#1
Let's say I'm doing some chromatic exercises and I first play 4-3-2-1 on the high e string and I want to switch to the b string and play the same pattern. The picking pattern was down-up-down-up and now logically it should probably be a downstroke and it's the thing I do when I play this pattern, but wouldn't it be more efficient if it was an upstroke? Should I practice switching strings when going up with an upstroke? I'm currently more comforatable with downstrokes but I want to maximize the efficiency of my picking and need advice with this. Thanks.
#2
1nsane000 practice both! economy picking is where you're changing strings in direction of last pick stroke. But this is more practical for odd numbers of notes on a string prior to changing. In your chromatic 4 note per string pattern if you continued to descend with an upstroke to the b string you'd then need to switch to g after a downstroke. You're then fighting against direction of travel so it's harder to change. With strict alternate picking with even notes per string it's easier to start with a downstroke as you'll always change strings after an upstroke so escape the plane of the string. Less chance to get caught up! But economy picking is good for odd notes like I said when going in one direction across strings.
#3
1nsane000, there's a couple of things to consider with this question: efficiency, and tone.

Efficiency It is theoretically true that economy/directional picking is more efficient in terms of pure speed... in reality it doesn't seem to make much difference to how fast you can play. If you look at the greatest pickers in the world, there's a pretty solid mix of both styles and they all seem to top out at about the same speed for picked lines. That said... the two do lend themselves to different lines, but it's not quite as simple as the "odd numbers = economy picking, even numbers = alternate picking" thing that you will hear from a lot of people.

Take this line for example (an example that has very little musical value I must add):


e|---------8-7-6-5---------6-5-4-3-
b|-8-7-6-5---------6-5-4-3---------
g|---------------------------------
d|---------------------------------
a|---------------------------------
e|---------------------------------


There are two ways we can pick this. A lot of people would have you believe that economy picking doesn't apply to this and that you should alternate pick it always:


e|---------8-7-6-5---------6-5-4-3-
b|-8-7-6-5---------6-5-4-3---------
g|---------------------------------
d|---------------------------------
a|---------------------------------
e|---------------------------------

p|-d-u-d-u-d-u-d-u-d-u-d-u-d-u-d-u-


But I would argue that economy picking is perfectly valid here:


e|---------8-7-6-5---------6-5-4-3-
b|-8-7-6-5---------6-5-4-3---------
g|---------------------------------
d|---------------------------------
a|---------------------------------
e|---------------------------------

p|-u-d-u-d-d-u-d-u-u-d-u-d-d-u-d-u-


If you really get in to economy picking it's actually much more about the context of the line than it is purely about the number of notes on each string. Another example, with actual musical use this time:


e|---------------------------3-7-
b|-----------------3-7-----5-----
g|-------4-7-----5-----4-7-------
d|-----5-----4-7-----------------
a|-4-7---------------------------
e|-------------------------------

p|-u-d-d-d-u-u-d-d-d-u-u-d-d-d-u-


The conventional wisdom of when to economy pick kind of falls apart here because of the mix of even and odd numbers of notes, but it's pretty perfect for economy picking.

I don't want to pile on too much information here, partially because there's a lot to go in to, and also because I'm at work and don't really have time to fully explain everything about economy picking in depth. It's all about the direction you need to go in next and what pick stroke you're on. If you want to learn more about it then look in to the instructional material of Frank Gambale, he really an absolute master of these kind of mechanics.
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#5
Efficiency picking is alternate picking except when it's not... the determination of when it's not may depend on your own mechanical level of articulation and clarity of using the pick, or it may be a stylistic choice. In other words, the transition from alternate to efficiency occurs at different speeds of playing for different guitarists; some stay in alternate all the way up to top speed, others shift to efficiency at relatively slow speed... and for whatever speed some chose to do most or all of their playing as alternate picking to get a certain feel of the sound while others may use most or all efficiency picking for the tone and swing that it imparts to phrasing (blues and jazz players often like to stay with efficiency picking because of its effect on phrasing).

Theoretically, efficiency picking should be potentially mechanically faster than alternate picking but you rarely hear it done because much of the nice tone and swing it imparts to the sound is diminished at higher speeds and approaches the regularity and articulation of alternate picking.
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