What This Is
This is a many entries long project to crunch some numbers about the show. Like numbers? Empirical data? Statistics? You're gonna dig this.
Because I'm an insane fan, I did a line and scene count of each episode, put out season-by-season summaries, then played with the numbers to try to find meaning. In particular, I started out interested in the trends revolving around Spike's character (testing the oft-repeated claim that he took over the show). However, my interest grew more general as the project went on. In addition to counting lines and scenes, I kept track of how many times characters were referred to by other characters. Doing so revealed interesting patterns not apparent in the line/scene counts.
There are several notable drawbacks to this study. For one, line and scene counts don't necessarily correlate to importance or focus (hence why some odd episodes end up in a character's significant and/or centric pile). These counts aren't meant to measure anything except what they say: The number of lines or scenes a character has in an episode. Interpretation from there is up in the air. I chose this method in an effort to avoid more subjective forms of measurement which are vulnerable to bias and perception flaws. Line and scene counts - as well as references - are hard, objective measurements.
Another drawback is that different people authored the transcriptions as the series aired. As such, some transcripts have different styles, as it were. One transcriber may be more prone to breaking up a character's dialogue with action markers while another just plops the whole speech down. This would mean that a character ends up with more lines in the former than in the latter. Given this, raw numbers aren't useful for comparing across seasons (rendering the line:scene ratio useful only within seasons). Percentages give a much more accurate picture when looking at cross-season comparisons.
Your graphs are shoddy and your number-taking skills questionable
Yeah, I'm an amateur. It probably shows. Take this for what it is: An immense project undertaken by one person with no experience doing such a project. Mistakes have probably been made. I got a bit tired during all the graph-making and snoozed a bit. I tried to be as rigorous as possible, but, you know, I'm human. We all fuck up. If you think you can do better, I encourage you to do so. It's a difficult, though ultimately rewarding, challenge.
I'd Like to Expand on What You've Done
Feel free! All the numbers are freely available in a text file in the season overviews. Do with it what you will. I don't own numbers.
Where Do I Start?
It's best to read this as I posted it, starting with the season overviews, moving on to the character break-downs, then ending with the final cross-season analysis. The methodology is outlined (and further defined) in each season overview, and a lot of terminology begins to become assumed as the series goes on. Still, if you're feeling adventurous, start wherever you want. I'm going to list the links in their best-read order, though.
All the Seasons!