No, No, No...never notch...always drill. I can’t think of a circumstance where a notch is better than a drilled hole ...even a drilled hole in a “bad” location.
A hoist can fail 3 ways...so we check for 1) extreme fiber in bending, 2) horizontal shear, and 3) deflection. (We check for other things to, but is immaterial here.)
1) Extreme fiber in bending means what happens when the joist bends due to the load and stretches the extreme wood fiber. The fibers are stretched most along the bottom edge and compressed most along the top edge. (In fact, there is no “bending” stress in the middle of the joist. That is called the “neutral axis”.)
Each species is tested and their limits are known and rated. When you notch the joist, you reduce the effective height of the joist. (If you notched it 1 3/4”, you’d have a 2x8 instead of a 2x10. But if you drill a 1 3/4” hole in the center of the joist, you’d still have a 2x10, because the extreme fiber in bending is still the same distance from the “neutral axis”.)
2) Horizontal shear is the stress of the fibers trying to slide past each other. This happens furthest from the neutral axis too. (To test this, stack up 6 or 7 2x4’s that are 20’ long on two chairs 20’ apart. Stand on them in the middle of the span and you’ll see the ones at the edges slide more than the middle ones.)
3) Deflection is greatest in the middle 1/3 of the joist span. Deflection is resisted by area of the joist from the “neutral axis”. Again, notching the joist removes a portion of that area that is furthest from the neutral axis, causing a greater deflection.
This phenomenon is greatest in the middle of the span, but affects the joist anywhere along its edge...top or bottom.
Without knowing anything about the loads on the joists or the span of the joist, I’d drill a hole in the middle of the joist (from top to bottom) and locate it 1/3 distance of the span from the bearing point.
Also, when people tell you it doesn’t matter, because the joist have knotholes, don’t believe them. Lumber is graded with knots, grain, etc. accounted in the stress rating...so adding more “holes”, etc. will reduce its value (strength).
Also, design of beams and joists is set up so that when they fail, they fail in tension...not compression. That way, you’ll see a crack develop and can take action. (If it failed in compression, it would fail with an explosion...no warning...clever, huh.)