In this battle, we managed to construct a Ditto with an ostensible 16,128 speed in USUM. It had to be Ditto because Ditto alone gets to take advantage of the single largest speed boost you can possibly get out of the item slot: if it's holding Quick Powder and hasn't transformed yet, then it gets a +100% speed boost, whereas Choice Scarf only gives +50%. By Baton Passing +6 Speed to Ditto and immediately hitting it with Speed Swap (on something that's already swapped its speed with max-speed Deoxys, who started with 504), Skill Swap (giving it a weather or terrain speed boosting ability), and making sure that both the appropriate weather and Tailwind are in effect on its side, the total setup can be achieved quickly enough that Ditto hasn't yet had a chance to transform and spoil its Quick Powder boost. In Sw/Sh, if we tried this again but used Regieleki as the Speed Swap donor instead of Deoxys (who isn't even available there), the nominal speed would be 17,536 instead.
However...it doesn't actually get to make use of all that speed, even for the limited purpose of transforming. The last few steps of speed computation, in order, are:
- If your speed is greater than 10,000, reduce it to 10,000.
- If Trick Room is in effect, replace your speed with (10,000 minus speed).
- If your speed is greater than 8191, replace your speed with (speed minus 8192).
So in the case of a Ditto (or anything else) with 16,128, 17,536, or any other number above 10,000, the first of those steps will cut out the excess and make it fall to 10,000, and at the last step it's still too high and wraps around to 1808, which is all it gets credit for. If you keep watching the battle to the fifth turn, you can verify that since the naive maximum speed really only counts as 1808, it manages to get outsped by a Swoobat that "only" has 2512 speed that turn. (The purpose of that battle was in fact to discover what effect these speed-capping operations had on Gyro Ball: as it turns out, Gyro Ball in this case sees a speed of 10,000, not 1808 or 16,128. Electro Ball behaves similarly.)
The maximum effective speed you can possibly have is 8191, as anything slower gets outsped and anything faster wraps around to 0 or other low numbers in the final step. However, the only way to actualize this highest of perches is to get a speed that would otherwise be exactly 1809 (such as a starting speed of 402 at +4 with a Choice Scarf) and then put Trick Room up. Without Trick Room, it's impossible to land exactly on 8191 no matter what starting speed or combination of modifiers you try to use--the closest you can get is 8190, from 455 at +4 with Choice Scarf, Tailwind, and a weather-speed-boost ability.