It depends on what you consider to be a 'large event'.
The way I have seen airsoft is as a form of 'scenario walkon'
I began playing paintball just in time for the hey day of scenario paintball with events typically being run by players for players at their local site, these were generally one scenario event per month at various parts of the UK, these varied in scale and there were a very few 'big games'
For the past few years things contracted in size. There was an organiser that tried to monopolise and take over the world, but went from well run games to overly hyped games, and with the recession people began to be more careful with how they spent their disposable income, most likely to be playing walk-ons locally and only travel to whats really worth it.
There are special cases such as hiring active Army training sites, that is novel at first but still needs a good quality organiser capable of keeping it fresh (let alone be able to take the financial risk of booking such a site and hoping people turn up or that you don't have your booking cancelled for Defence priorities)
We have had great paintball events on such sites, but other than Swynnerton have only been able to do so with specialist clear paint, and these sites are 'easier' to book for airsoft as the mess just needs to be swept away rather than cleaned away.
There two paintball big games that now also run airsoft alongside. Paintfest / airfest by NPF and North Vs South by Warped.
They are well established organisers with Paintfest having run for 10 years. The site NPF ran the first Hyperball tournament in the world in 1996, and the owner Ged Green has been running things since paintball came to the UK in the mid 80s. He is also responsible for how modern tournament paintball is run having taught the Americans how to do it at Huntingdon Beach in 2003.
They have had airsoft on site for many years and added airfest alongside Paintfest two years ago.
Warped have been running North vs South at Swynnerton since approx 2008/2009?, and elsewhere for years before.
To run paintball on an Army site though Swynnerton is more 'rough' a training area than Copehill etc they have to take over the site in advance to set up and keep on site during the week after to fully clean up.
I'm one of those people who looked at other organisers and thought that I could do that too. It's far from easy, and we run events in other peoples sites, and collaborated with other organisers. We have run large and small games - hundreds of people and 6 to 8 people (the 6-8 were 'special experiences' with one-to-one.
There are people that I would trust and wouldn't trust to run different types and scales of events (and there are things that I would not be happy about committing us to do)
I've seen events go horribly wrong, with the ways those were managed being handled very differently. One event destroyed a brand new group of organisers, their team and friendships. A lot of money disappeared. With pure luck there were no injuries resulting to very dangerous circumstances
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Then for big events were you use multiple or even all the game sites. You can hire in marshals and game leads for just those events instead of having them on staff all year round.
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This is a pretty spot on description of scenario paintball events.
The other issue is that 'normal marshals' may not be able to manage large rolling games as opposed to standard short games/skirmishes. But that comes with experience.
We have run most of our games opening up the entire site, which changes the dynamics of a sites designed game zones, and often used site staff as the 'safety marshalls' and ourselves as 'event marshalls'