The bonus 15 movement speed provided innately by boots of swiftness combined with the 20 provided by alacrity is multiplied by the percentage bonus provided by ghost.
Take someone with 345 movement speed innately:
alacrity swiftness boots
(345 + 80)*1.27 = 539.75
Softcap: 539.75 * 0.5 + 230 = 499.875
distortion swiftness boots
(345 + 60)*1.4 = 567
Softcap: 567 * 0.5 + 230 = 513
distortion any other boots
(345 + 45)*1.4 = 546
Softcap: 546 * 0.5 + 230 = 503
So basically, distortion over alacrity on swiftness boots provides roughly 13 more movement speed while in ghost. Without ghost, the distortion swiftness boots does not innately provide more than 415 movement speed so it is not softcapped, but the alacrity swiftness boots does so it the lesser softcap is applied, (the greater softcap isn't applied until a person has more than 490 movement speed)
425 × 0.8 + 83 = 423
Compare that with the 405 provided by distortion swiftness.
So the question is, would you rather have 13 more movement speed during ghost or 18 move movement speed at all other times? This is why I never by distortion for the speed boost. The only reason I might pick up distortion would be if I have both teleport and ghost or teleport and flash for the cooldown reduction on those spells combined with the other effects. The teleport CDR combined with the summoner spell CDR found not too deep in the utility tree with the fact that teleport already has a lower cooldown when used on allied towers in particular makes it have a 140 second cooldown, which is shorter than a TF ultimate.
