I thought this was a nice analysis. Not too surprising to see that PIO check/raises less with OESD, and more so with weak draws.

3for3 said
This one didn't get past the flop.  I defended BB with 86hh against a cutoff opener in a $100 local event.  Most players at this level don't 'steal' enough from this spot, so I gave Villain a range that might look more like a lojack range for the rest of the world.

With an SPR of 12, we see a flop of 9s7s3d.  Villain bet .7pot, I check raised to 3x, Villain gave it a long look and folded.

I would like to point out villains c-bet sizing. Villain, or anyone in this spot, would benefit more from choosing a smaller sizing, or just checking back. If villain had cbet .3%, he could have gotten away a lot cheaper and saved himself some chips or felt more comfortable calling your c/r IP. And since he didn't call your c/r, it's likely he had complete air and/or the pot was getting to big to justify calling with two over cards. So he should have just checked back in that case, or used a different sizing.

With an SPR of 12, we see a flop of 9s7s3d.  Villain bet .7pot, I check raised to 3x, Villain gave it a long look and folded.

This seemed like a routine hand at the time, but I took a look anyway.  One thing I did want to see was what kind of sizing PIO would use for its check raise.  I default to ~3x (used that exact size here).  I gave it 3 sizes; 2.5x, 4x and 5.5x.  I also ran 2 sims; one with PIO betting its usual range for 1/3 and 2/3 pot; one where I forced Villain to bet.  Once again, this is a strong field tendency, Villain's cbet close to 100% of the time on all but the wettest boards.

When I forced it to bet, PIO check raised my range about 24% of the time, mostly using 2.5x.  I suspect if I run it again with only 3x for check raising size, my ev won't change.

The first thing I always check is what my hand does; PIO does check raise, but not routinely, only about 1/4 of the time.  It never folds (duh).  

What hands does it check raise the most?  Well, this is where I learned something new.  It prefers to check raise more often with weaker draws than an open ended straight.  It uses gut shots like 85s about as often as it uses open ended straight draws.  It also loves to check raise the naked As, especially as the kicker gets smaller.  

How should Villain defend my check raise?  It only folds 1/4 of the time.  It never folds a hand as strong as 66, and usually calls at least with any pair.  Here, I think we can see another 'player pool' leak.  Would most of us call a check raise here with a small pair that bet the flop?  It even calls hands as weak QTs.  There is just no way that is what Villains do.   

Which, of course makes our check raise more profitable with draws; we are folding out hands that are ahead of ours with that PIO is calling.