Pool photograph/Ezra, via Reuters

On Wednesday evening, Roy Halladay became an answer to two trivia questions (“Name the only pitchers to throw postseason no-hitters” and “Name the only pitchers to throw two no-hitters in the same season”), and pictures of his triumph were splashed across front pages nationwide. On Thursday night, Tim Lincecum had a strong outing that got him a nice applause from the fans in San Francisco. Yet Lincecum’s performance was actually both more impressive and more valuable than Halladay’s.

COMMENTS Rosenheck responds to readers A number of commenters have noted that I did not account for the quality of the opposing lineups in the piece. Yes, the Reds led the league in runs, while the Braves were fifth. However, Cincinnati’s regulars were healthy all year, while Atlanta’s battled injuries, reducing the Braves’ run output. One of the Reds’ biggest offensive advantages over the rest of the league was the strong performance of their bench players, which matters less in the playoff sprint than the regular season marathon. A few Cincinnati hitters clearly played over their heads this year — the catching duo leaps to mind — and should not be expected to retain their 2010 regular-season level of performance into the postseason or in 2011. And finally, Atlanta added Derrek Lee late in the year. Over all, the Reds’ lineup on Wednesday probably was stronger than the one the Braves put out the next day — but I’d guess by an average of only 0.15 runs per game or so, which is not nearly enough to negate Lincecum’s enormous strikeout advantage. For readers who want to learn more about the question of pitchers’ control over the outcomes of balls in play, which has perhaps been the single most studied question in all of quantitative baseball research over the last decade, here is a summary article with a series of links to some major papers on the subject. It’s six years old, but the analytical consensus has not changed much since then. — Dan Rosenheck

At the most basic level, the two aces’ showings were identical: both threw complete-game shutouts. But most fans recognize that a perfect game is a greater achievement than, say, an eight-hit shutout. That is because most pitchers have very little control over the order of their opponents’ hits and walks: if the guy who tossed the eight-hit shutout had given up all of those hits in the first inning and then thrown eight perfect innings, he would have given up a fistful of runs.

The common fan thus distinguishes between shutouts by suggesting that the pitcher who allowed fewer base runners was superior. On that score, Halladay’s night comes out ahead: he allowed no hits and one walk, to Lincecum’s two hits and one walk.

But there is another variable that is very difficult for pitchers to influence: the share of balls hit into play against them that drop for hits.

Although most fans have been led to believe that good pitchers can “induce” weak contact and generate easily fieldable balls, while bad ones will surrender a parade of blistering line drives, extensive research into the subject shows that the vast majority of pitchers wind up giving up hits on about 30 percent of balls in play over the course of their careers.

As a result, the only ways for most pitchers to reduce the number of hits they allow are to avoid surrendering home runs and to get more strikeouts, so batters never put the ball in play to begin with. This is why the list of pitchers who have whiffed 15 batters in a game over the last decade is so much more impressive than the list of pitchers who have thrown no-hitters in that timespan.

Neither Halladay nor Lincecum gave up a home run, so they were even on that score. But their strikeout totals were markedly different: Halladay punched out “only” 8 batters to Lincecum’s 14. By my calculation, with normal luck, a pitcher with Halladay’s eight strikeouts, one walk, and zero home runs allowed in 28 batters faced would give up an average of 1.55 earned runs per nine innings, while one with Lincecum’s 14 strikeouts, 1 walk, and 0 home runs allowed in 30 batters faced would surrender just 0.37.

This approach tells you who pitched better. Whose pitching was more valuable is an entirely different question — and the answer is even more favorable to Lincecum.

The Phillies didn’t need Roy Halladay to throw a no-hitter, or even a shutout. Since they scored four runs, they would have triumphed even if Halladay had allowed three. Lincecum’s shutout, by contrast, won the Giants a 1-0 nailbiter — with anything less than Tim Lincecum at his best on the mound, they would have gone into extra innings or lost outright.

A statistic called Win Probability Added (WPA) measures the added value of pitching under pressure: Halladay’s pitching improved the Phillies’ chances of winning by 30.6 percent, while Lincecum’s increased San Francisco’s likelihood of victory by 75.4 percent.

But the gap in value between their two performances is not quite as big as their pitching WPA would suggest, because Halladay helped the Phillies on both sides of the ball. Halladay’s pitching was less important for Philadelphia than Lincecum’s was for the Giants because he pitched most of the game with a 4-0 lead — for which Halladay can thank none other than Roy Halladay.

In the bottom of the second, with two outs and the bases empty, Carlos Ruiz walked and Wilson Valdez singled. With the pitcher at bat, the rally seemed almost certain to die, which would have left the Phillies with a 61 percent chance to win.

But Halladay poked a single to left, scoring Ruiz and improving Philadelphia’s win probability to 75 percent. Jimmy Rollins and Shane Victorino followed with a walk and a two-run single, and Halladay was free to coast. In that one at-bat, Halladay added 14 percent to the Phillies’ chances of winning — almost half the value of his nine no-hit innings on the mound.