People talking about the “post-steroid era.” In 2002, the average baseball team hit 169 home runs. In 2008, the average baseball team hit 162 home runs. Of course, pitchers take steroids too…I only mention home runs because it’s something people who talk about the “post-steroid era” generally point to when arguing about steroid use. Barry Bonds, David Ortiz, Miguel Tejada, and even Manny Ramirez have not tested positive for steroids since MLB instituted real penalties for a positive test. The tests are clearly flawed and the guys who are getting caught are simply being careless (like Manny — who, again, did not test positive for steroids). Take a look at the guys in the Mitchell Report — half the guys are still in the league and many of them (including, coincidentally, Jack Cust) have had their best years post-testing. Maybe testing has helped, but I don’t think we are anywhere near a “post-steroid era,” in baseball or any other sport.

I agree about Cust…but even if he’s slightly below average, he’s well worth what we pay him and what we’ll have to pay him next year. I also think the -17.5 positional adjustment for a DH makes sense. Sure, not everyone has a Thome/vintage Ortiz/Hafner for a DH, but most teams with a regular DH have a guy who is in Cust’s range. I can only think of two teams (the Mariners with Griffey and the Royals with Jacobs) that have a regular DH significantly worse than Cust, and given why those guys were brought in they’re not really good comparisons. I think Cust is worth $3MM, but it seems like there are always Luke Scotts and Jeremy Giambis floating around baseball that could mostly replace Cust’s production.

Anyway, I didn’t want to hi-jack your thread with steroid talk, just wanted to put that out there.

at Fangraphs they are park adjusted figures that are derived from wOBA. Pretty soon we will have a glossary for them but they are pretty common like WAR so I feel that they don’t really need to be written out, though I chose for some reason to do so in my response. If non statheads want to learn about stats thats great and with the new glossary that Im working on it will be easier, but if you aren’t interested in looking up what FRAA or BRAA are then chances are you probably aren’t going to be interested in going very far in the stats community.

dfa, I appreciate your defense, but it’s not necessary. I certainly don’t mean to exclude. I just use some things (like WAR and FRAA) so commonly that I forget that not everyone is used to them. Haven’t been around today but will change it now.

It just seems to me that everyone seems to say either, screw Jack Cust and his strikeouts or Jack Cust is teh awesome!!!! and I wanted to offer a stathead-y kind of argument that shows that just because strikeouts aren’t bad doesn’t mean that he’s all that good.

he wasn’t that valuable. And in a bad year like this one he’s a Crosby level sinkhole.

Otherwise it would be a very successful strategy.

Ill write it back but its going to take some time.

A lot of this:

The net expected run value is converted to wins (I’m not sure if playing time is factored into that). It’s not clear to me if the expected wins are simply a function all past performance or a certain sized sample, nor whether any sort of general regression is applied to it. The expected wins thus arrived at are then compared against an assigned value for "replacement player" which I gather varies according to position and league.

is close but not really accurate. wOBA is explained above but Ill go into a little more detail. OPS doesn’t really work because it cant be converted into runs, because it undervalues OBP and because slugging is a faulty measure is a faulty measure since a triple isn’t really worth three times a single, a home run isn’t worth 4 times a single, and so forth. Therefore you need wOBA to find the average value of a play (without regard to the situation) that a hitter produces compared to an out to properly give it weight. This is the formula for doing that.

(0.72xNIBB + 0.75xHBP + 0.90×1B + 0.92x Reached Base On Error + 1.24×2B + 1.56×3B + 1.95xHR) / PA

The reason why wOBA is valuable is that it easily converts to wRAA which is linear weighted runs above average. You do that by using this formula:

Run value per PA above average = (wOBA for player – wOBA for league) / 1.15

To find BRAA, which is a park neutral linear weighted runs above average, you need to apply a park factor. BRAA is the batting component of WAR, and where you get offensive runs from. It is easily available on Fangraphs, which is quite possibly the greatest website on the internet.

