The Baseball Economist: The Real Game Exposed (27 page)

Recent history reveals that for hitters each “point”—every 1/1000th—of OBP is worth about 3.013 runs, and each point of SLG is worth about 1.688 runs to a team’s total runs scored in a season.
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By multiplying each player’s statistics by these weights, we generate a prediction of how many runs a lineup composed of only this player would score over an entire season. I then adjust the number of runs scored to account for the run impact of the home park of the hitter. This is necessary because some parks are more friendly to offense—like Coors Field in Colorado—while others hurt offense—like Dodger Stadium in Los Angeles. It would be incorrect to credit or punish players for producing something that is beyond their control, and this method puts all players on equal footing.

While this calculation is useful for our exercise of estimating player values, it is also fun to see which player would produce the most runs as a team all by himself. Table 31 lists the top 10 run producers by league in 2005 if the player had taken 100 percent of his team’s plate appearances. Not surprisingly, the list includes some of the more prominent sluggers in the game.

For pitchers, every strikeout per nine innings lowers runs allowed by 25.8 runs. Every walk and home run allowed per nine innings increases runs allowed by 60.7 and 249.5 runs.
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Just as we did for hitters, we multiply the weights times the pitchers’ statistics to generate a prediction of the number of runs a pitcher would allow if he pitched every inning for his team over an entire season. One slight modification is necessary because defense plays a large role in preventing runs, even though pitchers cannot do much to help their defense prevent hits on balls hit into play—the central result of the DIPS theory already discussed. To view pitchers on equal footing, I assign pitchers the average rate at which defenses convert balls hit in play into outs (70 percent) and multiply this value times the regression-predicted impact for fielders generating outs in balls in play—every one-tenth of a percent increase on outs on balls in play lowers a team’s runs allowed by about 4.2 runs a season. This gives all pitchers the same defense to help them prevent runs so that no pitcher receives credit or blame in run prevention from luck or defensive quality. Again, the estimates are adjusted for the run environment of the home park. Table 32 lists the top 10 pitchers by league in preventing runs over the course of the 2005 season.

These leaders are a little more interesting than batting leaders, because the list includes many players who make their living as part-time
players. Only nine players on the list are full-time starters. The relief pitcher used to be the role for pitchers deemed not good enough to start. Now the reliever is a pitcher used for getting outs in key spots during the game. The closer, who often pitches late in a game when a win is on the line, has grown into one of the most prestigious members of the team.

A reliever normally pitches differently than a starter: he may have only one or two pitches and normally throws at a high velocity for short stints. He is less concerned with in-game endurance than a starter, so he can expend more energy. There is no way Mariano Rivera, possibly the best closer in the history of baseball, could sustain his usual level of pitching excellence as a starter, pitching more than twice as many innings. We can see how this is true from the example of John Smoltz of the Atlanta Braves. Smoltz spent several years as both a reliever and a starter, making the All-Star team in both roles. In 2004, he struck out 9.37 batters and walked only 1.83 per nine innings while pitching nearly 82 innings as a closer. When he returned to the starting rotation in 2005, Smoltz struck out 6.62 and walked 2.08 per nine innings over 230 innings. These are good numbers, but not as good as his reliever numbers. Clearly, Smoltz adjusted the way he pitched according to his role. Keep this bias in mind when comparing pitcher statistics that are normalized for playing time, and remember that generally all pitchers can pitch better in short relief stints than as starters.

We can now calculate the difference in runs that a player contributes compared to a player who would produce the average number of runs in the same amount of playing time in the same league—AL teams score more runs than NL teams because of the designated hitter. Better-than-average hitters will produce more runs than average hitters, and above-average pitchers will produce less runs than average pitchers. This step is especially important for evaluating pitchers, because even the best pitcher will always yield runs to opposing teams. The average provides a useful baseline for comparison, as pitcher contributions ought to be valued according to the runs they prevent, not the few they produce.

Finally, to account for playing time, we multiply the percent of a team’s total plate appearances or innings pitched times the difference in runs scored/allowed from the average. A player’s runs scored above average (RSAA) or runs allowed below average (RABA) reports how much better the player is than the average player with the same playing time in terms of producing/preventing runs. For example, let’s look at the top hitter and pitcher in 2005 in terms of RSAA and RABA. Derrek Lee of the Chicago Cubs produced 74.30 runs more than an average player taking 11.22 percent of his team’s plate appearances. Chris Carpenter of the St. Louis Cardinals saved 35.51 more runs than the average pitcher throwing 16.72 percent of his teams innings. This does not mean that Lee is necessarily more valuable than Carpenter. To determine the overall value of the player, we need to value playing time.

We have the basic ingredients to calculate what players are worth in dollar terms: we know what players contribute to winning through runs, and what runs are worth to team revenue. The first step is to calculate the dollar value of runs scored/allowed above/below average by multiplying the dollar value of runs, estimated in Step 1, times the run contribution above or below average, generated in Step 2. The relationship between the run difference and revenue is increasing, which means each additional run produced/prevented is more valuable than the previous run. This result is the dollar value above average ($ValAA), which measures the value over what the average player would produce given the same playing time.

