The rules changed. That was the dominant factor! Whether new tricks were developed, is harder to ascertain!
None of the poll options are satisfactory for me. The first and third options don't work because boxing technique adapted to a different set of rules. That isn't progress, just adaptation to another environment. The second option doesn't work, because there's no link between ancient "boxing" and the English sport that became modern boxing. 1) I base my opinion on the fact that boxing was a bareknuckle professional sport for 200 years. Even a community of blitheringly stupid, slow-learning professionals are going to figure out how to fistfight within the rules of the day if you give them two centuries. 2) I additionally base my opinion on the fact that boxing technique in the late 18th and early 19th century manuals looks more modern than boxing technique in 1890. If you believe that late 19th century technique was awful under its own rules, then why would boxing evolution move TOWARD worse technique? Makes no sense to me. 3) Finally, some modern historical martial artists have experimented with the older stuff and believe it makes sense with small or nonexistent gloves. This is by far the least persuasive evidence, in my opinion, because the modern reconstructionists are hobbyists rather than combat sport athletes. EDIT: And implicit in my points is this: when you change the rules, you expect the style to change as well. I can support this assumption with numerous examples from all sorts of combat sports.
In answer to the main question, technique improved a lot from 1890 to 1915-20, not so much afterward. Most relevant, I think is Mike Gibbons' "How to Box" volume, also his work in the film of his fight with Packey McFarland. I think Langford also shows particularly well early on. Modern conditioning has improved in all sports, though I think boxing was ahead of its time compared to other sports until relatively recent history.
I think there was progress 1880-1900, but a big part is there had been regression leading up to 1880, and large rule changes around this time. We have so little from this period it's hard to assess how much progress there's been, but I'm not convinced there's that much progress beyond this time. If there was much, it's hard to account for old past it fighters keeping having success against younger and allegedly more evolved fighters. I think a sport with a large body of professionals adapts pretty quick, and they weren't starting from scratch either, just adapting, while coming out of a really poor period.
@cross_trainer If there is indeed no lineage from ancient boxing to early modern, which is possible, but I don't think is settled, modern boxing was probably still influenced by ancient sources, which people seemed pretty aware of around that time, and going to ancient sources was happening a lot at that time and before.
with each adaptation of boxing, each change, the most evolved boxers responded by using that to their advantage, or being replaced by those that did, and those that used the ways that didnt fit the new environment didnt prosper so well. this is the evolution of boxing, and of anything. Alis flicked jab, so potent in the 70s, might well have been ridiculed in the 1870s.
I'm going more by the manuals, and I don't think combinations beyond the 1-2 were used much under LPR, which the old style was built around. IIRC, the older fight reports in Boxiana and Pugilistica sometimes refer to rapid sequences of blows, etc., so I'm sure combinations did appear from time to time. On film, guys like Corbett and Fitzsimmons don't look like they throw as many combinations as their successors, and they're at the end of the line for the older style. So that's consistent. I think most of it had to do with the clinch rules. You don't get as much time for combination punching when the other guy can close the range and headlock you while hitting you.
I don't have any problem with lineage existing; I just think it needs to be established with very good evidence. As far as ancient sources go -- There are certainly plenty of Classical allusions in Boxiana and Pugilistica that I remember (it's been a while). That was typical of educated people of the time. Do we have evidence of direct influence on boxing trainers, though? And what would the influence be?
Honestly the evidence I've found so far isn't great, it's just my assessment of what's likely. There was a lot of manuscripts going around at the time on ancient writings. Boxing seems to be an understood concept before when we know it was happening. There was the Cotswolds Olimpicks, which started a bit before we know of boxing, and that wasn't exactly a highbrow affair either. The extent of influence is hard to say. Probably the thing to do is try and find contemporary works on ancient boxing, and see if any technique could be derived. I don't think we should require that much evidence for continuity, because I don't think we'd expect to see much.