66% total efficiency.
15.75lb of grain
crushed the grain at .035mm
5.25 gal of water and mashed at 153 for 60 mins. (stirred really well)
3.25 gals of wort for 1st runoff. 1.069 gravity
sparged with 3.30 gal of 180 water. temp in mash was 160. sparged for 10 mins then drained into brew kettle.
2nd runnings 1.036
boiled 60 mins at end of boil had
5.5 gal wort into fermenter. 1.065 gravity.
shooting for a starting gravity of around 1.073 which would of got me 72% efficiency.
A couple of quick things first,
What was the makeup of the grain? You said it had rye but how much and what other specialty grains? Rye has a max yeild of 63% while two row is closer to 80%. If the grist was 40-50% rye this makes a huge difference.
What temperature was the water/wort when your took the volume measurements? Boiling water is 4% larger than water at room temperature. That can have an effect on your measurements.
You said you use a refractometer, have you done side by side tests with a hydrometer to find your specific correction factor? see
Here and
Here for details.
All of that aside, your main issue seems to be one of conversion. Your mash thickness was 1.33qt/lb (21qt/15.75lbs) which should give you a first runnings of about 1.089 where as you got 1069. SO your conversion efficiency was only 74%. Conversion should be close to 100% and anything lower than 90% demonstrates a problem in your process.
There are several things that can affect this. As has already been mentioned several times, grain crush has a big impact here and may be your issue. I crush my grain at the LHBS and have no issues, so sometimes i think people point to crush only when other issues may be the problem, they include:
1. Mash Temperature: What kind of thermometer are you using and when was it last calibrated? Do you check the temperature in several places in the mash? Too low a temperature (below 150*F) can have an effect on conversion.
2. pH: I know little about this and can't really direct you on how to deal with it if this is your problem (But it is likely not the issue many people, including me, get efficiency in the 80s without adjusting or checking pH).
3. Time: lower temperature mashes take longer to convert. If your thermometer was off, you might not have gotten full conversion because you ended the mash before it was done. This might be the case becuase your second running were 1.036, while the expected runnings at 74% conversion would have been about 1.030. So you had some additional conversion during the sparge. Often lower temperature mashes (<154*F) are held for longer (90+ minutes) to allow for full conversion. Bud Light is mashed for 3 hours!
4. Mash Intensity: You do a single infusion and didn't mention stirring during the mash, so you have a very low intensity mash. This could mean you are not getting full conversion because the grain is not getting fully saturated with liquid. Stirring part way through the mash may help you reach full conversion (however I don't stir) Strike temperature has an effect here too. It is possible that you mash in with water so hot (to preheat the tun) that the first grains added to the mash water are being denatured before they can convert. I would only consider this if your strike temp is more than 10* higher than your desired mash temperature.
5. Mash Out: Adding an infusion of hot water at the end of the mash may help you finish conversion by bringing the mash into the range for alpha amylase (158-167*F). This may help convert fully, since you saw further conversion during your sparge.
6. Mash Thickness: 1.33qt/lb is not super thick, but you could go thinner to allow the mash more movement. Conversion gets easier the thinner the mash up to 2.5qt/lb. I normally mash at 1.5qt/lb. Increasing your mash liquid would increase conversion, but might have a negative effect on the launter efficiency due to less sparge water. Often people shoot for equal runoffs from the first and second runnings, but the first runnings are of higher quality (why people do no sparge sometimes) so equal running are not necessarily desirable to make good beer.
7. Dough Balls: Dough balls are much more likely to occur when you are adding the grain to the liquid at higher temperatures. You are infusion mashing so you don't have this option, but adding the grains to water at a temperature below 140*F will not have dough balls. For your system, you have to make sure you stir like crazy. (You said you did, but more stirring doesn't hurt) I have seen Yooper say " stir like it owes you money" this is a good thought for both mashing in and before your batch sparge.
Doing the math on your first and second runnings I come up with a preboil of 6.55 gallon and 1.052 gravity. This gives you a lauter efficiency of 80% which is good for batch sparging. You could increase this by switching to two sparges or collecting more liquid and boiling longer, but I think your issues lie in the conversion and trying to get a better lauter is chasing the wrong issue.
You have virtually no kettle losses, so I would guess you pour the wort into the fermenter. No issues there.
So short answer, fix your conversion and you will jump to 75-80% efficiency. I think the first places to look (other than grain crush mentioned by others) is your temperature, mash thickness, and stirring.