# The quickest 6-3 play in baseball: to bounce or not to bounce?

What's the quickest way the get the ball (say from shortstop) into the first-baseman's glove, given some fixed initial (throwing) speed? Directly or with one bounce?

I'm fairly sure that the answer depends on the initial throwing speed, but where's the cut-off point (roughly)?

PS 1: Numbers, if needed:

Under the current rules, a major league baseball weighs between $5$ and $5\frac1 4$ ounces ($142$ and $149\,\mathrm g$), and is $9$ to $9\frac1 4$ inches ($229–235\,\mathrm{mm}$) in circumference ($2\frac7 8–3$ in or $73–76\,\mathrm{mm}$ in diameter).

The horizontal distance to be travelled is $36\,\mathrm m$.

PS 2: The surface is "clay" (around first base). The ball is covered in leather.

PS 3: Let's assume that throwing accuracy and catching abilities are not issues.

• I assume the quickest way is to maximize the horizontal component of the ball's velocity, i.e. release the ball horizontally, if you have the arm to make it reach without bouncing. Assuming you don't have the arm muscles, the question is: is it faster to throw with a little vertical component, and hence less horizontal, or to throw it horizontal anyway and let it hit the ground (at least once) and be slowed down by the bounce(s)... I'd guess more than one bounce was suboptimal, but one bounce might be close... Commented May 25, 2013 at 20:21
• Another factor is that the first-baseman can shorten the time of flight by stretching toward the fielder. This requires the ball to reach first closer to the ground, which, if recognized by the fielder, can further reduce the time... Commented May 25, 2013 at 20:52
• One more complication: the fielder could get a slower, arcing throw off on the run rather than stopping and planting for a faster throw. Commented May 25, 2013 at 20:56
• I think that one of the reasons that players bounce the ball is that they can throw faster if they throw down. I don't have any evidence of that, but it makes sense: the longer the ball is in your hand, the faster you can accelerate it. So it would be worth investigating if a throw can be faster slightly downward instead of straight ahead. Commented May 25, 2013 at 21:46
• The pure ballistic and collision physics are probably not the guiding factors here. Human bio-mechanics and the danger of the ball hitting rough ground and taking a bad bounce seem like more important factors. Commented May 25, 2013 at 22:07