Defense is a less well understood and more variable thing to measure. UZR is widely considered the pinnacle of defensive evaluations, its creator was hired by the Cardinals, and I read that the A’s were using a slight variant at one point. UZR looks at the probability that a ball in play become out, based on the type of batted ball it ground ball, fly ball, line drive, etc.), the zone that ball was hit to, and how hard it was hit. UZR also adjusts for park factors, whether the batter is a lefty or righty, the situation with runners and outs, and the gb to fb ratio of the pitchers. I think that this link will explain UZR better as it comes from the guy who created it, Mitchel Lichtman. Basically its uses balls in play data (and where you get that data is one of the reasons there is a variation in win values, Fangraphs uses BIS rather than gameday I believe) to judge how often a fielder makes a play on a ball thats hit with the same characteristics and to the same place. It comes out at the end with FRAA which is the defensive component of WAR.

Then there is positional adjustments

Catcher: +12.5 runs (all are per 162 defensive games)
First Base: -12.5 runs
Second Base: +2.5 runs
Third Base: +2.5 runs
Shortstop: +7.5 runs
Left Field: -7.5 runs
Center Field: +2.5 runs
Right Field: -7.5 runs
Designated Hitter: -17.5 runs

Which are derived from historic data to make up for the difficulty of playing those positions and the historical offensive contributions that those positions make. If you want to find out more Tom Tango et al’s The Book is where you should go.

Then you get to replacement level. Since what we have looked at so far is is all based on an average you can stop there if you want or if you don’t like the concept of replacement rate players. The replacement runs do something that is valuable though, it gives players who actually play more runs than someone who is chronically hurt. Yes they get more runs based on the number of PAs they have or the possibility of making more plays in the field. What replacement runs do is give players credit for not getting hurt and being replaced by a crappy player. Basically you want to penalize Nomar for never being able to play and forcing them to replace him with filler. Historical studies have show that replacement level players are about 20 runs below average, so it has now been codified that replacement is equal to 20 runs over 600 PAs. Therefore, a player is rewarded .03333 runs per PA to account for the replacement rate.

So you add those all together to get RAR. Then you look at Bill James’ Pythagorean wins theorem. Dave Cameron explains

RS^2/(RS^2 + RA^2) = Pythagorean Winning Percentage. So, if a team scored 775 runs and allowed 775 runs, they’d have a .500 Pythag Win%, or 81 wins and 81 losses – even amounts of runs scored and runs allowed should lead to something like an even record. Not as scary as it sounds.

What happens if we subtract 10 runs from the runs scored column, so that we now have a 765 RS/775 RA team? Pythag spits out a .4935 win%, and .4935 * 162 = 79.95 wins. So, instead of 81 wins, you’re now expected to win just barely less than 80. By subtracting 10 runs, you lost a fraction more than one win.

Same thing happens if you add 10 runs to the runs allowed column – 775/785 RS/RA spits out .4935 as well. How about if you add 10 runs, so we have a 785/775 team? .5064 win%, or 82.03 wins. Again, 10 runs added equals one win gained.

For an even more precise look at the issue, you could use the improved PythagenPat method, which places a better exponent in the calculation, but the conclusion is going to be the same; 10 runs = 1 win.

So there you have it.

A couple of your questions that I don’t think I go to

3. How much of a player’s history is used? are minor league results included?

No none of the history is used WAR is a historical contribution and not a projection. You can however project WAR, just like you can project HRs or batting average. What they do is project the components of WAR most notably wOBA and then build from there.

What defensive numbers are used to project defensive value, and what is the basis for those?

UZR is used for defense like I said above but there isn’t a established way besides guesstimation to look at minor league performance and say oh they will be this good or bad at a ML level. Often for big leaguers people will use UZR/150, which prorates someones defensive contribution to 150 defensive games, to project FRAA.

Just not something we should be desperate to hold onto. Cust is certainly an excellent hitter, and I do have my misgivings about how hugely DHs are penalized, but to articulate any kind of argument against that I have to go up against Tango, Cameron et al and explain why I understand it better, which I certainly don’t. Or maybe a better way to explain it is that I would have to explain why current times demand a different adjustment than the historical data suggests, and I don’t feel equipped to do that. Maybe that there just aren’t that many good DHs is all I need to say, but even so, I’ll stand by the opinion that he’s not someone we should be investing in long-term.