Runs Accounted For

So what exactly are "Runs Accounted For?"

Well, in order to understand Runs Accounted For, first you must understand Runs Produced. If you don't know about RP, the formula is RP=R+RBI-HR. From Wikipedia (yeah I know, but it's a great description):

Runs produced is a baseball statistic that can help estimate the number of runs a hitter contributes to his team. The formula adds together the player's runs and Run batted in, and then subtracts the player's home runs. Home runs are subtracted to compensate for the batter getting credit for both one run and at least one RBI when hitting a home run. Runs produced is a teammate-dependent stat in that it includes Runs and RBIs, which are affected by which batters bat near a player in the batting order. Also, subtracting home runs seems logical from an individual perspective, but on a team level it double-counts runs that are not home runs.

Like a lot of sports stuff, this stat got me thinking. I realized in short (as mentioned in the description) that a 3-run home run actually produces 5 runs. In long, the batter hits a 3-run home run, notching 1 R, 3 RBI, and 1 HR. RP gives him 1+3-1=3. But there are two men on base, each of them score a run (1+0-0=1). 3+1+1=5. As mentioned in the description, it doesn't double count home runs, but it does double count other runs, turning 3 runs into 5. This makes no sense to me, and following in Bill James' footsteps, I sought to fix it.
I finally came up with Runs Accounted For. I wrote up a short description and I present it in a Wikipedia fashion:

Runs Accounted For is similar to Runs Produced except that it does not double count runs. It is a similar figure to basic Runs but allows more credit for those who bat runs in. For instance, a fast lead off hitter will score more often giving them a lot of runs. However, a slow power hitter will accumulate a large number of RBIs but very few runs scored. This stat gives power hitters credit for knocking in the runs and takes runs away from the fast hitter for the runs they scored when the power hitter batted them in. The final formula is simply (R+RBI)/2. If you add up each players RAF, it should equal the entire teams Runs Scored. However, due to unearned runs (usually caused by errors,) an error category is needed because the errors account for a few runs. The players RAF plus the error RAF is always equal to team Runs Scored.

A good example of the above description is Dustin Pedroia and Mike Lowell in 2007. They scored 86 and 79 runs on the season, respectively. However Lowell knocked in 120 compared to Pedroia's 50. This gave Lowell a 50 RP advantage over Pedroia. He accounted for 31.5 runs more than Pedroia as well.

The changes that take place from this formula causes RAF to be equal to runs scored on a team level, but not from an individual standpoint. This way a 3-run home run accounts for, you guessed it, THREE runs. Not five, three. In the case of a 3-run homer, each runner is to account for half of a run each, since they did their part in getting on base in the first place. The batter then accounts for the 2 other half-runs from these players for batting them in. He then receives one more run accounted for for batting himself into score. Basically, in this situation, the batter gets 2 RAF, and each runner receives .5.

I think that is the best I can do to explain it. If anyone has anymore questions, leave a comment anytime during the season, and I will be more than happy to explain why a certain player accounts for a run (or doesn't). I am also including a short FAQ section at the end of this post to hopefully answer just a few more unknowns you may be pondering.

During the season, Joey D and myself (N8Dogg) will be following 2 teams along on our quest to find the true meaning of the RAF statistic. I will be covering my Milwaukee Brewers, and Joey D will take on his home state Detroit Tigers. I am very excited to see where I can take this and I would like to thank Joey D for all the help he has done (and will do) so I can focus better on 2 teams instead of just the one like my original plans called for.

And now for some FAQs:

Why is it possible for a player to account for half a run?
A typical run consists of 2 players, the batter and the batted in. The run should not be solely credited to the batter, nor should the batted in get the full run. They each did half the work to produce the run, therefore they account for half of the run each, totaling one run.

Is it possible for a player to produce the same number of runs as another player yet account for more or less?
It's a complicated answer, but in a word, yes. However, they must play for different teams. If two players play for the same team the following holds true: If you produce more runs, then you must account for more runs*. But since different teams score more or less runs than another, runs produced may account for more or less per team. For example, in 2007, Brewers' Ryan Braun produced 3 fewer runs than Gary Sheffield of the Tigers. However, Braun actually had 3 more RAF than Sheffield.
*The opening series for the Royals resulted in Gordon hitting for 3 RAF and 4 RP, but Grudzielanek had 2.5 RAF and 5 RP. The reason for this is because Gordon hit 2 home runs, therefore those 2 took away from his RP. On a large scale (over the course of the season,) the greater RAF means more RP (on the same team) because it is impossible to hit as many home runs as runs scored.

Is RAF a team stat?
Yes and no. RAF is based off the team's runs scored. However, it is calculated on an individual basis. A team RAF should be exactly equal to the team RS.

Is RAF an estimated stat like Runs Created?
NO!!! I don't want an estimated stat. I want a stat that accurately tells how many runs a player accounted for out of all the runs his team scored. Since all runs scored in a game are accounted for by individuals, no estimation must take place and total RAF of all players on a team equals total runs scored of that same team.

If you have anymore questions or need clarification on anything else, please let me know and I will do my best to answer them for you. Thank you everyone!
--N8DOGG