How much does a "clubhouse cancer" cost his team?

This past weekend, the Cubs suspended outfielder Milton Bradley for the remainder of the 2009 season. Bradley had made some remarks to the press critical of the "negativity" he had received in Chicago. That, combined with his reputation as a complainer who apparently didn't get along with his teammates, prompted GM Jim Hendry to send him home for the rest of the year, with pay.

Do "clubhouse cancers" cost a team wins? In an excellent article at Baseball Analysts, Sky Andrecheck admits he doesn't know. But he looks at the anecdotal evidence of other oncoplayers to at least try to get a handle on how much a team is willing to pay to get rid of him.

This season, Bradley had accumulated 1.2 wins above replacement (WAR) up to the day of his suspension. Andrecheck suggests that he's probably a little better player than that because he's having an off-year. So for Hendry to be willing to lose Bradley's contribution, he must think think that his continued presence would cost the team wins at at least that rate. Otherwise, he'd bite the bullet and keep him around.

That figure is in line with another recent disgruntled clubhouse influence, Shea Hillenbrand, who was projected as a 1.4 WAR player when he was released by the Blue Jays in 2007.

Finally, Tom Tango adds a third anecdote. He notes that no team was willing to sign Barry Bonds in 2008, even at minimum salary, when Bonds was projected to be around 1.5 WAR.

As for other "cancers": Albert Belle and Barry Bonds had poor clubhouse reputations, but weren't released by their teams. Those guys were substantially better than 1.5 WAR per season. That strongly suggests that the cost of keeping a player around is less than the cost of losing an all-star. Andrecheck writes, "I can't think of even a 3 or 4 WAR all-star caliber player ever having been given away or released largely due to clubhouse attitude. Instead, teams learn to deal with these players, rather than oust them."

So, it would appear, poisoning the clubhouse is worth somewhere between 1.5 and 3 wins a year.

That's very cool stuff. But I'm still wondering about a related subject, one that the article doesn't try to answer. My question is: just *how* does a clubhouse cancer cause the 1.5 win dropoff? It's unlikely that the personalities of the players affect their team's Runs Created or Pythagorean estimates (unless clutch play is affected more than non-clutch), so the dropoff must come in the performance of the player's teammates. How does one player's negative attitude cause another player's performance to suffer? Do the disheartened fellow players not try as hard? Are they less motivated to receive coaching, or stay in shape? Do they concentrate less on pitching strategy, maybe spending less time in with the coach going over scouting reports on opposing batters?

And whatever it is, how do we gather evidence? I suppose we could check the performance records of pitchers while Bradley is on the team, and compare them to their records before he arrived and after he left. But 1.5 wins a year, with the equivalent of 18 full-time players (nine hitters and nine pitchers), is only about an 0.8 run shortfall per player. That's not much signal to find among all the noise, isn't it? I suppose you could check the records in the few weeks prior to the player being kicked out, on the premise that that's when the situation became most intolerable. But you might find that the situation reached the breaking point only because the team was losing, so you might mix up cause and effect.

Or maybe it's that one guy who's on the cusp of breaking out, or having a comeback season, just gets discouraged and flames out: some 23-year-old prospect winds up a little less hungry, and gives up a bit too early. That doesn't seem like it could be 1.4 wins, but I guess it's possible.

Any suggestions? I'd even be interested in hearing plausible suggestions for how the 1.4 wins (14 runs) are lost. At least if we have some reasonable hypotheses, maybe we can think of some ways to test them.

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My suspicion, though, is that the Milton Bradleys don't actually cost their teams 1.4 wins that way. I think there are other reasons that the Cubs might have for releasing Bradley than just a sober calculation of his effect on the team's on-field performance.

First, there's deterrence. There has to be some mechanism by which teams prevent their players from going off half-cocked and ruining team chemistry. There has to be the threat, explicit or implicit, that if the player is disrespectful towards the team, he will pay a price. For most players, who want their time with the team to be as pleasant as possible, the desire to get along with their teammates might be enough incentive. But when an anti-social player crosses the line, the punishment may have to have a negative cost to the team.

For instance, suppose a world-famous surgeon commits murder. Putting him in prison might cost the hundreds of lives his skills would save over the years. But society has to jail him anyway; otherwise, they give every surgeon a license to kill.

The same thing might be happening here. Even if keeping Milton Bradley on the team wouldn't cost only a small fraction of a win, they'd have to get rid of him anyway, just to make sure the other 24 players don't get similar ideas.

Second, Bradley's presence might cost the team wins in other ways than just on the field. If the clubhouse atmosphere is poisoned, the other players are unhappy. If they are unhappy, they are less likely to want to stay on the team. And so, the Cubs would have to offer them more money to stick around as free agents. Indeed, they'd have to pay *all* free agents more money than they would otherwise. If Chicago is a crappy team to play for, but Boston is wonderful, why would anyone sign with the Cubs? (You might also get an increase in disgusted players demanding to be traded.)

If word gets out around the league that Cubs' management is not willing to enforce normal standards of civility from their players, it could cost them a lot more than 1.4 wins per year.

Third, and thinking out loud: is it not possible that while a poisonous Milton Bradley costs his team 1.4 wins a year, a poisonous player of higher ability might cost the team nothing? Whatever mechanism it is that has Bradley hurting the team on the field, there's no doubt it's because of the reaction and chemistry among the other players, right?

Now, people get upset when social norms are violated: I'm going to be more upset if you steal $20 from me than if my taxes go up $20. Is it possible that putting up with an arrogant superstar is a social norm, but putting up with a marginal player is not?

Isn't it possible that when a superstar acts like a disagreeable moron, the other players kind of shrug and accept it? If the social norm is that some superstars are a**holes, and you just have to get used to it if you want to win, then it might cause no harm at all. Where I used to work, if the manager was being a big jerk, the rest of us would talk about it over coffee, and we'd grin and bear it and get back to work. But if one of our fellow grunts was acting like an idiot, that would be different: that would upset us a lot more, because he was one of us.

Could it be the same thing happening here? When Barry Bonds was a jerk, maybe management took the players aside and said, "yeah, we know he's acting like that, but he's our best chance of winning, so try to deal with it?" That wouldn't work with Milton Bradley, and so the players are less likely to put up with it, and management would have to get rid of him.

Anyway, as I said, just thinking out loud on this one.

Finally, could it be just money? If Milton Bradley is pissing off the other players, and the fans find out, and they start booing Bradley, and the team does nothing about it ... might that not get in the way of the fans' long-term loyalty to the team? The fans are loyal and rabid. They're proud to be Cubs supporters, and many have spent their whole lives dreaming a World Series win. Then Milton Bradley comes along, winds up in the absolute dream job of Chicago Cub outfielder, but doesn't appreciate what he's got, and starts insulting the Cubs and the fans and the tradition.

Doesn't getting rid of Bradley fulfill an obligation to those fans? Doesn't that build the brand and cement the relationship and lead to fan loyalty and revenues?

Bradley is only going to miss two weeks, and may get a chance to reform. Those two weeks are worth, what, maybe .1 wins? That's less than $1 million -- and, considering that the Cubs are out of playoff contention, it may be only a few hundred thousand. The suspension could pay for itself in no time at all.