Alright, I got a spare minute to answer this question. You've got me curious, so I'm gonna try really hard to do this justice. I love stats, so I hope you're excited; Fizz on a tangent is quite the sight to behold as you'd all know. ;)
I did some trawling through the Wayback Machine for the stats you'll find below. The archive doesn't have recordings of PokeBase's main page for 1 Jan each year, but has something close enough for each. As such these figures are not 100% accurate, but perfectly fine as an estimate. I decided to include questions and answers as part of the graph as well as users, which has turned out to be very interesting.
2010's stats were harder than others to ascertain, as there were no stats on the front page for that year. The stats for questions and users will be accurate for that year, as there were lists of both you could use to find the exact quantities, i.e. checking how many 20-question-long pages there were on 1 Jan 2011. No such thing existed for answers though, so I've made an educated guess of about 6,500.
This also includes provisional statistics for 2018 (i.e. 1 Jan 2019). As the year is not yet complete we do not have exact numbers, but with over 300 days of the year gone, we can calculate averages that will give good estimates.
Final note: this graph is not cumulative. It shows how many new users, questions and answers were added per year, not how many there were in total. But with all that aside...
Pretty interesting! Here are a few observations:
The short answer to your question is 2014 had the most new users, followed by 2013 and then daylight. However, 2014 also recorded a massive drop in new questions and answers. Very strange!
This graph basically affirms popular opinion among us old codgers that '12, '13 and '14 were the glory years for this community. However, with a smaller community, '16, '17 and '18 have been pleasingly stable.
The ratio of both questions to users and answers to users was above one for three years, before the whole thing flipped on its head to favour users quite significantly. 2015 was quite anomalous though.
Dividing these annualised stats by 365 shows how many posts we could expect in an average day on the site each year. On average, 24 new questions were posted per day in 2013, compared to only six in 2018.
We've had less new questions and answers than 2010 for three years in a row. However, we still get more new users per year than in 2012. Our decline in activity isn't based on a lack of personnel!
So let's not beat around the bush: we're a whole lot smaller than we were several years ago. Why is that? There are a few explanations that could be offered here:
I'd say this community rode the X and Y hype hard. Really hard. A late 2013 release of a major title would certainly generate interest in '13 and '14, and that's exactly what we see in these user stats.
The drop in answers compared to users (and more recently, compared to questions) could be explained by our moveset threads. Those filled up in our early days; their influence would be felt less today.
Every passing year makes it harder to post a question that isn't a duplicate. Inherently, the potential amount of questions that could be added each year is lower. We manage pretty well considering.
Pokemon has been slow to embrace the Nintendo Switch, which I think has limited 2017 and 2018 considerably. 2019 will be interesting with Let's Go, and also main series games releasing.
These days I think a lot of people would rather use social media to discuss video games than an internet forum. Being a Q&A makes us even more niche, though that has its upsides too.
I'm going to stop now. I hope you enjoyed reading this! It was fun to unpack it all.
