# Dismal Rocket Science

## Crunch the numbers: Roger Clemens might be worth every penny.

Roger Clemens, the winningest pitcher alive and still an ace at an age when most ballplayers are selling cars, recently stood up in George Steinbrenner's box at Yankee Stadium, like Mussolini at the balcony, and told a cheering crowd that he was coming back to the Yankees. New York sports being New York sports, the muttering started a half-second after the cheering. Did the Yankees just buy another pennant? Or another Kevin Brown? Is Clemens really worth $18 million?

The question has been chewed over in the sports media since the announcement. But what's been missing from the debate is the quantitative question at its base. Four months of Clemens is worth a certain amount to the Yankees. How much?

Let's break it down. First of all, how much money is a playoff berth worth to the Yankees? According to the late baseball statistics guru Doug Pappas, the Yankees' postseason revenues in 2001, a year they made it to the seventh game of the World Series, were $16 million. So, even if we assume that a Rocket-fueled Yankees team will go all the way, Clemens still might not pay back the Yankees' investment.

Of course, fielding a contending team puts more rear ends in the seats during the regular season, too: If the Yankees finish fourth this year, don't expect sellouts for next year's weekday homestand against Kansas City. Revenues coming directly from playoff games don't tell the whole story—there's a value to just being in the hunt, even if Yankee fans of the "nothing but a ring will do" variety won't admit it.

Luckily, Nate Silver has come up with a computation of the cash value of adding wins to your regular-season record. That value depends on which wins you're adding: Going from 56 wins to 62 is worth much less than going from 90 (wild-card contender) to 96 (probable division winner).

So, where are the Yankees starting from? That is, how many games would they win without Clemens? My go-to source for real-time predictions of this kind is Clay Davenport's postseason odds page. His projection uses a so-called Monte Carlo system, which means it operates by running simulations of the baseball season again and again to see, on average, what happens. Every day, starting from that day's standings, his computer runs through 1 million fake seasons, making a best estimate of the odds of each team winning each game. As of this writing, he has the Yankees winning an average of 86.6 games and making the playoffs 36.6 percent of the time. (At the outset of the season, before the Bombers' current struggles, those numbers were 90.8 games and 52.6 percent.)

Starting at 86 or 87 wins is just when extra victories become really valuable: According to Silver's computation, it would take just four extra wins in the Yankee ledger to make the $18 million payout to Clemens a black-ink transaction. Surely the Rocket's going to win four games, right? But that's not the question. He needs to win games the Yankees *otherwise wouldn't have won*.

Pitchers win games by preventing runs. To determine whether Clemens will help the Yankees win games they would have lost without him, we need to know how many runs Roger Clemens will deny the Yankees' opponents.

If he suits up at the beginning of June, Clemens is likely to make about 23 starts. At his current age, he's averaging just under six innings a start. So, let's say he'll throw 130 innings. Clemens' ERA last year in Houston was a sterling 2.30, best in the National League. His numbers won't be that gaudy in the offense-rich AL East (in his last three years in New York, he posted ERAs of 3.51, 4.35, and 3.91), but there's every reason to expect him to be effective. The most popular baseball prediction systems project Clemens to have an ERA between 3.00 and 3.50 as a Yankee. That means he'd allow between 40 and 50 runs over the course of those 23 starts.

But what we really need to know is how many runs Clemens *won't* give up—in other words, how many runs would Yankee opponents score in those 130 innings if the Bombers keep sending out the pitchers they're currently using? And now we come to the crux of the matter. The Yankees pitching, already thin, has been brutalized by injury, and the resulting parade of last-minute replacements to last-minute replacements was certainly a factor in Steinbrenner's willingness to open his wallet for a season-saving ace.

Then again, Chien-Ming Wang and Mike Mussina are already off the disabled list, and by the time Clemens is ready to pitch, only *one*, not *all*, of the replacements—Kei Igawa, Matt DeSalvo, Philip Hughes, Chase Wright, and Jeff Karstens—will be starting regularly for the Yankees. Some of these pitchers have shown great promise and one (Igawa) has a long record of success, at least in Japan. It's hard to imagine there won't be one of them who's maintaining, at worst, an ERA of 6.00.

If that's the case, that pitcher would give up 87 runs in the same 130 innings we're expecting from Clemens. Assume Clemens saves the Yankees 40 runs over the course of the season. How much does this boost the Yankees in the standings? For this, we need to use a remarkable tool developed by Bill James in the early days of sabermetrics, the Pythagorean formula. Though it has the same name as one, it isn't a mathematical theorem, but it's about as close as you get in baseball statistics—and it allows you to predict the effect a change in runs scored or runs allowed will have on winning percentage.James' formula reads

PCT = RS

^{2}/ (RS^{2}+ RA^{2})

where PCT is the team's winning percentage, RS is runs scored, and RA is runs against.

This season, the Yankees are on pace to lead the league in runs scored with 900. If we take this 900-runs-scored figure as fixed, then for the Yankees to end up winning 86.6 games, they'd be expected to allow about 840 runs. Take away the 40 runs saved by Clemens and you would get a record of 90-72. In other words, Clemens would get the Yankees those four wins. Thus, in our admittedly rough approximation, Clemens would help the Yankees to the tune of just about what they're paying him.

Of course, whenever you carry out probabilistic computations like this, you're dealing with what Don Rumsfeld would call "known unknowns." If any one of the Yankee spare parts (or a new one picked up cheaply along the way) steps forward and pitches adequately, the benefit of having Clemens could be cut in half. (Though any serious injury to oldsters like Mike Mussina or Andy Pettitte could make adding Clemens seem genius.) If you think Davenport's simulation places too much weight on the Yankees' bad start and expect New York would have won 90 games without Clemens, that brings the break-even point down closer to three extra wins. And if you're certain, as some are, that Clemens would be pitching for division-rival Boston if he weren't in New York, you need to take that into account, too. All of these factors are hard to get a quantitative grasp on.

And then there's the fact that the dollar value of Clemens might not be what's ultimately in question. If Steinbrenner is willing to spend however much it takes to increase the Yankees' chances of winning the AL East, even by a fraction, he may simply not care all that much about the expected cash benefit of signing Clemens. Indeed, the Yankees, for all their on-field success and huge fan base, lost money last year. Adding one of the best pitchers in baseball certainly makes the Yankees better; whether it will make them richer remains to be seen.