When it comes to PvP, more players always makes it easier. Sometimes, that's not a good thing, like when you're specifically trying to fight outnumbered to stretch yourself. But in some situations and against some enemies, it's prudent and useful.
While most people offer the advice to join a player-run corporation so you have a group of people to talk to in game, that advice is usually offered more to ensure long-term engagement than to occupy each play session. The simple fact is, joining a corporation isn't enough. Nor is it enough to have a certain corp size.
The real factor you should be looking for is how many mains your corp has in the same place.
Tamerlane purportedly said, "It is better to be on hand with ten men than absent with ten thousand," and Napoleon preferred to occupy the central position in a battle so he could deploy his full force to any particular part of the battle. Earlier this year, the CFC learned that it wasn't how many characters you had in your coalition, but the effective number you could bring to a battle that mattered.
Community is created by people not only talking together, but doing things in the same area. This is one of the reasons many people will warn new players against joining "jack-of-all-trades" corps that do "industry, mining, PvE, PvP, and incursions". At best, it's a lie. At worst, you aren't joining a corporation, but rather five separate corporations under the same ticker. And that sort of divided attention can really dampen your experience with that corporation. The key to any successful corporation is to have a single staging system, and focusing all corp operations out of that system.
An alliance operates the same way. Pick a single staging system and set the expectation that corporations need to compel their members to base out of that system. Sure, that definitely benefits you when it comes to efficiency. You can mine more, boost indexes, or run more complicated and expensive fleet comps if you can draw more people for your fleets, but that's not the only benefit.
Eve is a game about emergent gameplay, right? Well, emergent gameplay doesn't happen unless you have people to interact with. Allow me to give you an example.
Since about three months after I left the CFC, I would roam through the north hunting ratters. During most of that time, I rarely came across a fight in progress and never saw another corpmate. I collected more than a few killmarks, of course, but roams tended to be hit or miss, depending on whether I caught anyone. Sometimes for a couple unlucky days, I'd spend my time warping from system to system with no real enjoyment to show for it.
You may have heard about NC.'s deployment to attack Tribute, based on the dozens of propaganda posts on Reddit. If you haven't checked them out yet, do so now. This one, in particular, was highly creative to commemorate a Pandemic Horde welp.
But the whole alliance moved, and is now staging out of the same system, close to lots of fertile hunting grounds for whalers. In between large fleets, it's absolutely viable for solo roamers to travel out from KQK and catch a few folks.
For those of you who haven't gone through a hunting ground in both wartime and peacetime, the nature of the space changes dramatically. In peace, carebears fill systems as far as the eye can see, and often your challenge isn't in finding enough targets. The difficulty rests in discerning their location and catching them before they warp off. Often, you'll find a target, only to realize you don't have the dps to break him by yourself - for instance, a Rattlesnake or Thanatos. That's a good problem to have, though; you have people to shoot, if you can demonstrate enough skill to catch them.
On occasion, someone forms a gang to fight back, and you either have to try to split them up or run from them. But more often than not, this doesn't happen, although it is more common now than when the CFC owned the space.
During wartime, the problems are quite a bit different. Most of the systems between you and the enemy have eyes watching them, so you're quickly reported in intel. Very few ratters are bold enough to rat in between two staging systems, so targets are slim, and as you move closer to enemy staging systems, you find response gangs become more frequent and larger.
Nonetheless, there are other targets. Transports supplying the war and people traveling to and from ratting systems are plentiful. Some pilots will bring in their own doctrine ships to avoid the alliance contract markups, and those tend to be easy targets for a solo PvPer. Most doctrine fits, for instance, don't include scrams or warp disruptors, and tend to be weak against either kiting or brawling. The trick here is in being able to slip behind enemy lines to attack them.
Yet, when you're truly on your own, there's only so much you can accomplish. Response gangs won't be gangs, but rather full fleets of a dozen or so pilots (usually with jams and heavy interdictors).
Yesterday, though, I had a different experience. I decided to roam through the warzone in my Stratios to catch anyone I might be able to find. I didn't succeed, but I did land on anoms as a couple pilots warped away to safety. Missed it by that much.
A few jumps in, I see an alliance mate in local... and promptly ignore him. The habits of solo roaming run deep, and I assumed he was just a scout for our FCs. You can imagine, then, how surprised I was to see his Stratios engaging a Svipul he had split up from a couple additional hostiles. I was cloaked and 100 km away, and he seemed to have things well in hand, so I kept cloaked and began moving towards him.
Help arrived, and just as I was about to decloak, he warped off to safety. Naturally, we convo'd and fleeted each other up, and started going after the targets together. Fits were shared, situations were updated, and we tried to bait them out into another fight. At the time, the CO2 pilots didn't know what ship I was in, so we figured there was a chance they'd assume I was his eyes and not really a threat. And, indeed, CO2 and my alliance mate sparred a bit.
Consider what might have happened. Easily, CO2 might have decided to engage him, and another Stratios would have doubled our neuting and dps capability. Working together, we could have taken down more targets than either of us could alone, even by combining our totals. We might have been able to take down a rattlesnake in Tribute, for instance, but could only take down an Ishtar each if he was in Venal and I was in Fade.
In the end, I didn't score any kills (though he killed a couple small ships before my time). Nonetheless, the mere presence of that pilot from my alliance doing the same thing I was doing in the same area was enough for me to really enjoy myself. I had more fun, even though I didn't get any kills, than I would have on my own. Meeting up and cooperating with my alliance mate turned that solo activity into an engaging, interactive one. That fact alone justified the time spent.
That wouldn't have happened without us both basing ourselves out of the same system. That simple operational expectation placed on us by our alliance and corp leadership created that piece of emergent content. The really interesting part? Leadership enabled that while they were logged off, blissfully unaware and living their lives. They didn't need to find an FC, scouts, and a titan bridge. They didn't need to call a CTA or employ our Jabber services. They didn't need to scream for "more dudes" in local. They just had to get us in the same system and we handled the rest.
That's the real value of a player corporation. It isn't just corp chat, but rather the practical effects of having all your members in one location, doing things in close proximity, that generates culture, camaraderie, content, and cohesion. Sometimes, it's not the scripted, scheduled events that a corp provides that provides the value of a corp. Rather, that fill-in content can sometimes be more thrilling and satisfy us longer.
That's something to keep in mind if you're starting a corp, trying to resuscitate one, or looking to join one. It's not numbers or skill level that really matters, but rather the degree to which the group works together in a single location. Yes, it tends to limit a corporation to a single or a couple areas of focus, but in the end, this is a good thing. The corp that tries to do everything ends up doing nothing very well.