I'm reminded of Boston's "see what sticks" theory of filling easily filled gaps from the 2004 season. Ortiz, Giambi, Millar, and others had injury histories as part of the package, and it brought down their value to an acceptably low level (low enough to stockpile them). I think that Jeff's analysis could even extend to the likely higher risk of attrition among oft-injured players, because every injury has the risk of sapping someone's value for good. I think that part of the calculation was central to the A's getting Thomas last year, even moreso than the likelihood that he would injure himself at some point. In terms of quantification, the attrition risk might be the most difficult part.

On the other hand, I think the section about compiling injuries is just slightly off. The fact that independent events cause injuries to different players (collisions and food poisoning aside) does not make it more likely that players will be injured at different times. The probability for each player's injuries is entirely independent of what happens to every other player. The only effect they could have on one another actually works against the theory, as an injury to, say, Kielty force Stewart into more playing time, elevating his injury risk. This concept works the same way as what he mentioned about Hughes and the Yankees band of merry AAA men; their risk doesn't show up so much at first, but once Mussina or Wang goes down, it becomes a major factor. Going from the bench to the starting lineup exacerbates that risky business. In other words, if Kielty gets hurt, that doesn't mean that the gods are likely to wait until he heals to injure Stewart, it actually makes Stewart more likely to get injured (probably).

I don't think this objection even begins to undermine Jeff's analysis; I mean it as a complementary piece. The article is in the vein of the very best of baseball analysis, to my mind. And if it serves as the introduction to some sort of quantitative system for injury analysis, then I would be very excited. I hope that he would take that part of the risk into consideration. Great work!

Terry Ryan may also have started wokring on a new inefficiency. I describe this as Really Crappy Guys Who Would Normally Be On Their Way Out Of The Game But We'll Give Them Their Last Chance model.

The scenario starts with a possible candidate for a position at AA or AAA, and some uncertainty about his readiness. Then sign Tony Batista, Juan Castro, Rondell White, Sydney Pontoon, Ramon Ortiz et al to take the job out of spring training and let the kid defer service time while you see what the vet has left.

One of two things happen: the old guy has enough left to keep the job and you have a player for cheap, or he's toast and you bring in the kid. Even if the kid can't quite handle the job, most of the time he's better than Juan Castro's last stand (before CIN.)

I say this is new not because the notion of picking through the rag bag to provide competition for rookies is revolutionary, but because Ryan does so much of it every year. He even does it when the kid is totally ready (Bartlett), when the veteran is completely, utterly and universally decried as forked (Fat Tony), when there's no competition for a spot (before 2007 Mike Venafro was signed for the already loaded bullpen). If building a multi-headed platoon from guys with tenure on the DL list can be new, so is compulsive retreading.

Not a bad market inefficiency in that, unlike the appreciation of OBP and defense, it will take more than the mere circulation of the idea for its proponents' competitors to exploit, and thereby nullify the inefficiency. It will also take hard work and guts, because any GM who seeks to exploit this inefficiency will be spending way more time on the phones and in his office juggling the roster, and will get way more flak from fans and the media for bringing in the often injured, the no names, and the other assorted castoffs that tend not to generate excitement about a team's chances. Fans have come to accept chunky players who know how to take a walk, but they still don't like ten-man rotations and DL casualties.

Added bonus: given the deft roster management such an approach would require, it may cut down on the number of armchair GMs who struggle to manage their fantasy rosters on a week to week basis from believing that they could do just as good a job.

But I wonder: is Sackmann's citation to Beane and Ricciardi's use of 10 man roatations and a cast rotating bad hamstrings evidence a belief that this was the grand plan going in, or does he think it was an ad-hoc thing that may be useful if actually adopted as a plan going forward? I'm a bit skeptical of the former, just as I am always initially skeptical when the stathead community offers praise of Beane and Ricciardi. No knock on Sackmann (I think he's on to something really neat here), but I've seen (and have been guilty of) enough irrational Beane-love to be cautious.

or does he think it was an ad-hoc thing that may be useful if actually adopted as a plan going forward?

I'm sure the plan was to get 150 games out of Swisher, 120 from Bradley, 80 from Kotsay, 80 from Stewart, with Kielty and Buck filling in the gaps.

All this latest roster shuffling is desperation moves, not some great new master plan, and I hope Jeffrey was being tongue in cheek with the whole new "market inefficiency" thing that's been done to death.

I enjoyed this article a lot - nice job Jeff! Andrew does bring up an important caveat with regard to independence assumptions, though.

As a mini finance geek, I started wondering what kind of metrics are appropriate for risk. CAPM says that the riskiness of a stock (Beta) is its relative covariance of returns with those of the market, divided by the variance of the market returns. So, Beta for a baseball player is his relative riskiness compared with the riskiness of all baseball players.

