Spin Doctors

Once the ball leaves the hand of a pitcher there is nothing he can do but hope. There are four components that determine what the ball’s trajectory and speed will look like – two of them have to do with the pitcher himself (velocity and the spin) and the other two are environmental (gravity and air density). Obviously, the environmental ones are not constant from park to park (and the air density actually makes a difference) , but I will not get into the park effects here, just show the principle.

If we view it from the third base dugout, a traditional fastball with backspin will look something like this:

The air resistance will result in a so called drag, which is a force in the opposite direction of the ball’s travel, effectively slowing the ball down along the way.

Now, many of you know that the amount of drag relates to the square of the velocity of the ball, but the differences are not really that big, as all the thrown baseballs travel at what are scientifically similar speeds. Over the length of the distance between the rubber and the plate, drag will put just above 10% price tag on the speed of the ball, rather regardless of the initial velocity. A fastball thrown at 100 mph will reach the plate at around  88mph as the effect of the drag, whereas Jamie Moyer’s 70mph heater will slow down to about 60 mph.

This drag is calculated for non-rotating objects, but our fastball spins. If you look at the above graph, you will notice that the backspin of the ball has a further effect on the air resistance. On the bottom of the ball the ball surface moves towards the resisting air, and its apparent velocity is higher than the velocity of the ball itself. Imagine being on a big ship moving against the wind and running towards the bow – you will notice much more wind than when you ran back. That’s what happens to the ball  – its bottom is running towards the bow, its top running away from it. Therefor the real air resistance looks more like this:

The air is “thicker” at the bottom and as a result the ball will be “pushed mostly upwards”. Assuming for perfect backspin and adding the gravitational component, we finally have all four components responsible for the ball movement:

Velocity should actually be called “Initial Velocity”, but I deleted the Power Point already

The Magnus force is a very complicated component to calculate and I will not get into details of it. Apart from the air density it depends on the relation of rotational velocity (the spin) to translational velocity (the speed of a baseball). Adair, Hubbard and many others had a go at it, trying to precisely quantify it, accounting for all complicated variables. What we need to know here is that such a force exists, that it depends on the spin (the faster it spins, the better) and that it is not a negligible force –  a 90 mph fastball rotating at 2200 rpm will have  a force of gravity of some 1.4N, force of drag of some 1.7N and the Magnus force of some 0.9N. So, we are talking about a very important component of ball movement.

This is why such a fastball will “rise”. Dan mentioned it numerous times – it doesn’t actually rise, it just falls less than a similar ball without spin would. But, can spin actually make such a ball any faster? That depends on what you define as the speed of the ball, but the answers are basically yes and yes. The ball will have higher horizontal velocity due to the spin (albeit minimally) and it will appear to be even faster on top of that.

First, if you look at the vector of the Magnus force and break it down into two component vectors, you will see that it points towards the plate and up.The positive X-component (towards batter) actually makes the ball faster in its horizontal movement and a positive Y-component (towards up) makes it appear faster.


Combined with the other forces, it has the following effect on the ball:


This is really, really simplified and definitely not something I would present to the patent office. But I hope you get the general idea.

Another important aspect that Dan mentioned is the ball “appearing” to get there faster. Batters speak about the balls “jumping on them”. The balls we try to hit cross the plate underneath our eyes (well , the balls we should try to hit do, at least). That means that apart from actually crossing the plane earlier, the ball seems to get there even faster, as the changed angle adds not only to movement towards the plane, but even more so towards our eyes. If we had eyes on our feet, such a rising fastball would still cross the plate sooner than its non-spinning counterpart, but as the angle towards our eyes would increase, it would seem slower.

And, to cap it off, this is the effect Magnus force and the spin have on a 12-6 curveball Topspin_medium

Nothing what you didn’t know already – such a ball will dart towards ground and it will lose more velocity on the way than the non-spinning or back-spinning balls. This is because the Magnus force in this case has a negative X-component (towards the pitcher) and a negative Y-component (towards ground).

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