How much is a walk worth compared to a hit?

When comparing one hitter with another or one pitcher with another, how much less weight should be placed on walks compared with hits, in general?

I have not found much science about this. OBP WRONGLY weighs walks the SAME as hits. WHIP for pitchers does the same.

On average, would it be safe to say that a walk is, perhaps, HALF as good as a hit, in general, given that hits could be singles, doubles, triples or home runs and that runners may advance more than one base with a hit, etc? A rule of thumb would be helpful for me, when comparing a high-walks hitter with a free-swinging hitter or a high-walks pitcher with a low-walks, higher-hits pitcher.

Is there science on this?

Mostly, it depends on the type of hit...obviously. There are several systems like linear weights, runs created, etc that place a run value on each type of event. Been a while since I've looked at all the formulas, but most are somewhere in this ballpark:

BB - .33 runs
1B - .5 runs
2B - .75 runs
3B - 1.1 runs
HR - 1.4 runs

wOBA (weighted on base average) uses linear weights to come up with one number that's on a similar scale to OBP. Here's the basic formula:

wOBA = (0.72xNIBB + 0.75xHBP + 0.90x1B + 0.92xRBOE + 1.24x2B + 1.56x3B + 1.95xHR) / PA

There is an incredibly complicated formula that actually determines the linear weights for each outcome, and generally the wOBA formula can get a little more tricky, but It's an extremely useful stat.

For the most part you can't just generalize hits as one thing, so we have the stat, wOBA, to easily compare hitters with different (or similar) styles. Would you agree with me that two recent Redsox acquisitions, Carl Crawford and Adrian Gonzalez, are certainly different players? Here are some of their 2010 stats:

CC: 6.9 BB%, 17.3 K%, .307/.356/.495 (.378 wOBA)
AG: 13.4 BB%, 19.3 K%, .298/.393/.511 (.378 wOBA)

So there are some players who have a very different composition to their stats but still have the same wOBA. Crawford has less power and on-base ability and Gonzalez, but his hit tool (and speed) makes up for it. There are also plenty of cases where two guys have the same OBP but a 30-40 point spread in wOBA.

Very very good answers. Thank you!

Dave H:
Now I understand wOBA better. However:
What about for pitchers? Is there a stat that, similar to wOBA, factors in the value of walks compared to a hit, and the extra value of a double compared to a single, and a triple compared to a double and a single, and a home run compared to a triple, etc, like wOBA does for a hitter? WHIP just doesnt cut it! WHIP is as bad as OBP!

And for hitters, is there anything that combines the wOBA with the defensive value? for an overall weight? On my own personal excel spreadsheet, I try to come up with a value that includes offense AND defense, so that I can compare the value, say, of using MY instead of Blanco for a utility role, or so that I can compare Borbon with Gentry.

GaGYM - You could simply use wOBA in the same way we have opponents BA/OBP/OPS for pitchers. As of right now, no one is posting wOBAA (wOBA against); however, you could essentially use the same formula. It wouldn't be on a runs alowed scale like ERA, FIP, xFIP, tERA, SIERRA, or others, but you could certainly use it to compare pitchers.

As for the hitters combined offense/defense stat, you're essentially looking for the components that make up WAR. You can convert wOBA into wRC (runs created as a function of wOBA) and TZ, DRS, or UZR into runs saved. The common point between defense and offense will always be runs created or saved (1 run created = 1 run saved). So if you have an accurate stat giving you how many runs a players was worth on both offense and defense, you can compare the total value of players. This is the overall goal of WAR. The problem with these overall stats is reliability. In general, offensive metrics are pretty reliable (in a statistically significant way). On the other hand, defensive statistics are extremely unreliable. Even if we could all agree on the right method for analysis (TZ, +/-, DRS, and UZR produce widely varying results), the input data is extremely suspect. They are begininng to implement a field f/X system (similar to pitch f/X) that will accurately measure what happened on every play. Once field f/X is rolled out, we've had enough time to work out the bugs, and the new data format is worked into new formulas for defensive metrics, we'll be able to have some degree of confidence in defensive stats (I'd give it at least another five years before trusting any of them). So for now it's best to view defense and offense separately. Use the metrics for offense, but rely upon your eyes and the opinions of scouts to form your opinions of defense. One thing you can do is to look at three years worth of multiple defensive stats, and compare it to the opinions of scouts and your own "eyeball" test. If everything aligns, then you've probably got a fairly accurate idea of that player's defensive value. However, if the numbers say he's good, but the scouts think he's bad, trust the scouts.

Here's a spreadsheet showing the historical linear weights for wOBA:

https://spreadsheets.google.com/ccc?key=0AuA3CVxiszdWdHhuZVB0YjBldmRSSlBWMUk0NG9ySmc&hl=en&authkey=CL7ukZMK

and here's a link to the MySQL code used to produce those historical values.

http://basql.wikidot.com/woba

I'm really not the expert here (at all). This originated from Tom Tango, was adapted by Colin Wyers, uses data from Baseball-DataBank.org, and was brought to my attention by Matt Klaassen of Beyond the Boxscore. It wasn't the easiest process for me, but it's all already set up. I ran it and produced pretty much the same results as Matt. I basically just wanted to see if I could the code to run on my computer at work (it worked I guess).