As he did once before, in 2005, prolific baseball analyst and writer Bill James has just e-mailed me a write-up he's done on a hot hand-related topic, with permission to post it here, if I choose. The topic this time is pitching, namely the question, "If a starting pitcher has been pitching well in his recent starts, is he more likely to pitch well today?" James describes three separate studies he conducted to investigate this question. Because his write-up is 19 pages long, I'll just summarize the main parts.

Key to the whole endeavor is defining how well a given pitcher is doing, both in a particular game and over his last few starts. Here are some foundational definitions:

Game Scores are a method that “score” each start by a starting pitcher essentially on a zero-to-one-hundred scale. To convert this into a “Hot Pitcher Scale”, each pitcher’s score after each game (and thus, heading into his next start) was 20% of his score from his last start, plus 80% of whatever his score was prior to his last start.

The first study, using all pitchers from 1960-1969, created two dimensions, both coded from A (best) to H (worst): performance quality for a given season (to equate pitchers on prior ability), and "hotness" coming into a game. Pitchers were then evaluated on how well they pitched in their next games. Summarizes James:

...at the conclusion of this I had 64 groups of pitchers, coded AA, AB, AC, AD, AE, AF, AG, AH, BA, BB. . ..HE, HF, HG, HH. AA was high-quality pitchers who came into the game hot; HH was low-quality pitchers who came into the game pitching badly, even by their own standards. We had about 500 starts in each group of games. The essential question was whether and to what extent pitchers would pitch better, relative to the quality of their overall performance, when they were “hot” than when they were “cold”.

They did not pitch better.

The second study, using all starting pitchers from 2000-2009, looked for temporal sequencing; did a given hurler's well (or poorly) pitched games tend to cluster consecutively? (This approach is conceptually similar to a statistical technique known as the runs test.)

"Is there, in general, any tendency for Game Scores to form clusters? None whatsoever."

James's third investigation, again examining 2000-2009, "compared pitchers with identical or near-identical year-to-date records, but one of whom came into the start hotter than the other." There were 504 matched pairs. Finally, in this study, support was obtained for pitcher streakiness:

In this study the pitchers who were “hot” did out-perform the pitchers who were not hot in their next starts, and over the balance of the season —- not by a huge amount, but they did outperform them. The “hot” pitchers, in their 504 “next starts”, had a won-lost record of 199-175, an ERA of 4.28, and an average Game Score of 50.62.

The “cold” pitchers, in their 504 next starts, had a won-lost record of 177-177, an ERA of 4.74, and an average Game Score of 47.94.

James concludes with a piece of practical advice for fans:

...suppose that you are going to a ballgame tomorrow, and both starting pitchers are 11-7 with ERAs of 3.45, but one of them is hot and the other is cold. Is the one who is “hot” more likely to win the game?

Yes.