Next, we need to establish a baseline dollar value for the average player, to add to the value above average, which will give us the MRP of a player. The average hitter would produce the league-average amount of runs if he took 100 percent of his team’s plate appearances, and the average pitcher would produce the league-average amount of runs if he pitched 100 percent of his team’s innings. I estimate that an average team—a team that is predicted to win eighty-one games based on runs scored and runs allowed—will earn approximately $109 million in revenue. Assigning an equal weight to the run contributions of offense and defense, each side is responsible for half of that value, $54.5 million each. Therefore, the average player will produce a percentage of $54.5 million equal to the percentage of his team’s plate appearances or innings pitched. For example, a player who generates the average run production, like rookie shortstop Ronny Cedeno of the 2005 Chicago Cubs, would be worth exactly his percentage of playing time multiplied by $54.5 million. Ronny Cedeno took 1.45 percent of the Cubs’ plate appearances in 2005, which was worth approximately $790,000 ($54.5 × 0.0145 = $790,000) in terms of the revenue he generated to the Cubs.

We then add the dollar value that players generate above/below average to the baseline average dollar value. Let’s look at two of Cedeno’s Cubs teammates who contribute value above and below average, Nomar Garciaparra and Neifi Perez. Garciaparra produced 0.75 runs above what the average player, taking 4.01 percent of the Cubs’ plate appearances, would produce, thereby generating a value of $100,000 more than the average player. An average player taking 4.01 percent of his team’s plate appearances generates $2.18 million ($54.5 × 0.0401) for his team. Adding Garciaparra’s $100,000 to the average raises his total hitting value to $2.28 million. Perez is a below-average hitter; hence, we must subtract his contribution from the average to calculate his worth. Perez took 9.89 percent of the Cubs’ plate appearances in 2005, costing the Cubs $1.85 million versus the average player with the same playing time ($54.5 × 0.0989 = $5.39). Therefore, Perez generated $3.54 million ($5.59 − $1.85) in revenue for the Cubs from his hitting.

It is important to note that these estimates value
only hitting
contributions, just as the estimates for pitchers value only pitching contributions. Why did Cubs manager Dusty Baker put Perez on the field for so many plate appearances if he was worse than the average Ronny Cedeno, who logged most of his defensive time at shortstop when Perez was out of the lineup? Some would say Baker is a stubborn man with an irrational preference for a “proven veteran” like Perez. I think that a manager with thirteen years of experience and three NL Manager of the Year awards (1993, 1997, and 2000) probably has a decent idea of what he is doing. It is more likely that Baker went with Perez because he brings something to the team other than his offense. Perez is a noted defensive specialist, who is an out-machine, not just as a hitter, but as a defender. I can’t say how much Perez’s defensive contribution is worth, but I suspect his contribution with the glove makes it worthwhile to keep his poor bat in the lineup.
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In fact, many shortstops and catchers, which are primarily defense-first positions, earn less $ValAA with the bat than most of the other position players. Cedeno was a twenty-two-year-old rookie in 2005, who was still learning the game. It is certainly possible that Cedeno deserved more playing time than Perez, but Baker’s decision is defendable.

In addition to defense, the MRP calculations do not account for base running, leadership, community goodwill, etc. All of these characteristics are valuable to teams. If I were the GM of the team, I would need to figure these things out using a similar, but more complicated, set of calculations. For simplicity, I’m going to stick with valuing batting and pitching.

Fans love to argue every year over who is worthy of the Most Valuable Player awards (MVP); however, the word
value
means different things to different people. Many fans believe the award should go to the best player in the league. Others think it should go to the best player on a contending team—the idea is that a good player on a bad team isn’t adding value toward getting the team to the postseason. Another argument is that pitchers should not be eligible, because the best pitcher in the league wins the Cy Young Award. I cannot say that any of these criteria are wrong, but what if we took
value
to mean value in dollars, meaning the MVP ought to be the player with the highest MRP.

Who was the most valuable player in MLB in 2005 according to estimated MRPs? Table 33 lists the top 50 “most valuable” players in the majors in 2005. The table also notes the MVP and Cy Young award winners for the season. Because the official definition of the MVP award is open to interpretation, it is not surprising to see that the player who generated the greatest dollar returns to his team, Derrek Lee of the Chicago Cubs, did not win the award. I suspect that playing
on a bad team really hurt him in the eyes of the Baseball Writers’ Association of America, who vote for the award. However, the writers certainly didn’t give the MVP awards to undeserving candidates. In the AL, the actual 2005 MVP, Alex Rodriguez, was the MRP MVP as well, and the NL MVP, Albert Pujols, had the second highest MRP in both leagues.