The Verification Venue · a thing everyone gets wrong
The Fastball That Only Falls Less
A curveball curves because spin drags the surrounding air off-centre and the air shoves back — the Magnus force. The same force is supposed to make a good fastball rise. It doesn't. Even the hardest pitch on record makes less lift than the ball weighs, so it never accelerates upward: it just falls less than it would.
Here is the record itself, loaded and ready: Aroldis Chapman, a fastball averaged over 25 pitches at 104.4 mph with 2360 rpm of backspin — the fastest human throw Statcast ever measured. Watch the lift it makes stack up against the ball's own weight. Then push the sliders past what any arm can do and find the exact point where a baseball would finally rise. Everything you see is recomputed from the aerodynamics as you drag — nothing here is a stored answer.
Magnus lift force
0.28 lb
vs 0.32 lb of ball weight
Net vertical accel
1.30 m/s²
downward · 13% of gravity
Break at the plate
21.6 in
less drop than a spinless ball
Chapman's record is 104.4. Drag toward the right edge and watch the lift climb — at this spin it takes about 115 mph before lift finally beats weight.
More spin, more lift — but a human tops out near 2600–2900 rpm. Net rise at 104.4 mph would need roughly 3140 rpm.
12:00 is a 4-seam fastball (lift straight up). 6:00 is a 12–6 curveball (Magnus pulls down, adding to gravity). 3:00 / 9:00 are sidespin — a slider or sweeper.
Toggle it on: the seams steer the wake in a direction the spin axis does not predict. Two pitches, identical spin — different break.
The lift on a spinning ball is FL = ½·CL·ρ·v²·πR² — half the air density ρ, times speed squared, times the ball's frontal area πR², scaled by a lift coefficient CL that grows with how fast the surface is moving relative to the ball's flight, the spin parameter S = Rω/v. Alan Nathan's peer-reviewed measurements put CL ≈ 0.22 for an ordinary pitch. Here is that formula with the current numbers poured in:
At Chapman's record, that lift comes out to 0.28 lb — against a baseball that weighs 0.32 lb. The lift is real, and large, and it cancels 87% of gravity: instead of dropping like a stone, the ball sags only a few inches over sixty feet. But 0.28 is not 0.32. The net acceleration is still downward. The "rising fastball" was never a ball climbing — it is a ball dropping so much less than the batter's eye predicts that the brain reports the miss as a climb.
Rotate the spin axis to 6:00 and you have the curveball, honestly: the Magnus force now points the same way as gravity, so the ball drops more than gravity alone — the famous break is gravity plus Magnus, not Magnus fighting it. Every archetype lives on the same dial.
The check — every number recomputed in front of you
Below is the record pitch, recomputed live from the sourced aerodynamics and set beside the independently published figures. The green column is the cross-check, not a claim — dial the instrument back to 104.4 mph / 2360 rpm / 12:00 and the readouts land on exactly these rows.
| quantity | recomputed here | published source |
|---|
The CL = 0.5·√S curve is a smooth fit chosen to pass through Nathan's measured CL ≈ 0.22 at ordinary spin and to reproduce his "steep, then slow" shape; it lands the two rise thresholds within ~2% of the Hardball Times figures (113 mph, 3100 rpm). Run it yourself: node research/why-a-curveball-curves/verify.mjs.
What's exactly true, what's idealised, and where the record stops
Exactly true. Spin makes lift through the Magnus force, and FL = ½·CL·ρ·v²·πR² is the standard form. Nathan's measured lift coefficient for ordinary pitches (spin parameter 0.10 < S < 0.25) is CL ≈ 0.22 and is roughly independent of speed at fixed S. Plugging in Chapman's record gives a lift of 0.278 lb — matching the Hardball Times value of 0.28 lb — against a ball that weighs 0.32 lb (5⅛ oz). Lift is below weight, so the vertical acceleration is downward: the record-holder's fastball falls.
The honest boundary. A rising fastball is not physically impossible in principle — Nathan is explicit that with enough spin, enough speed, or a lighter ball, lift could exceed weight. The exact, defensible statement is narrower: no regulation baseball thrown by a human has ever had net upward acceleration. This instrument shows why the ceiling is so far away: at 2360 rpm it takes about 115 mph, and at 104.4 mph about 3140 rpm, to break even — both past the edge of human mechanics (the hardest pitch recorded is 105 mph; elite fastball spin tops out near 2600–2900 rpm).
The mechanism, stated carefully. The Magnus force is not the equal-speed Bernoulli story. The spinning surface drags the boundary layer around with it, delaying separation on one side and hastening it on the other; the wake is deflected, and by Newton's third law the ball is pushed the opposite way. (A perfectly smooth ball can flip into a "reverse Magnus" regime at certain speeds — but a seamed baseball sits in the normal regime.) Robert Hooke and Isaac Newton described the effect on tennis balls in the 1670s and Benjamin Robins on musket balls in the 1740s — Heinrich Magnus (1852) named it, he did not discover it.
Idealised, and named. The trajectory here uses a constant Magnus acceleration and no air drag, released horizontally, so the picture is clean; real drag slows the ball and shaves the break. The "break at the plate" is the idealised induced vertical break — the gap between this ball and a spinless one at 100% backspin efficiency. Measured Statcast break runs lower, because a real pitch is never pure backspin: an elite 4-seam fastball posts about 18–20 in of induced vertical break, and the 2024 MLB curveball averaged about −10 in — the spin-induced part only, with gravity removed. That last distinction is the classic trap: induced vertical break is not the two-foot total drop your eye sees, which also includes gravity.
The seam-shifted wake — the part still being written. The whole story above assumes the spin axis dictates the break. In 2019, working with Prof. Barton L. Smith at Utah State, Andrew Smith showed the seams themselves can trip the boundary layer asymmetrically and steer the wake in a direction the spin axis never predicts — comparable in size to the Magnus force for some sinkers, two-seamers, and changeups. Its fingerprint is public: the gap between a pitch's observed movement and its spin-inferred movement, both in Statcast. The toggle in the instrument is a schematic of that deviation, not a calibrated per-pitch magnitude — those are still being quantified. It complements Magnus, it does not replace it: spin is most of the story for most pitches, just never quite all of it.