Mash efficiency this low would point to a procedural error. Most likely a poor crush which was made even worse by the use of the smaller wheat kernels.
If you want to try to pin point where there may be room for improvement it may be worth measuring
- conversion efficiency. How much sugars are in the mash tun after the mash/theoretical maximum sugars available (TMSA) You need to know the volume of water transferred into the mash tun and the gravity prior to lautering
- Mash efficiency: How much sugars have been removed from the mash/TMSA. You need a preboil volume and gravity
If 1 is low (90+ percent is readily achievable with this grain bill) it points to either a poor crush or inaccurate temperature reading or non-optimal mash pH.
If 1 is good and 2 is low it points to an inadequate lautering process.
The brewhouse efficiency will of course be a bit lower as you lose some volumes to trub, hoses, plate chiller, hop absorption etc. Aside from the perceived bragging rights that many seem to equate the quest for high efficiency with, the numbers themselves can help highlight errors in the process. Crush, pH, sparging methods etc. There are lots of variables but each number will nail down the area that can be improved.
Better efficiency through refinement of the process leads to consistency as the pleasant byproduct. Consistency in brewing is something few could argue against. Many will not care one iota, but by the nature of the post I'm guessing you are not in that category.
I hope I have not confused things further. I am certainly no expert but am a bit of a fan of the number crunching game in brewing. A welcome outlet for my inner geek.
Note. For accuracy make sure the gravity is measured at the correct sample temp. I'm sure this is something you are already doing but if you are trying to nail down a system flaw it's very important to be as accurate as possible with both volume and gravity measures.
- Easy Volume measures

[*]Correct Gravity Readings