From Diablo Wiki
Breakpoints are found in 2D games, and they refer how fast animations for attacking, spell casting, hit recovery, and many other things are displayed in frame-based games such as Diablo II.
Since Diablo 3 runs in a 3D engine, it does not have literal breakpoints; animations can display however fast or slow the game wishes. That said, there might be values that must be met in various bonuses for the improvements to become noticeable, and improvements will likely run into diminishing returns.
Bashiok spoke on Breakpoints in Diablo III in April 2011.
I’ll make two statements on break points:
- Break points were an effect of the Diablo II engine, not a gameplay mechanic specifically designed into the game.
- Even modern games run at specific tick rates, and Diablo III is no different. I’ll only say it’s more than 25.
It’s just not very sexy to chase single digit increases, and tough to itemize, so they’re given some weight and a curve, and it becomes a bit mathier, but a lot more fun to go after.
I believe that wasn’t the point of the post. I think he was suggesting that the minimum gain from any stat that deals with breakpoints only increase based on the lowest break point value, thus eliminating the need to learn break points.
...If there’s still that very old problem, maybe the items that make no real effect on the attack speed have some asterisk near their AS value? Because this isn’t something that can be “fixed” as far as I’m concerned.
Well, you could say (for Diablo II) there’s only 24 points of attack speed increase possible to obtain. Each one removes a frame of animation. That’d be pretty clear.
 Breakpoints in Diablo 2
In D1 and D2, breakpoints referred to how fast animations for attacking, spell casting, hit recovery, and many other things function in frame-based games such as Diablo II. Since D2 runs at 25 frames per second, various calculations had to be increased to a certain level to show an improvement; incremental changes didn't matter.
For instance, it took an unmodified D2 Barbarian 7 frames (meaning 7/25 of a second) to swing an unmodified one-handed weapon. He required 9 IAS (increased attack speed) to drop down to 6 frames, 20 IAS for 5 frames, 42 IAS for 4 frames, 86 IAS for 3 frames, and 280 IAS for 2 frames. 1 frame was not possible. So a Barbarian at 20-41 IAS was at 5 frames. Not until he reached 42 IAS did the speed of his attack become one frame quicker.
This sort of thing applied to every character and the pace at which they swing weapons or cast spells, and it always took progressively more increased speed modifiers for each frame of improvement in their actual speed. The slowest base attack was an Amazon with a one-handed weapon, at 17 frames. However that speed could drop all the way to 5 frames with a huge amount (over 480 points) of Increased Attack Speed.
- See extensive discussion of in the D2 section of this wiki.