Though this deserves a much more thorough macro-level treatment, let’s just take a look at the density of home runs in either half of the season for each player who participated in the Home Run Derby. Those players include David Ortiz, Hanley Ramirez, Chris Young, Nick Swisher, Corey Hart, Miguel Cabrera, Matt Holliday, and Vernon Wells.

For each player, plus Robinson Cano (who was of interest to Andy in the Baseball-Reference.com post), I took the percentage of games before the Derby and compared it with the percentage of home runs before the Derby. If the Ruined Swing theory holds, then we’d expect

The table below shows that in almost every case, including Cano (who did not participate), the density of home runs in the pre-Derby games was much higher than the post-Derby games.

Is this evidence that the Derby causes home run percentages to drop off? Certainly not. There are some caveats:

• This should be normalized based on games the player played, instead of team games.
• It would probably even be better to look at a home run per plate appearance rate instead.
• It could stand to be corrected for deviation from the mean to explain selection bias.
• Cano’s numbers are almost identical to Swisher’s. They play for the same team. If there was an effect to be seen, it would probably show up here, and it doesn’t.

Once finals are up, I’ll dig into this a little more deeply.

Owings was being used as a long reliever. For a big-hitting pitcher like Micah, that’s death to begin with. Relievers need to be available to pitch, so the Reds couldn’t get their money’s worth from Owings as a pinch hitter, since he wouldn’t be available to re-enter the game as a pitcher unless they used him immediately. They also weren’t getting their money’s worth as a pitcher, since, as Cincinnati.com notes, the Reds’ starting pitching was doing very well and so long relief wasn’t being used very often.

Letting Owings start in AAA will give him the best possible outcome – he’ll have regular opportunities to pitch, so he won’t rust, and he’ll get to bat at least some of the time. Owings needs to be cultivated as a batter because that’s where his comparative advantage is. I doubt he’ll ever be at the top of the rotation, but he could be a competent fifth starter. If he pitches often enough to get there, he’ll add significant value to the team in terms of his OBP above the expected pitcher. He’ll get on base more, so he’ll both advance runners and avoid making an out.

A baseball player is a factory for producing run differential. He does so using two inputs: defensive ability (pitching and fielding) and offensive ability (batting). In the National League, if a player can’t hit at all, he’s likely to produce very little in the way of run differential, but at the same time, if he’s a liability on defense, he’s not likely to be very useful either. Defense produces marginal runs by preventing opposing runs from scoring, and offense produces marginal runs by scoring runs. Having either one set to zero (in the case of a pitcher who can’t hit at all) or a negative value (an actively bad pitcher) would negatively affect the player’s run production. This is similar to a factory situation where labor and equipment are used to produce goods, and that situation is usually modeled using a Cobb-Douglas production function:

with Y = production, z = a productivity constant, K = equipment and technology, L = labor input, and is a constant between 0 and 1 that represents relatively how important the input is. K might be, for example, operating expenses for a machine to produce widgets, and L might be the wages paid to the operators of the machine. This function has the nice property that if we think both inputs are equally important (that is, = .5) then production is maximized when the inputs are equal.

In general, production of run differential could be modeled using the same method. For example:

where P = pitching contribution, F = fielding contribution, B = batting contribution, and and are both between 0 and 1 and would vary based on position. For example, David Ortiz is a designated hitter. His pitching ability is totally irrelevant, and so is his fielding ability outside of interleague games. The DH’s would be 0 and his would be very close to 0. On the other hand, an American League pitcher would have an very close to 1 since pitcher fielding is not as important as pitching and his hitting is entirely inconsequential in the AL. Catchers would have at 0 but much higher than other positions.

The upshot of this method of modeling production is that it shows Owings can make up for being a less than stellar pitcher by helping his team score runs and be a considerably better investment than a pitcher with a slightly lower ERA but no run production.

Barry Bonds is, without a doubt, one of the most controversial figures in baseball. He’s currently trying, again, what he tried last year – shopping himself around for the league’s minimum salary. (Thanks to the Sports Law Blog for the link.) Inside, I’d like to briefly discuss collusion and look at the incentives involved with this situation.

Collusion in the economic sense involves an agreement to act inefficiently. To give an oversimplified stock example, suppose a competitive market for chili peppers. That is, there are many people growing chili peppers and many people who want to buy chili peppers. Each bushel of peppers costs about $1 to produce and process from seed to sale. The market is big enough that no one producer or consumer can affect the overall price of the peppers. If one person raises his prices, the others can easily undercut him, and if he wants to sell his peppers he’ll have to meet them. As a result, the sale price approaches the (marginal) cost of production ($1).

Now suppose that only one person grows chilies. They still cost $1 to produce, but the chili monopolist can maximize his profits however he chooses. (The standard assumption is that he’ll set the price equal to marginal revenue, not marginal cost.) If I had made up a demand function and were in the mood to do calculus, I could figure out exactly how many bushels he would produce, what their price would be, and how many fewer bushels that would be than the perfectly competitive market would yield, but the important thing is that monopolies derive more profit than competitive firms, at a cost to the consumer. (Let’s leave aside the idea of a natural monopoly, where high production costs make it more efficient for only one firm to produce.)

