Inspired, perhaps, by the news that a group of player agents are considering filing a collusion grievance against the owners, a number of readers wrote to ask that I verify my claim by analyzing the collusion year markets of 1986-1988. Thanks to a variety of electronic newspaper archives, and a fantastic new transactions database put together by the good folks at Retrosheet, I was able to do just that.

I restricted my analysis to the 1986-87 off-season, which featured the strongest free agent class among the collusion years. Tim Raines, perhaps the best player in baseball at the time, led the way, along with a variety of near-great performers like Jack Morris, Willie Randolph, Lance Parrish, and Andre Dawson.

Blissfully ignoring a variety of intelligent feedback I received on the discount rate and other matters, I decided to apply the same methodology as in the previous study. Salary was calculated based on a net present value approach, discounting future seasons at a rate of 5% and averaging income across all contract years; value was approximated based on a weighted, three-year average of Clay Davenport's WARP statistic.

Working with the 1987 data presented a number of challenges that hadn't surfaced in the original analysis. Under the fog of collusion, contemporaneous data on contract terms and dollar figures were difficult to come by, especially in the case of marginal players. In order to remain consistent with the 2001 and 2002 studies, which considered only guaranteed income, I did my best to track down and exclude any income in the form of incentive payments. Even where I could find such information, however, the result was problematic: The 1986-87 market, if nothing else, was tremendously risk-averse, and incentive clauses constituted a larger share of income than in today's market. Players received bonuses for things like not suffering a chronic back injury (Parrish), or making a pedestrian number of starts (Doyle Alexander), which they were very likely to achieve. Nevertheless, I considered only base salary in the analysis.

I was able to find reliable information for 69 free agents. Here's how everything shakes out:

Keep in mind my hypothesis: In a collusive market, because there is no mechanism to ensure that a player is paid what he's worth, salary should not align very closely with performance. The best way to test that is with the R² values of the two regression lines that appear in the chart, and on that account, the evidence is mixed.

• Pitchers. Variance in WARP' explains 72% of the variance in pitcher salaries, almost exactly the same as in 2002, and considerably greater than in the decidedly non-collusion year of 2001. (There are two data points that are particularly influential - Morris on the high side, and Alexander on the low side - but the R2 is even higher if they are excluded, and the regression line is not significantly affected).

  It is worth noting that the relationship between salary and performance is roughly Linear. The squared term that appeared in the 2001 and 2002 regressions, and caused the regression line to bend upward, is not significant in 1987. I posited last week that one explanation for the non-linear relationship between salary and performance is the relative scarcity of elite players in a competitive bidding environment. That the regression line is flat for 1987 suggests that this may in fact be a good measure of the competitiveness of a market, but to reach a conclusion based on only three years of data would be premature.

• Hitters. The hitters don't do as well, with an R2 of 66%, considerably less than in either 2001 or 2002. As in the case of the pitchers, the squared term on the regression line is not significant, and the function is approximately linear.

  The hitters do worse still if we remove Tim Raines, an extreme outlier in terms of both salary and performance. As indicated by the dashed line, the R2 decreases to 62%, and the relationship between Salary and WARP' is slightly downward sloping. Rather than receiving a premium relative to their marginal value, the better players can be had at a discount; it's hard to imagine a condition like that arising in a competitive market.

Something seems fishy, certainly. Beyond a reasonable doubt? On the basis of this evidence, probably not.

Indeed, after further consideration, I'm not so certain that my proposition (competitive labor market = efficient labor market) is correct, even in theory. Teams differ in the way that they assess a player's value. For that reason, it is certainly true that a market with a greater number of bidders does a better job, on the average, of performing that assessment accurately.

The problem is that a player's salary is not determined in accordance with the average assessment of his talent. It is determined, rather, in accordance with the most favorable assessment of his talent. (This phenomenon has a name, the winner's curse, that is apropos to baseball). A player need only accept one free agent bid, and more often than not, he's going to accept the one that pays him the most. The really absurd contracts in recent memory - Darren Dreifort, Mike Hampton, Jay Bell - all came in highly competitive markets in which a single owner had an unreasonably favorable view of the player in question.

Does that mean that there's no conclusive way to distinguish 1987 from 2003?

Flash back to January 1987. Walk Like an Egyptian is at the top of the pop charts. The Dow Jones Industrial Average has coasted past 2,000. John Elway has broken Cleveland's heart for the very first time. And in baseball, the free agents are getting utterly and completely shafted.

What's remarkable, pouring through the newspaper stories circulating at that time, is how obvious all of it was. Far from being a well-kept secret to be revealed only years later, collusion was pervasive, profound, and explicit. Collusion and drug suspensions were the dominant stories of the off-season. The owners, under Peter Ueberroth's direction, were crying poor. Don Fehr was bitching up a storm. Arbitration on a grievance over collusion in the 1986 market was going on at the very moment that the 1987 free agents were soliciting offers.

It is worth recounting the experiences of some of the prominent free agents from that year's class:

• Tim Raines. Raines was 27 years old and coming off a batting title. He turned down arbitration from the Expos after they offered him three years and $5.5 million, but the only documented counteroffer was from the Padres, and that was a shameless lowball at just $1.2 million annually. Raines finally signed a three-year contract with Montreal on May 1 for close to what they had offered him originally. The Expos went 8-13 in his absence, and 83-58 the rest of the way as Raines posted one of the best years of his long career.

• Jack Morris. Morris tested the market, but like Raines, found that the other offers weren't to be taken seriously. After numerous expletive-filled tirades about collusion, Morris and his agent reluctantly submitted to arbitration with Detroit. It was a good decision; Morris won his case and was awarded $1,850,000, more than twice as much as any pitcher made in the open market.

• Gary Ward. Ward was the first major free agent to sign elsewhere, leaving Texas for the Bronx. The deal didn't take place until Christmas, however, and Ward took a 25% pay cut.

• Rich Gedman. See also Tim Raines. An All-Star at 27, Gedman couldn't get what he wanted from the Red Sox, but nobody else came calling, and he re-signed with Boston on May 1. Having missed Spring Training, Gedman didn't hit a lick upon his return. With the Red Sox languishing in fifth place, Walt Hriniak decided to tinker with Gedman's swing, with notoriously disastrous results.

• Lance Parrish. Turned down more money with the Tigers to sign a one-year deal with the Phillies in March; his base pay was $50,000 less than he had made in 1986.

• Doyle Alexander. Alexander was offered two years at $1.87 million by the Braves in November. Acting as his own agent, he turned the offer down, but like Morris and Gedman, couldn't get so much as a sniff anywhere else. He finally re-upped with the Braves on May 5 for just $450K guaranteed.

• Bob Horner. Turned down three years, $4.3 million from the Braves, and unable to find a better offer elsewhere, fled to Japan.

• Andre Dawson. Dawson turned down two years at $2 million from the Expos. He tested the market without success, and in March, agreed to let the Cubs sign him for whatever they felt was "fair and appropriate." They settled on one year at $500K plus incentives.

The only free agents who had anything resembling a normal winter were those like Brian Downing, Bob Welch, and Willie Randolph, who acceded to their former team's initial offer with little resistance. To a man, players who tested the market were punished - forced to take a pay cut, or sit out until May, or both. No contemporary player has had an experience anything like what the free agents of 1987 went through as a matter of course.