Let's go at this from another angle:
Fact 1: Changing developing time will affect film speed. Longer development times result in faster effective film speeds (E.I. = exposure index); shorter times result in a slower E.I. all other things being equal.
Therefore, it is possible that if you are using box speed but underdeveloping you will get underexposed negatives.
Fact 2: The term "pushing" for film exists. It is commonly understood to be, "intentionally underexposing film and adding extra development time to compensate."
The extra development time used in pushing increases the contrast thereby resulting in a more printable negative. It also (according to Fact 1 above) slightly increases the the E.I. of the film, which to a small extent will ameliorate the underexposure. However, the amount of the speed increase is usually in the fractions of a stop faster, and doesn't completely balance out the intentional underexposure. Pushed negatives exhibit loss of shadow detail and increased contrast by definition.
Let's use these facts to answer the OP's questions and analyze the situation:
Does the "1/2 box speed + 25% less development time" translate over to pushing also?
First, the answer: No, this is not pushing, by definition (see above).
Qualification: 25% less development than what? Than your time for "normally exposed and well developed negatives"? This is what I would assume you mean and what would result in underexposed and too-thin negatives. To push, you accept the loss of shadow detail and develop enough more to get the highlights to the place they would have been if normally exposed and developed.
So...let me ask.
Normally, I've been finding out that based on setting my camera at box speed, I underexpose HP-5+ about a stop, and my negs suffer. So the solution is to preset in an "error factor" that counteracts that by setting my ISO to 200 and thus with my usual exposure method, and usual camera combo...I end up with well exposed negs. But....what about pushing where you are intentionally underexposing and then over developing? Is it possible to do the same?
Not sure what you're asking here: If it's, "is it possible to push film by exposing the film at half of the E.I. that I really want to push it to?" then the question doesn't really make any sense. Pushing is an artificial construct to compensate for underexposure and the resulting loss of overall negative contrast. If you get usable negs by exposing at E.I. 800 and thinking E.I. 1600 at your development time, then, fine, but you're really not thinking about this clearly then.
As for using less than box speed for "normal" negatives, you're in good company. Many do this for a couple of reasons. It builds in a one-stop safety factor for underexposure, it gives a longer-scale negative, it overexposes a bit giving more printable highlights at a too-short development time, etc.
Let's look at this a little closer: When people say to me, "I'm using box speed but my negatives are underexposed" I often recommend exposing more. However, there is also the possibility that the "normal" development time is simply too short. Often just increasing development time solves the problem alone. In other words, the exposure/development system has to be balanced using both variables, exposure to get good shadows, development to get good highlights. Given also that underdevelopment is often mistaken for underexposure and I'm skeptical anytime someone says their negs at box speed are severely underexposed.
Conclusions: Pushing as commonly understood will slightly increase the film's E.I. Underexposing and underdeveloping is not pushing. Pushing is underexposing and developing enough to get printable highlights, which should be more development than needed to get printable highlights for normally exposed negs. What E.I. you use pushing is arbitrary if you get the results you want; it's just an artificial construct to guide you in the right amount of underexposure and overdevelopment to get the results you want. Using less that box speed for "normal" is common because many like the longer-scale negative and/or the look achieved plus the safety factor against underexposure.
Best,
Doremus
) this really has nothing to do with the film's ISO speed. We live with underexposure and make the best of a bad situation when pushing. It has a certain look than many like and for that reason has a life of its own as an expressive approach. Pulling is a down-and-dirty way to get a long-scale neg and tame contrast a bit without taking the time to learn one of the more-complicated exposure and development systems (BZTS, Zone System, etc.).