Calculating player beta is going to be tough. One component is a player's propensity for injury. This obviously differs a lot between players (i.e. zito and prior, for instance). Another is a player's relative variance in performance while healthy. This is much tougher to figure - and I imagine that some analysts would say we can ignore it as it doesn't vary between players - MGL, care to weigh in? There are probably other factors at play here as well.

Food for thought. Again, great article, Jeff. I'll definitely have to think more about this.

But if Kotsay+Bradley+Swisher+Putnam+Kielty+Langerhans+Snelling produces more than Roberts does, who did the better job running a baseball team?

Well, there are obviously opportunity costs in requiring 7 guys to provide league average production at one position.

I feel the stathead community has never grasped the value that a guy like Pierre brings to the table in his low-risk profile of providing 162 games and 700 PA of a little above average play at a central defensive position. Maybe Jeff could write an article about that.

A guy like Pierre is like a bond or a utility stock, while Frank Thomas last year was like a smallcap NASDAQ issue.

BLB, we could apply the same model to pierre-like players. Presumably Pierre is much lower risk (but also lower return, at least for some of the OFs) than the 7 OFs that Beane has run out there. A good model should generate prices for all levels of riskiness and return. Then we could determine who was undervalued and who was overvalued.

I think of Frank Thomas as more of a REIT, for some reason.

I don't think you can count on anyone, not Pierre, not Tejada, to give you 162 games and 700 PA every year. Some players are bigger injury risks than others, but the true difference is a lot less than observing one guy averages 160 games per year and the other only 110.

Players can go from ironman to injury prone just like that. For pitchers, even faster. My definition of durable pitcher is this: "Pitcher who has not been injured yet".

Terry Ryan may also have started wokring on a new inefficiency. I describe this as Really Crappy Guys Who Would Normally Be On Their Way Out Of The Game But We'll Give Them Their Last Chance model.

Yeah. Whenever Beane does something, it's brilliant, regardless of whether it's caused by, say, a sudden and "inexplicable" dropoff in the quality of their minor leaguers. Say, mightn't that have something to do with their no longer drafting in the top 10-12 slots for most of this decade?

Half of me thinks this is a brilliant article.

The other half is astounded that the A's have 17 people on the DL and right-thinking sabermetricians are writing articles saying that say this (1) is Billy Beane's fault and that (2) it is in fact a "good" thing.

Wow.

Well, to make everyone feel better, Ken Williams has been following somewhat the same MO. Thome was an injury risk -- and he managed to get Philly to pick up a huge chunk of the salary. Dye was an injury risk. Pierzynski was a pariah. He carried at least 6 starters (5 very "durable"). He "gambled" on Iguchi. He hasn't had (much at least) the 7 interchangeable parts aspect to it.

Anyway, I don't think it's new knowledge that players with injury histories and, to a much lesser extent, bad reputations can usually be had cheaper precisely because they are high risk/high reward. To the extent that such players may be undervalued I'd guess (1) their future injury risk is probably estimated as too high and (2) their production while healthy is undervalued. Though to be honest, #2 may be more fans and sportswriters -- e.g. how JD Drew is often portrayed as nearly worthless because he misses 25 games a year.

Anyway, the A's have been pursuing something of a mix & match strategy in the OF for some time. They haven't had an actual good-hitting OF in ages it seems. At times they've had a similar approach to 1B/DH. But this is where most teams have most of their depth. Adding Walker maybe gives the A's the sort of backup IF bat they've never had before.

Anyway, no, guys on the DL obviously isn't a market inefficiency. But if you can get 8 OFs/1B/DH who, say, can post a collective league average OPS across 5 positions for an entire season for the same price as 5 guys with 3 replacements who will do so only as long as the 5 starters stay pretty healthy, then yeah, you've found a "market inefficiency."

Sal Baxamusa follows up. I think that we should continue discussing this on this thread rather than starting a new thread, but I'm open to suggestions. It's pretty heavy stuff. I may have to reread it later.

A guy like Pierre is like a bond or a utility stock, while Frank Thomas last year was like a smallcap NASDAQ issue.

And superannuated pitchers are like bulletin board stocks.

"Well, to make everyone feel better, Ken Williams has been following somewhat the same MO."

But a key difference is that Williams follows this MO because he knows that his training staff (starting with trainer Herm Schneider) is, from what I've heard, widely considered to be among the best in baseball. Is the same true about the A's?

Williams is very good at using the strengths of his organization. I assume that's why he feels more comfortable acquiring players who are injury risks. It's also why he likes to acquire high-velocity pitchers with control issues -- Don Cooper seems to work well with those types of guys.

It's hard to judge the A's training staff because the A's are notorious for putting up a complete smokescreen about injuries, but they certainly don't seem to have done a good job keeping their players healthy (with the exception of Thomas.) Also, things like Kotsay having surgery before spring training (what, you couldn't have diagnosed that need before so he wouldn't miss baseball time?) don't exactly fill me with a lot of confidence in their ability.

That, and Larry Davis's porn mustache and mullet.