If you are referring to Mountain handbook for more beta on Babcock, there seems to be some differences regarding the west, middle and east summits and which may be the true. We follow the opinion of LoJ that indicates the middle summit to be the high point.
For Babcock Peak, park just off the main road, just after crossing Boren Creek or a few yards up the Boren Creek road. If you are wondering would be possible to drive up the Boren Ck. road you will soon find an answer. Very quickly the road becomes quite rocky and stays that way most of the distance up the canyon. It also stays very narrow with virtually no turnout places or wider areas. Higher up, a fallen tree, parallel to the road forces any vehicle over to the side and tilting heavily. Only ATV’s, and short wheel based 4WD’s should attempt the road. There are 4 sets of switchbacks. Just a short distance up from the beginning of the road, most vehicles with decent clearance could drive to a level camp spot, but it is marked NO Camping.
Hiking up this road, we arrived at the old mine site near timberline at 11,300 ft. in 1:20. We supply this info so you can estimate your time. At this old mine site, there is a large, flat area where you could easily camp and turn around if in a vehicle. From that point on, the road quickly disappears. Identify the correct couloir to ascend at this point. The best way to do this is to identify the east and middle summit. Difficult to do with confidence from this vantage point. The couloir we used is the one left of the middle summit. This couloir has a dogleg in it so you cannot see all the way up it versus the next couloir to the right. Another way to identify the correct couloir is that it is the 3rd counting from the right. Finding the right couloir is critical in making the correct summit. See our photo gallery for help.
Begin working your way up the steep, mostly open hillside toward the base of the couloir. At first, you will be walking on tundra laden with flowers which will then give way to rocky rubble as you approach the couloir. You will need to angle upward toward the left from the mine to reach the couloir and the steep talus slope below it. Once you enter the couloir, the real fun begins. For a short while, we worked our way up on more very loose rubble, stacked, small boulders, etc. Then we came to a snow-filled section about 300 feet up from the entry point to the couloir. The snow was still quite firm and without crampons, we did not feel secure hiking directly on the snow, even though we had our ice axes. So we wedged ourselves in between the snow and the rock on the right side and worked our way up, sometimes using the pick of our axes to pull up on or using our hands on the rock wall on the side. Often, we had one foot on the snow and another on the rock. Talk about “mixed climbing!” There were plenty of dangerous loose rocks to worry about putting down on each other, so we had to be slow and very careful. This is certainly helmet terrain.
As you ascend, keep a watch out for a small side gully that enters from the east side beyond the dogleg where the couloir bends left. It appears that Coopers preferred route begins near the dogleg. The small side gully we refer to is beyond that point - so climb higher. This will be about 200+ feet down from the West Babcock - Middle Babcock saddle. About 150 feet down from the head of the main couloir you've been climbing in, there is a section that “pinches” with a small trickle of water running down. Right in the pinch there is one large chockstone and a pile of other rocks behind it. On the left side of this "pinch," there is a short, nearly vertical wall. If you arrive at this point, you have gone past the small side gully. Go back down to find it. Only go up past the "pinch" if you have a strong desire to mount the west summit, which can be done in about 10 minutes from the west-middle saddle with a brief, 3rd class type move that's not too exposed. If you're curious about climbing Middle Babcock from that saddle, what we found there was a near vertical wall of rock, soaring up another 100 – 200 feet. We did not see any non-technical route to the summit from the saddle but when we were there, the weather was bad and clouds were swirling around and partially obscuring our view at times.
At the side gully that enters in from the east, scrambled up that short gully about 50 feet. Cross over a rocky rib and then descend a short distance into another more prominent gully before ascending more on 3rd/almost 4th class, steep terrain before exiting that gully through a narrow crack and emerging onto the south facing slopes of Middle Babcock. The "more prominent gully" we believe to be the one Cooper refers to.
From the south facing slopes, it is mostly 3rd class scrambling in a shallow trough that will lead to the summit. We came out on the summit ridge about 200 feet or so east of the high point. There were a couple of 3rd/4th class moves along this ridge. We found a small summit cairn, shelter of sorts and a register. It is now that you should see that this summit is easily higher than either of the other two. If not, then you've climbed the wrong one.
To go down, we followed our ascent route carefully back to the narrow slot and gully, but instead of dropping immediately back into the main couloir, we followed a secondary couloir on the east side until it finally merged with the main one farther down. It was steep and dangerous going and we had to be careful not to put rocks down on each other. This was definitely helmet terrain. Some sections were very loose gravel & sand while others were more loosely stacked boulders of medium size. Once you finally reach the bottom of the main couloir, pause for a well-deserved break and celebrate being free of all the hazards. The remainder of your descent and trip back to your vehicle should be far less stressful. Enjoy the abundant wildflowers on the trip back.
Links to other information, routes & trip reports for this peak that may be helpful.