When Blez asked me to write something for the front page, the first thing I said to him was, "How much money is involved?"  When he told me "zero," I knew immediately that I was getting a good deal.

(Tip number one for aspiring writers: be self-effacing, it helps you connect to you readers, who are invariably dumber than you.  Otherwise, you'd be reading what they write.)

Okay, imagine you've just landed from another planet, and you ask the leaders of Earth to describe the most popular game on the planet.  After watching five minutes of soccer, you destroy the television set with your death ray and ask for for the greatest game on the planet, rather than the most popular.

(Tip number two: extended metaphors are best used generously, with tortuous logic, since it helps clarify your point.)

A-ha, says your human host.  That game is baseball.  What is the object of baseball?  The object of baseball is to score more runs than the other team.

So, you say, how do you earthlings measure the contributions of the individual toward the team scoring runs?

Your human host goes on to explain that one looks at things like the ratio of times a hitter reaches base to the times he comes to the plate (on-base percentage); the ratio of his hits to the number of times he comes to the plate, except for some reason discounting the times he came to the plate and walked (batting average); the ratio of total bases gained to the number of times he comes to the plate, but counting a walk as neither a base gained nor a time he came to the plate (slugging average); sometimes the first and third measure are added together for no good reason, and so on.

WTF?  Your hyper-advanced alien brain thought the object of the game was to score runs?  Why do earthlings have such funny measurements of individual offensive performance?

Screw it, you say, and you use your death ray to blow the whole damn construct up and start over again.  That's right, we're going to look at baseball statistics from scratch.

The first thing to do is to understand the currency of the individual baseball game.  That currency is runs.  Runs matter - not OBP, not SLG, not AVG, not small-ball, not big-ball, not Schweddy balls.  Runs.  That is the only thing that matters.

So, you enslave the smartest members of the human population and set them to understanding how individual offensive events - outs, singles, home runs, etc - affect run scoring.  They spare you the gory details, but give you the basic concept:

1. Find every situation where there is 0 out and nobody on base.  Determine how many runs the average team scores from that situation.
2. Repeat for 1 out, nobody on; 2 out, nobody on; 0 out, man on first, etc.  There are 24 such base/out situations, and the results are summarized in the following table.

         0 out  1 out   2 out
Empty    0.555  0.297   0.117
1nd      0.953  0.573   0.251
2nd      1.189  0.725   0.344
3rd      1.482  0.983   0.387
1st,2nd  1.573  0.971   0.466
1st,3rd  1.904  1.243   0.538
2nd,3rd  2.052  1.467   0.634
Loaded   2.417  1.65    0.815

So, if a team has a man on 2nd with 1 out, they will, on average score  0.725 runs.  Bases loaded, two out results in 0.815 runs on average. [EDIT: per mdl's request, I am clarifying - this is the number of runs that a team would score before a third out ends the inning.]

3. Find every single that was hit in every game, and determine what the added run value was.  So, for example, if a single was hit with nobody on and 0 out, the run expectancy goes from 0.555 to 0.953.  That's .398 runs added.  If you do this for every single hit in every game, and divide by the total number of singles, you will get the average run value of a single.  Your enslaved army of human computers give you this average run value for every single offensive event as follows:

Event    Run Value
Single   +0.47
Double   +0.78
Triple   +1.09
Dinger   +1.40
Walk/HBP +0.33
Steal    +0.30 +0.175
Caught   -0.60 -0.467
Outs     -0.09
(UPDATE: see erratum)

4. To figure out the number of runs a player contributes to his team, simply multiply the number of singles he hits by 0.47, doubles by 0.78, etc.  That is:
Runs = .47*(singles)+.78*(doubles)+1.09*(triples)+1.04*(homers)+0.33*(walk+HBP)+0.30*(stolen bases)-0.60*(caught stealing)-0.09*(outs)

You are so pleased that you decide to dine on the brains of the shortest human slave, which is a great honor on the planet you come from.

(Tip number three: cannibalism jokes allow you to connect to an important niche audience.)

That's it.  No batting average, no OPS, nothing like that.  Just runs.

Does this really work?  To test the numbers, you run it against the aggregate team stats from last year.

Team   Actual Runs   Predicted Runs
NYY     968          944
DET     887          881
BOS     867          898
LAA     822          789
TEX     816          776
CLE     811          806
SEA     794          779
TBD     782          813
BAL     756          778
TOR     753          760
OAK     741          782
MIN     718          722
KCR     706          667
CHW     693          700

Not too shabby.  Your number-crunching gnomes assure you that the equation holds up well against years and years worth of historical data.

