Are you letting them crossface you? If they crossface you they can use that for leverage to sprawl. If they aren't crossfacing they have nothing to post against to sprawl, unless they have a wizzer.
If the guy on top in the picture had his left arm crossfacing bottom, he would be able to sprawl.
Being cross faced sucks, no doubt about it.
The half guard is something I've been really working on because at first I would try it and even though I knew to never be flat on my back and have the near side underhook. I couldn't stop from being flattened it was miserable! Even when I had the underhook some guys that were good or big or both, would keep me flat regardless of the underhook.
So I kept working on it and asking my instructor about it.
Here's a few things I wanted to share that's been really working for me:
1) Brushing the hair
This is when you do the motion that those "cool" fonzie lookin guys with the leather jackets in movies do. (lol i know) Of course prevention is key to anything bad happening to you in BJJ but you can't always "prevent" something for whatever reason. So when I feel a cross face coming I take my arm that's not trying to get the underhook and "brush my hair". If you guys can picture it, it looks like you are doing just that as it guides the top man's cross facing arm over. It's mostly about timing.
2) Grappler's Sit up
I recall watching a half guard sweep video with this guy in an orange shirt teaching it. I recall I believe Frodo saying he was in the video or that was his instructor. The guy basically showed the move and showed himself doing a situp. He crunched his knees into his stomach causing him to ball up and he shot but his arms up. The arms look like what people do when they shrug their shoulders and doing an "I Don't Know" pose, BUT when you do it, you throw your arms/hands way past the line of your shoulder to really throw his weight up and over your head. This will cause him to do the "superman" pose and post his weight on both his extended arms. You can now just simply go under him with ease at this point. Also note you can take out your underhook arm and "traffic cop" or stiff arm him at the ribs to keep him away if needed.
3) Long Distance Half Guard
Ok, so far I've covered the grapplers sit up and the brushing of the hair. The long distance half guard has been working excellent for me. If I feel like he is putting his weight on me and my arms aren't in correct posture. (Near side arm across my belly ready to underhook, Other arm ready to make a "paw" to block crossface) I will post both my arms out to check his shoulders and get my knee between us. This will give me time to recompose myself to play the half guard. I usually do this off a takedown that he gets on me so as he lands he won't be in correct posture since his weight isn't able to help him due to my knee holding it off. Also, I can grab his near side arm and look for the arm drag to the back or if I see it, attempt to kimura his other arm which leads me to #4.
4) Kimura
Yep, an actual submission to help out here. Usually, I will not get the submission unless I surprise him or if he's less skilled or what not. However, in order for him to counter the kimura he must posture up to try and straighten and pull his arm out. If he does this, I maintain the figure 4 grip and do a hip escape and throw my hips over right into a belly down armbar. Another thing he will do is try to "re-kimura" you. He can clasp both his hands and force your arms up. If you do not let go you will be kimura'd. So if he does this, his arms fly upwards which means it's a perfect time for me to simutaneously shoot for the underhook and/or shoot my other arm under his legs and throw myself under him. If this doesn't work for whatever reason. I will push him away. (If I feel him beating me and his weight coming)
So then I can throw in my knee for long distance half guard and play from there. (Look for Kimura again, arm drag, try to shoot back quickly, etc)
5) Double Paw Grip
I saw this in this super long half guard instructional that's like an hour and a half from some guys name Indrek Reiland and Jorge Matsi from SBG. Aesopian wrote about double paw gripping as well. I feel much safer vs the crossface using this. I will use it when I find he's giving me a hard time with getting the underhook, or I will just take my underhooking arm out if I feel I am about to lose it and reinforcement the other arm blocking the cross face. Also if I double paw I can use my top arm's elbow to push it into his throat/face/chest to create space and get the underhook back OR use it like Zankou says and throw his cross facing arm over your head. It's easier cause you got 2 on 1 right? Once you can throw it over, dive under him. It's timing, as he tries to cross face you, throwing both arms into double paw allows you to throw the arm in motion over your head much easier. If you can't throw it over your head try pressing his arm towards his body and since both arms are near, you can try #4 and kimura him from there. Another thing I've found with double paw is I can just take the arm back and underhook again if I feel the opportunity presents itself. One neat little trick that's more cool but somewhat practical is I will double paw him and I will push his cross facing arm up high. If I can keep it there and pummel for the underhook I will pass his cross facing arm off over his back and into my hand that's underhook. Can you picture it? Thumbless grip of course, then I will have a lot more leverage to roll him over me. (Plan B lookin sweep) I haven't tried that one much just saw it today, can't wait till tomorrow to field test it!
6) Using your whole body, "see sawing", etc
I'm not sure if this should have it's own section but oh well. This is rather obvious but use your whole body in combination with one another. That means you will crunch your knee's into your body as you turn onto your side. He will cross face or what not and as you crunch up use the "brush your hair" technique. The first time I asked my main instructor how to play half guard he said "You gotta go one way and when he commits his weight the other way, go with it and etc". That didn't make sense to my 2 month white belt newbness at the time, but now it's so key to the half guard game in general. What I notice is people don't really combo things up cause they are so fixated on one technique.
For example, tonight I saw one of my buddies who's really gettin into half guard roll with a big strong wrestler. He had the underhook and was on his side, all good right? Yes and no, yes because he had correct posture and no because the next thing he did was just lay there and try to reach for the guys foot and go for the old school sweep. The wrestler just kept powering his foot out. He tried it like 6 times, then it clicked and as the wrestler straightened his leg out my buddy went for the Plan B sweep and dove under the guy and cupped his knee and rolled hard the other way and got on top.
Basically, he was just using 1 arm vs the guys weight and leg strength. Then he realized, he would combo it up and use his hips and whole body. This makes me think about when I first heard people say Jiu Jitsu's all in the hips and if you go vs someone good, you have to combo attacks and/or utilize setups. It's all in the hips came to mind because sometimes we forget how to do certain things and neglect small details like...well moving your hips. Just like with a kimura if someone grips hard pull the kimura'd him close to your body and pull and turn with your HIPS. I always see people using pure arm strength and not getting it. Also with the combos and setups statement. Well, he was so set on the old school he forgot about plan B so...
In conclusion what im saying is just practice these a bit, combo them up. If your opponent is worried about one thing go for another. I know I'm just preaching to the choir here but it's very crucial that you combo up your techniques for maximum efficiency..
Anyways, it's late and I'm tired and I gotta be at the gym at 8 in the morning. Hope this was some help in some way!