 seconds to get from the Batters Box to 1st Base during his 2nd base hit of the game. Brett ran 60 feet in 4.2 seconds or 14.29 feet per second.
There are 60 feet in 18.288 meters. Brett was running 4.35 meters per second; he wasn't up to top speed yet apparently.
Unfortunately, it is impossible to find a realistic time value for Brett's speed in a 100 meter dash. The best solution would be to just put him on the line and make him run it.
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It is reported that Brett Gardner can run a 40 yard dash in 4.38 seconds. It took him only 14 seconds to run 360 feet for his first inside the park home run on May 15, 2009.