April stats are meaningless. OK, that’s not entirely fair. March
stats are meaningless, April stats are just misleading. As Joe
Sheehan pointed out
yesterday, most everyone knows this and
understands it, but when you love talking about baseball, no one wants
to say “let’s wait until July.” Instead, we qualify all our statements
before launching into discussions of Brian Roberts
home run chase, Tim Hudson‘s hard luck, and
Edgardo Alfonzo chasing .400.

As an exercise in restraint, here are the Best and Worst hitters on
April 30, 2004 as ranked by MLVr

(min 50 PAs in April and 300 on the year):

Batter            Year  AVG  OBP SLG   MLVR

Barry Bonds       2004 .472 .696 1.132 1.481
Charles Johnson   2004 .333 .458 .875 .848
Lew Ford          2004 .419 .471 .710 .784
Adam Dunn         2004 .328 .538 .750 .767
Sean Casey        2004 .414 .458 .667 .698
Jim Thome         2004 .364 .456 .714 .682
Moises Alou       2004 .361 .400 .735 .645
Manny Ramirez     2004 .388 .448 .647 .617
Laynce Nix        2004 .365 .397 .714 .617
Ron Belliard      2004 .417 .500 .548 .582
Neifi Perez       2004 .220 .260 .275 -.371
Gabe Kapler       2004 .233 .270 .250 -.380
A.J. Pierzynski   2004 .236 .267 .250 -.385
Luis Rivas        2004 .190 .227 .317 -.391
Tike Redman       2004 .226 .229 .301 -.391
Jimmy Rollins     2004 .183 .263 .268 -.392
Ty Wigginton      2004 .188 .216 .333 -.394
Alex Gonzalez     2004 .182 .222 .312 -.413
Jason Phillips    2004 .162 .275 .221 -.435
Derek Jeter       2004 .168 .255 .232 -.460

While Barry Bonds had already established his dominance, there are quite a few names (Charles Johnson, Laynce Nix, Derek Jeter, Jimmy Rollins) who did not finish the year anywhere near where they began. Similarly, on the morning of May 1 last year, the Red Sox were 15-6, the Orioles 12-9, and the Yanks
12-11. Texas was leading the AL West and the Cardinals were 12-11, a
game and a half behind the Astros and Cubs, tied for the division lead
at 13-9.

Though there are always a few outliers every April, simply dismissing
the first month of the season is obviously not the way to go. Games in
April count as much as games in September, it’s just that the ones in
September have greater implications because the likelihood of various
outcomes is vastly different. Much like leverage as it pertains to
relievers, games later in the season have an apparently larger bearing
on the standings. But a slow April, much like a starter who gets shelled
in the early innings, can make those late games meaningless.

Similarly with individual player statistics, we can estimate just how
meaningful that first month is. There are a couple different ways to do
this. The first is to use something called confidence intervals for
population proportions (referred to as “p-hat” because the symbol is a
“p” with a”^” over it). P-hat allows us to determine how accurate our
data is with varying degrees of confidence and ranges. Essentially,
based on the sample size, the normal distribution curve, and the value
in question, p-hat provides a quick formula to provide a range under
which the “true” value lies.

The best way to think of p-hat is like a coin. We “know” the coin
will land on heads 50% of the time if we flipped it forever, but if we
only flip it five times, obviously it’s not going to come up at 50%. As
the number of flips increase, the more information we have about the
coin and the closer the total proportion of heads flips will be to 50%.
There’s a normal curve of outcome distributions with 50% being the most
likely (in the middle of the curve) and higher and lower proportions of
heads less likely (the tails). Selecting a certain percentage of the
area under the curve gives us that much confidence that the “true”
likelihood of a heads flip will come up. Using p-hat, we can estimate
the minimum and maximum values we need in order to cover the area of the
true likelihood. The more times we flip the coin, the tighter the curve
gets, and thus the closer the minimum and maximum values get to the mean
for a particular confidence level.

Getting back to ballplayers, in 2004, Bonds had an OBP of .696 over
his first 92 PAs of the season. Using p-hat, we can say that there is a
95% chance that Bonds’ “true” OBP is between .602 and .790. If we want
to scale back to an 80% confidence interval, the boundaries are .635 and
.757. While Bonds finished the 2004 season with a .609 OBP–within the
95% range but outside 80%–over the larger set of all ballplayers,
p-hat is very accurate.

Unfortunately, there are two problems with employing p-hat to the
data above. The first is that p-hat is used with binomial variables, so
something like OBP or AVG works well since it’s dealing with a simple
question of yes/no: hit/no hit; on-base/not on-base. SLG and MLVr,
however, are not simple binomials and thus we can’t use p-hat for them.

Secondly, even after the season is over, the confidence intervals
using p-hat are very large. This is because a 162-game season isn’t
nearly long enough to confidently determine a player’s “true” ability.
Woolner discussed this
with regards to teams a few weeks ago, but
the same goes for players. A total of 600-700 plate appearances is a lot, but
based on confidence intervals, even with a sample size that large, the
95% confidence range is typically between 90 and 100 points of OBP.
Looking at everyone who had an OBP of .350 in 2004, that means that one
out of every 20 of them had a “true” OBP of over .390 or under .310.
Given a larger sample size–over a career–they’ll likely regress
towards their “true” OBP. Thus, comparing confidence ranges based on
April stats to confidence ranges based on full-season stats gets us into
large areas of overlap as well as some rather complicated confidence
measurements of the results.

Instead, in an effort to keep things a little simpler, let’s see how
the actual April stats compare to the full-season results. Looking again
at the list above, some of those names are right where we’d expect them.
Bonds is on top, joined by Adam Dunn, Jim Thome, and Manny Ramirez. Aside from Jeter on
the bottom, most of those players are some of the lightest hitters in
baseball: Neifi Perez, Luis Rivas, and
occasional #3 hitter Tike Redman. Far from being
worthless, stats in April are more often than not a good indicator of
the season to come.

Getting back to the sample group of all players registering at least
50 PA in April and 300 PA on the season, here’s how well correlated the
stats are. In essence, how well April numbers predict the rest of the
season for 2000-2004:

Using April stats from that season, the coefficient of correlation
(r-squared) is .346, meaning that the April stats explain about 34.6% of
the variance in MLVr. Given that they comprise about 16.7% of the season
total, that’s not very impressive. Contrast that with the previous
season’s MLVr:

That’s not that much better, but notice both the change in scale (as
April MLVr has a much wider range) and slope, indicating that there
isn’t nearly as much regression to the mean from season to season as
from April to the end of the year. Looking at the previous year’s MLVr
reveals that we’re not dealing with a case where April stats pale in
comparison to other simple predictive measures. Running the two together
as a multivariable regression, r-squared rises to .5595 with the
previous season’s MLVr about twice as valuable as April’s MLVr.

So where does all this leave us? For starters, April stats are not
meaningless, but rather there are a few outliers every season that draw
a lot of attention. On the other hand, those outliers cannot simply be
written off as a hot streak or cold streak. Instead, when combined with
the previous season’s stats or other projections, they can give an early
indication about the expected performance of players this season.
Averaging two helpings of last year’s MLVr and April’s MLVr will get you
most of the way to an estimate of how a player is going to perform over
the course of the season.

The other lesson is that only 95% of players will fall into those
large confidence areas mentioned above. While it’s difficult to generate
them for MLVr, of the top 20 players in AVG or OBP at the end of April,
it’s a good bet that one of them will finish more than 90 points of OBP
or 80 points of batting average above or below their current pace. Will
it be Roberts? Clint Barmes? Jacque Jones? We’ll have to watch to find out.

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