Quick and (very) dirty math re: Andrew Brackman

There I was, reading Lane Meyer's excellent analysis of Andrew Brackman, and one part stuck in my head - since AB is so tall (about 6'10"), he will be releasing the ball considerably closer to home plate compared to an average sized pitcher, hence making the ball appear faster. How much faster does that mean?

For the purpose of making the math easier, let's say a 5'10" pitcher throws a 100 mph fb (e.g. Billy Wagner, Tim Lincecum) and Brackman, a foot taller, also throws a 100 mph fb. And let's also assume both pitchers have the same delivery/mechanics.

5'10" is 70 inches - Brackman is 12 inches taller (82 in).

Brackman's arm - from shoulder to fingertips - should be about 40% of his height (33" in his case). Lincecum's arm should therefore be 28".

Their outstretched fingers (over their heads) should be their height multiplied by 1.27 (27% higher). That makes Lincecum's release 89 inches compared to Brackman at 104 inches. Not done yet.

The distance from the back toe on the pitching rubber (horizontally across) to where the fingers release the ball is 101% of the pitcher's height. For Lincecum, that would mean he releases the ball 70.7 inches from the rubber - for Brackman it means a release distance of 83.2 inches from the rubber. That's a difference of almost exactly a foot. Wow, that could've been done much faster if I had merely assumed their difference in height was their difference in release distance.

Still not done. A mile is 5280 feet - a 100 mph fastball travels about 147 ft per second. A ball traveling 100 mph goes 60.5 ft (60'6" or 726 inches) in approximately .412 seconds.

But in reality, release points are closer to home plate. Lincecum's is (70.7 inches closer) 655.3 inches (~54.61 ft) to hp. Hence, his 100 mph fb reaches hp in .3712 seconds (54.61/147).

Brackman's fb (at 642.8 in = ~53.57 ft to hp) reaches hp in .3644 seconds.

Therefore, Andrew Brackman's fastball reaches the hitter .0068 seconds earlier (because he releases the ball 12.5 inches closer to hp) than a pitcher a foot shorter. From my limited experience hitting baseballs and my extensive experience watching baseball, that's a negligible difference.

Further study reveals the difference to be far from negligible though.
Brackman's 100 mph fastball travels 166.03 ft/second = 112.95 mph equivalency (from true release point - 53'7" from hp).
Lincecum's 100 mph fastball travels 162.98 ft/sec = 110.9 mph equivalency (from TRP).

So, the equivalent difference in velocity is somewhat significant: to the batter, it means that the ball gets to him 36.6 inches (3.05 ft) earlier (or 2.05 mph faster (1.01849% faster)) than a 5'10" pitcher's 100-mph fb would (which is a lot more significant than what .0068 seconds would belie).

Hence, an Andrew Brackman 97-mph heater is the equivalent of a 5'10" pitcher throwing 98.8 mph (97 x 1.01849). Not quite as large a difference as the 3 mph Meyer predicts, but certainly nothing to scoff at either. (Again) however, perhaps Meyer accounted for air resistance - since a shorter distance throw (Brackman's fb) would pass through less air, there's less resistance, hence it would maintain its velocity better.

Conclusion
I expected the difference to be less than what I found. The fact that Brackman's fastball is faster/quicker than a shorter pitcher will only accentuate his velocity. Hitters will also have to deal with his fastball entering on an extreme downward plane along with the intimidation factor super tall pitchers often have.


PS: I hope all my math was accurate and that it made sense in context. :)