I've seen Zach Sanders describe our league as a wRC/FIP league, and I think that's a good shorthand description. The scoring system is inspired by one invented by Tom Tango, but there are some key differences that I made that required it to be revised from the ground up (discussed below). Here is the system:
Note that the pitcher points have changed for the 2012 season. Here's a piece I wrote about this, and here's someone else's analysis of the change. For the most part, I want to emphasize that this matters little for pitchers as the season level, but will matter a lot for individual games. Also, I have bumped points for holds to be near-equivalent with saves to give more value to set-up men. It also raises replacement-level for relievers, which has historically been much too low in this league.
You can find a spreadsheet in the Spreadsheets section of our site that shows these points for 2009 players (these do not include the new pitcher scores--look at the article above).
The hitter points are designed to reflect linear weight relationships of each event (like these). Note that "hits" affect multiple point categories. So, a single is an AB + H = +4.6 points. A double is AB + H + 2B = 7.5 points. A player's total points will be roughly equivalent to wRC*10, which you can confirm on Fangraphs. Any discrepancies can be attributed to rounding or slight differences in the linear weights we use. You literally can use wOBA at FanGraphs as a measurement of points per PA in our system. It works really well.
Pitcher points are a bit less grounded, but there are justifications (note: this discussion is somewhat dated; see above):
First, the coefficients are the same as those used in FIP. We do not track earned runs because they a) are subject to luck, and more importantly b) are influenced by the performance of fielders. Using K, BB, and HR, however, do a great job of allowing us to get luck- and fielding-neutral pitching performances. They are NOT park-neutral. But neither are the hitting stats.
Second, innings are given 5 points or ~0.5 runs each. If we are using an absolute baseline (like we are with wRC), then an average pitcher should earn a half-win for each game they play. If 10 runs = 1 win, then a half win is worth 5 runs. 5 runs / 9 innings = 0.55 runs, or ~5 points in our system. Thanks to Michael Jong for this insight.
Saves & Holds are the most controversial categories because they rely so much on manager usage instead of player performance. I personally hate those stats as anything other than historical indications of use. However, including them allows us to have something in our scoring system that reflects the higher leverage that closers and, to a lesser degree, setup guys encounter. Essentially we're giving double credit for each inning in which a closer records a save. It's a very imperfect solution, but until Yahoo starts letting us score with shutdowns & meltdowns, or something else that lets us account for leverage, it's the only way to give appropriate credit to someone like Rivera or Broxton.
A key point about this system is that player scores are almost always positive. Therefore, it is almost always preferable to have someone playing than not playing. There are a lot of sabermetric leagues that are starting to use replacement-level baselines (VORP, WAR, etc) instead of the absolute baseline we're using. This is what Tango's system uses. The problem in that case is that there are a lot of players with negative point values. In such a situation, it is often better to just let an injured player stay in your starting lineup than to start the replacement scrub you can find on the waiver wire. This would be exacerbated in a deep league like ours where the vast majority of full time starters are owned and active. This is why we use absolute runs.
Fun fact: I developed this scoring system for the 2010 season, with small changes for 2011. And then, in the 2011 season, FanGraphs adopted it (minus the holds) as one of their scoring systems! Cool!