As I've said a few times in the past, the 4x4x4 is my favorite twisty puzzle to speedsolve. Right now my goal is to average below 2 minutes, and for the last month or month and a half I've been a bit stuck around the 140-145 second mark. So today I decided to do some analysis to try to figure out where I can improve.

This is a graph of my 4x4x4 averages for as long as my records go after I got my Eastsheen and started cubing again.

Day 1 (x axis) is June 1, 2007, times (y axis) are in seconds.

Some interesting points about the graph:
1. On day 42 I began using middle 5 of 7 averages instead of 3 of 5. Notice the change in the graph at that point.
2. On day 104 I began using a standard middle 10 of 12 average.
3. The two expanses of no cubing early on correspond to two of my summer trips.
4. Most obviously, there is a HUGE "quantum leap" at day 67. Funny thing is I didn't make any major method changes at this point, I just started going faster.
5. The black line is just Excel's expontential regression feature. It's not really working with much data and it doesn't fit very well, but I left it on there.

Since I don't solve the 3x3 very much anymore I took an average of that to make sure I was still doing ok. Then I took averages for the centers and edges steps and timed my execution of the parity fixes to figure out how much time parity problems cost me on average.

I got these times:
Centers Average - 27.73
Edges Average - 44.59
3x3x3 Average - 35.55
Parity Average - 7.29
Situational Overhead - ?

Adding the four averages gives 115.16 seconds. Situational Overhead is my own fancy name for the time I loose by not getting inspection time for the edges or final solve, and for having to solve the final solve on the more difficult 4x4 mechanism.

I figured situational overhead would be quite import, but at this point I was expecting the normal 4x4 average I was about to take to be in the low 140s, and 25 seconds of situational overhead would be appalling! If it was that bad I was going to be concerntrating almost exclusively on my final solve for a while!

However, I felt that I had done atypically well in the averages above, which would throw off my results if the normal average was just a typical performance. But it wasn't! I averaged sub-130 for the first time ever with a 126.84! The average included four sub-2 times, which are usually quite few and far between for me.

That makes situational overhead only 11.68 seconds. Pretty good in my book.

But then I got to thinking, what if I just made another "quantum leap", as the graph suggests I might be due for? Lars Petrus also mentions these leaps on his own website(http://www.lar5.com/cube/menthol.html)

Well, I don't really think I did, because while I did very well today, I also didn't hit very many problem cases. I also had much more warmup and a better night's sleep than normal.

Since I use Hardwick-ish centers and 2-pair chaining for edges, the only real problem case I have is that of having multiple pairs of "mutually exclusive" dedges. That is, when two edges look like theyr'e the last two edges, but they aren't. I call these "final pairs", and having more than one of them is pretty common. I've actually had four "final pairs" before! (ie, 2/3's of the edges were problem cases). I was wondering, is there any really good way for dealing with these, or should I just work through them the normal way (ie, as if they were the last two edges). I experiemented with a few things in the past but everything I've thought of ahs been eaither equally or less efficient.

I'm not really sure what the "point" of this post is, as I don't have any real questions about how to get faster (those questions have been answered countless times in other threads), but hopefully this post might be interesting to other cubers who are at the same level on 4x4x4 (or those at other levels).

Currently, I think I can improve my centers step the most. For a while, I would always solve red/orange, then blue/white, then green/yellow (on a standard Rubik's color scheme). I think that at this point it isn't so critical to learn to start with other first two pairs, but rather to pick whether it's better to do blue/white or green/yellow as the second pair of centers. When taking my centers average there were two times when I did green/yellow first because there were 2 2x1's of those colors, and those two times beat my centers average by 3-4 seconds. I think eventually I'll need to work on my first 2 centers, but right now they aren't the most important.

A few closing remarks that aren't really related to anything:
1. I like practicing with a metronome. It helped me get started smoothing out my 2-pair chaining.

2. Some data on mistakes. Twice during the centers average I messed up badly, once I put the first centers next to each other, another time I accidentally made a quarter turn instead of half turn and destroyed the 3rd/4th centers right as I was about to put together the 2x1's. The times on these solves were 42.17 and 47.49, respectively. Also, a few weeks ago while practicing just edges I lost the centers at one point and ended up with a 72.20 for that step. Those are just to give an idea of how much the "big 4x4 mistakes" can cost you. 15-20 seconds or more!

I would just recommend improving each step at a time.

I found centres easiest to improve when I used reduction. Instead of doing opposite centres, do the first two opposite then just work around the M ring with the first solved centres on L and R. You can easily drop 10 seconds there, and get that elusive sub2 average.

I do adjacent centers already. blue/white and green/yellow are adjacent colors on a normal color scheme. one thing I dont' do yet is, say, blue/yellow then green/white

I don't exactly consider sub-2 to be "elusive", but...

Anyways, adjacent centers is too slow for my tastes, while six-pair seems to ALWAYS mess up. I do two pairs at a time.

For the 3x3 phase, I suggest stopping for 1-2 seconds before starting your cross. That way, you don't lose too much to lookahead.