Okay, I'm going to drop the lame alien metaphor.  The point is that if we look at baseball from scratch and want to evaluate what a player contributes to a team, the best way to do it is to figure out how many runs he is worth.  This method of evaluating offense is known as runs created by linear weights. This is the most basic of linear weights formulas - there are lots of tweaks and improvements - but this simple version does a pretty darn good job.  And unlike OPS, OBP, ISO, SLG, and all the other component stats, it measures offense in the only units that matter: runs.  The object of the offensive game is to score runs, and that is what this formula measures.  Throw everything else out the window.  If you're not measuring offense in runs, you're not being honest with the game of baseball.

With that, let's take a look at some of the A's from last year to see how many runs they produced by using the linear weights formula.  I'll present the number of runs they contributed ("Runs"), but I'll also present the number of runs they contributed per 650 plate appearances (Runs/650 PA), which is roughly a full season's worth.  So, for a guy like Travis Buck who hit very well but didn't play the whole year, we'll get to see how many runs he contributed in real terms and how many runs he would have contributed had he received 650 PA.

Player        Runs    Runs/650 PA
DJ            66      86
MaEl*         86      87
BoCro         35      61
Chavvy        48      83
T-Buck        51      100
Kotsay        17      50
Swish         99      97
Scoot         42      71
Zooks         30      78
Face-tag      43      54
Piazza        39      77
Sparta-Cust   85      109
Hannahan      24      90

*(tested positive for unicorns)

(There is some debate as to whether one should present on a per plate appearance basis or on a per out basis.  I'll leave the details to interested commenters.)

Now, not all positions are created equal.  You want your mashers at the corner and your glovemen up the middle.  So now let's look at these players and figure out how many runs they gave our offense above and beyond the average at their position.

Player        Runs/650 PA  Position avg   Diff
DJ            86           (1D)  93       -7
MaEl          87           (2B)  84       +3
BoCro         61           (SS)  80       -19 (!)
Chavvy        83           (3B)  87       -4
T-Buck        100          (CoF) 90       +10
Kotsay        50           (CF)  79       -29 (!!)
Swish         97           (CoF) 90       +7
Scoot         71           (SS)  80       -9
Zooks         78           (C)   74       +4
Face-tag      54           (C)   74       -20 (!)
Piazza        77           (1D)  93       -16
Sparta-Cust   109          (1D)  93       +16
Hannahan      90           (3B)  87       +3
CoF = Corner OF
1D = 1B/DH

Now, I know that a lot of you probably won't go downloading the data, importing into Excel, and computing linear weights.  For a quick and reasonable facsimile, might I recommend The Hardball Times?  The fine folks over there present a statistic called "Runs Created," which is close to what a linear weights formula might give you.  Close enough for hand grenades, anyway.  

Also, these numbers are all for 2007, and past performance is not a guarantor of future success.  If you decide look at any projections for the upcoming year, I recommend using the formula above to convert the raw data into runs.  In fact, in a few weeks, THT will be releasing a preseason book, which is chock-full of projections.  (Yes, I write for THT and yes, I contributed to the preseason book.)  In fact, I just got the ok to give you a a sneak preview of the Oakland offensive projections.  I'll present them here in terms of runs/650 PA, using the above formula.

Player               Runs/650 PA
Jack Cust            105
Eric Chavez          91
Daric Barton         90
Dan Johnson          90
Todd Linden          84
Mark Ellis           84
Emil Brown           81
Jack Hannahan        80
Travis Buck          80
Bobby Crosby         76
Rob Bowen            76
Anthony Recker       72
Donnie Murphy        71
Jeff DaVanon         70
Kevin Melillo        67
J.J. Furmaniak       66
Ryan Sweeney         64
Kurt Suzuki          63
Wes Bankston         62
Richie Robnett       58
Danny Putnam         56
Nick Blasi           50
Gregorio Petit       50
Cliff Pennington     40

Roughly speaking, we can expect the offense to be much better than average at DH, average-ish in the infield (although that's a very optimistic for BoCro), and below average in the outfield.  I hope those guys can at least catch the ball.

(Tip number four: shameless promotional plugs help you build credibility.)

If Blez ever lets me back onto the front page, I'll talk a little bit about how to convert runs into wins and the meaning of "replacement level," so that you can create your own "VORP"-like stat without having to use somebody else's blackbox.  That said, I think overplaying the alien metaphor might have cost me a shot to do that!

If this kind of stuff interests you (linear weights, not the alien stuff), there are a lot of resources out there on the interwebs.  Just google "linear weights baseball" or "linear weights."  In particular, I do recommend these sites:

A Brief History of Run Estimators - Dan Fox
Runs Created and Linear Weights - Sean Forman
Base Runs and Linear Weights - Tangotiger