I finally had time to think about some of the points in this thread and to build a simple model to play with. Apologies for a long post and more science than most of you care about but FWIW….
1) Some of the early posts ignored drag effects which was noted by someone who also commented that drag is proportional to velocity squared. Actually, at low speeds in low viscosity fluids (think baseballs/softballs in air), drag is pretty well modeled as proportional to velocity (vs. velocity squared) so the math isn’t too hard.
2) All else being equal, a softball experiences more drag than a baseball at any given velocity because of its larger cross sectional area.
3) Drag is not the same as deceleration. Drag is a force, and the deceleration caused by that force depends on the mass of the object in question. Since softballs have more mass than baseballs, a softball will decelerate less than a baseball when subjected to the same drag force for the same period of time.
4) Netting out the effects of cross sectional area and mass differences, a softball will decelerate about 25% more than a baseball if both start at the same velocity and travel for an equal time. In other words, the difference in cross sectional area has more impact than the difference in mass between the two balls.
To see if this is just science or if drag actually matters, I built a simple spreadsheet model that calculates drag and the resultant deceleration of the ball in 6ft intervals of distance. The incremental step approach is needed since drag is being modeled as proportional to velocity. Hence, as the ball slows down, the drag is reduced, and the rate of deceleration also decreases.
To calibrate the model, I found a website (
http://www.baseballprospectus.com/article.php?articleid=6322) that had measured baseball velocities at release and as the ball crossed the plate and found that for a 90mph release velocity, the ball had decelerated 10% by the time it reached the plate. I used this to calibrate my model and then make the adjustments for what the effects would be for a softball following the logic above. Results:
Baseball (90mph) Softball (60mph)
No drag model 0.458sec No drag model (40ft) 0.455sec
No drag model (43ft) 0.489sec
Drag model 0.484sec Drag model (40ft) 0.471sec
Drag mode (43ft) 0.508sec
So drag adds a few hundredths of a second to the travel times – not sure that is significant, but given the precision timing needed for solid contact on a hit, maybe it is. Since someone is sure to ask, to make the baseball travel times with drag match the softball travel times, when comparing to a 40ft distance the baseball’s initial velocity would need to be ~92mph and when comparing to 43ft distance, the baseball’s initial velocity would need to be ~86mph.
However, I agree with others who posted that these numbers are not the ones that really matter when trying to figure out how “hard” it is to hit either ball. To me, hitting is a process of observing the flight path of the ball, and then attempting to accurately extrapolate when/where the ball will come through the hitting zone and then trying to put the head of the bat at that location at the correct moment. If, as someone else posted, it takes 0.15sec from decision point to contact point to execute the swing, then what matters is the location of ball when it is 0.15sec from arriving at the optimal contact point. This imaginary “0.15sec line” moves closer to the hitter for slower pitches and further from the hitter for faster pitches, meaning that when facing faster pitching the hitter must extrapolate the pitch path for a longer distance with less observation distance on which to base the extrapolation. This will be inherently less accurate than the reverse situation of long observation distance and short extrapolation distance for slower pitches. It’s also why late pitch movement is so effective, a hitter can not accurately/consistently extrapolate what he/she hasn’t seen up to the point of deciding to swing.
Some numbers to illustrate, which are based on the assumption that the actual distance from release point to contact point for both sports is about 6 ft less than the official pitching distance, i.e., 54ft for baseball and 37ft for softball (43ft true distance):
For a baseball with an initial velocity of 90mph, the ball will have travelled about 36ft before it reaches the “0.15sec line” leaving the hitter to extrapolate about 18ft of additional pitch path. For a softball starting at 60mph, the distance to the “0.15sec line” is about 24ft leaving 13ft to extrapolate. You can decide which is harder to do. If however, the softball is slower, say 50mph, then the hitter can see 27ft of pitch path before the “0.15 sec line” is reached leaving only 10ft of distance to be extrapolated. That seems like it would be a lot easier to do (Duh!). On the other hand, increasing the speed to 70mph changes the observation and extrapolation distances by only about 1.5 ft (vs. 60mph) and so I’m not convinced that the extra 10mph buys the pitcher a whole lot.
