I've been studying/reviewing push fold charts and found a very good one on Jonathan Little Poker, since it provides optimal ranges for stacks from 1 BB to 15 BB, showing the different ranges based on position for each stack size.

I spotted one very interesting and surprising thing -- above 1 BB and below 5 BBs ranges actually tighten in the BTN and CO. For example, at 2 BBs push ranges are 100% in SB and 90% in all positions except for CO (84.3%) and BU (72.2%). That pattern holds for 3 BB and 4 BB stacks (with the ranges obviously tightening with each BB added).

Does anyone have a theory as to why this is so?

At first, I thought it was because callers will be wider when the raise comes from CO and BU. But this doesn't make sense for two reasons: (1) a GTO analysis would already factor in optimal call frequency assuming optimal shove frequency, and (2) once stacks get larger than 4 BBs the pattern reverses and CO and BU have wider shove ranges, even though the logic of those positions being called lighter should not change.

My second theory is that the CO and BTN are further from having to post the blinds and can therefore be a little more selective with such a tiny stack. The problem with this theory though is that earlier position raises will have to get through more potential callers that have a big equity advantage.

Any other ideas as to why this is so?

With < 5 bb's BB is going to call most of the time if you are raising from CO & BTN. They will expect just about ATC shoving.

So with < 5 bb's its better to raise with a stronger hand since we have so little FE.

Also, the earlier we raise, the stronger the hand others need to call. Because they will then be worried about the number of people who can re-raise behind.

And as you point out the closer we are to the blinds the fewer opportunities to get a decent hand.

But if this is a GTO chart, then it assumes players are making non-exploitable optimal calls on BB, and BB would do so knowing that your GTO shove range actually tightens on the CO and BU. Then shouldn't BBs range also tighten under the chart/GTO? I agree that this isn't the case in practice -- but it appears this is really because players aren't playing perfect GTO.

At 4 bb's we are getting basically 2:1 odds when calling. In the BB I don't even look at my cards in these spots.

Once I turned over AA.

Once I turned over 72o. I flopped a 7 and the guy's girlfriend started chastising me from the rail. He turned a pair at which point she started mocking me and my stupidity. Then I rivered a 2. He had to stop her from committing assault and battery.

I'm guessing that they are picking 72% because they will fare somewhat better than ATC. And they can do the ATC on a later hand if they hit the BB.

We only need to win one out of three times to break even.

But if you have that mindset to call ATC from the BB a 4 or less bb shove, does it matter what position the jam comes from?

Also if BB is going to call ATC, we should shove ATC -- that's clearly +cEV when you factor in the SB and antes -- unless there are ICM implications. Maybe, then, the differing percentages are the chance BU or SB calls when you make the shove from CO, and SB calls when you make the call from BU?

Also, in the real world the stack sizes behind the short stack should matter. Monster stacks and micro stacks (on BB) are probably going to snap you off with ATC, but stacks with around 10 bbs or so may be more reluctant to put in almost 1/2 their chips with ATC if they think they have the chips to wait for a better spot.

In the end, I think the tighter ranges for CO and BU here really do have to do with the fact that BU and CO have more opportunities to wait for better equity hands than positions closer to BB.

edit: I don't think so. The overlay we are getting makes it a +EV call even if they are only jamming 72% from the BTN

We are already shoving 72% of our hands. It is the bottom 28% at issue. And our survival rate will be 28% on average. We will have the same chip overlay when we jam from an earlier position but at least we should have a much better hand.
This could be a good point for BB. If BB has like 5-7 bb they may mistakenly fold if they also have a bad hand. But at 10 bb's it has to be an auto call.
This I agree with!