So, what’s collusion? Simply, it’s an agreement by two or more firms to act like a monopoly and split the much higher monopoly profits. This is good for the firms and (generally) bad for the consumers because there’s a loss of welfare – some people want the product but at the higher monopoly price they can’t afford it and the monopoly produces fewer goods than the competitive market.

And what does this have to do with Bonds? Consider that Bonds is a producer of runs, and production can be roughly measured by the OPS stat. (There are other methods, but I’ll follow SI’s lead.) Assume that there’s a positive relation between previous OPS and salary (that is, that when negotiating contracts you can put OPS into a formula and that formula will spit out a salary, and that most salaries more or less line up with it), and that Bonds would play either right field or DH, so defense wouldn’t impose an additional cost. A rational team, when offered Bonds’ OPS number for a significantly smaller salary than it would otherwise have to shell out for the same number, should sign Bonds for $400,000. It would be fairly easy to make the leap from this statement of rational behavior to declaring that the teams are behaving irrationally and therefore must be colluding.

SI make a good counterpoint – in economic terms, Bonds’ clubhouse demeanor and notoriety would cause high amounts of negative utility in terms of unhappy and distracted teammates in the first case and customers unwilling to buy tickets to see Bonds in the second. Both of these can affect the profit of the firms and would have to be accounted for in any analysis of the value the team can expect to derive from Bonds. Suppose the most extreme case – that all fans are so disgusted by Bonds that they refuse to attend games he plays in, and that his teammates are so distracted by his attitude that they produce zero runs. In that case Bonds will still be a high producer, but he would still have a decidedly negative effect on profit and on his team’s record.

SI also makes two suggestions I don’t agree with – that Bonds’ felony charges might provide a disincentive in that the team has a high probability of losing him, and that Bonds’ age makes him unattractive. The first assertion ignores the fact that Bonds will still probably produce more than $400,000 worth of runs in a partial season, so in a strict runs-to-salary relation he still represents a net profit. The second doesn’t take into account that at age 42 in 2007 Bonds was worth $15.5 million dollars and that he would have to have declined at an almost impossibly high rate to fail to produce $400,000 worth of runs. Bonds will be out of shape and fragile, but the comparison need not be Bonds now to Bonds in 2007. I’d much rather have an out-of-shape and fragile Barry Bonds as my designated hitter than a $400,000 wet-behind-the-ears rookie. Hell, considering how fragile David Ortiz is, I’d rather take Bonds at $400,000 than Ortiz at his market salary. (The Red Sox could spend the difference on a new fifth starter now that Curt Schilling retired.)

Collusion thus doesn’t make much sense to me in this case, since the incentive to break collusion would be so strong. Stable collusion requires some method for the colluders to punish a fellow colluder who cheats. In a market this would be by simply returning to competitive prices, depriving the undercutter of his excess profits. Here, unless Selig is directly involved (unlikely), there’s no way for the teams to punish anyone for signing Bonds. (Yes, I suppose they could start plunking the batters every time, but that’s not sustainable.) The alternative explanation that makes the most sense to me is the disutility argument – that production and ticket sales will suffer for any team that employs Bonds. If, however, the SI article is correct in its idle suggestion that Bud Selig has ordered teams not to sign Bonds, Selig should be ashamed of himself.

Inexpensive runs
will not placate angry fans.
“Cheap offense” indeed.

What I take from Sauer’s post is that plus-minus is a surrogate variable for ability to be a team player. That opens the broader question of what can be measured and whether nonmeasurable statistics are ever useful in building a team.

If it’s not measurable, does it exist? Many people believe so. Think, for example, of clutch hitting, the vaunted (alleged) ability of certain players, such as Derek Jeter and David Ortiz, to hit more reliably in situations where the team’s expectation of winning or losing is weighted more heavily. The usual clutch situation is described as “close and late.” Clutch hitting is widely regarded by statistical analysts to be a myth, largely an artifact of small sample size. (In some cases, such as Jeter’s as identified in Wikipedia,the reputation for clutch hitting isn’t supported by any stats at all, but just a long memory for isolated incidences of close-and-late production.)

Jeter, predictably, thinks people who find statistical evidence that he doesn’t live up to his reputation should be defenestrated.

My opinion is that measurable and objective statistics are essential for valuing players (and coaching staff). The article on Battier is a red herring – Battier has what is presumably an anomalous plus-minus, particularly when accounting for distortions based on the quality of his teammates. Battier does, in fact, “have stats.” “Team player ability” isn’t a soft, undefined concept, but rather the ability to act as a multiplier for other players’ ability, and it’s measurable in final production numbers (probably as a factor of the player’s specific marginal product of labor). Battier’s plus-minus stat is evidence of an increased marginal product of labor.

Jeter, on the other hand, is a defensive liability who happens to be productive offensively. He’s a perfectly good hitter, but his numbers should be allowed to stand on their own rather than being propped up by some ephemeral idea that he occasionally produces at full ability and runs the rest of the season at some lower value of his optimal productivity.

High plus-minus is
evidence of production;
clutch hitting is not.