HSAC Blog

Here’s a piece written by Andrew Thomas, one of our graduate student members, on the likelihood of different “streaky” accomplishments in baseball. It uses some probability and statistics to try to prove the difficulty of reaching certain milestones.

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Fans of Major League Baseball have seen three major achievements in recent
weeks, each in a different discipline of the game. Jon Lester threw the
league’s 256th no-hitter for the Boston Red Sox, Ken Griffey Jr. became the
sixth player in history to hit 600 home runs in his career, and Lester’s
teammate Kevin Youkilis concluded a record-breaking streak of 238 regular
season games played at first base without committing an error.

Ask three fans which of these is the most significant accomplishment and
you’ll probably hear three different answers, most of which will depend on
the meaning of the words “lucky” and “good” — not to mention the loaded
context of the word “significant”. A lot of people in the know felt that
Griffey should have been able to top Hank Aaron’s home run record but for
his injuries in recent years, so it’s not unreasonable to wonder if reaching
600 home runs in the twilight of his career, rather than on a charge to 756,
is considered a letdown. As others have pointed out, any number of weird
things can happen to a player in his career, and the 600 club is a ticket to
the Hall of Fame.

But as a probabilist and statistician, that answer doesn’t quite satisfy me.
The path to Griffey’s accomplishment is the product of the kind of
randomness that’s difficult to model objectively. And while that doesn’t
mean I’m not willing to try, it does mean it’s tough to make a fair
comparison.

Roughly speaking, there are two different domains of randomness that are in
play. One is the area of “small but frequent”; flip a fair coin 100 times,
and it’ll reliably come up heads between 40 and 60 of those times, but only
exactly 50 times in about 8 percent of sequences. The other is the domain of
rarely occurring but big in impact, like winning the lottery or being struck
by lightning. And it’s the scope of the time in play that determines what
sort of randomness will dominate.

Within the scope of one game, the events that can alter a pitcher’s
performance are limited to the small scale. The “game of inches” comes into
play when an infielder dives to stop a ball going into right field, guesses
correctly on a drag bunt attempt, gets handcuffed by a bad hop on a ground
ball or misses a pop foul that drifts into the seats. These events rarely
mean a difference in isolation, but when taken in combination are often
decisive; ask the 2003 Cubs about the last two for just one example.

It’s at the level of the individual game that the little differences tip the
scale, which is what makes a no-hitter so exciting to watch, and why it’s
one of the last vestiges of pure superstition in the game to mention the
possibility of it happening before the feat is done – whether or not the
pitcher is even aware of such a comment. (Of course, if we’re looking for
freak occurrences to explain wild events, there could just be something in
the water the Red Sox give to their prospects – Lester only followed the
example of former fellow farmhands Anibal Sanchez and Clay Buchholz.)

By virtue of length, career statistics rarely if ever hinge on this kind of
single-game fluctuation. In the long run, the game of inches washes out to
years of repeated trials. But the big events that determine home run and
strikeout kings tend to be difficult to predict, and even trickier to
average out. It’s virtually impossible to determine the probability of an
injury occurring, or its future impact, let alone rule changes, substance
crackdowns or manager-player fallouts. These kinds of events usually go
unmodeled in analysis, or hand-waved away with “if these trends continue” or
“assume he stays healthy”. The best we can do is look at similar players and
circumstances and hazard a guess as to a range of outcomes.

It’s a combination of these two flavors of luck – small but frequent random
outcomes and freak occurrences – that make consecutive game streaks all the
more impressive on the outside. One bounce can handcuff an infielder; one
trade for a fly-ball pitcher can decrease the number of times that bad
bounce will happen. There’s also the lobbying element in play; the
persuasion of a team to the official scorer to count an occurrence as being
favorable, or unfavorable, to the player in question, as has been suspected
with Joe DiMaggio’s streak games 30 and 31, and outright overt in Orlando
Cabrera’s recent equal-opportunity protestations to his home White Sox and
away Blue Jays scorekeepers.

Stretching over parts of three seasons, Kevin Youkilis’s streak survived
small deviations, and had the benefit of no major events to interrupt his
play. In terms of lucky plus good, there’s little doubt in my mind that the
least-heralded of these accomplishments is the one that’s least likely to be
repeated by anyone else any time soon.