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A month ago,
my column "Making Statheads Cringe"
did exactly that, generating a ton of responses. Unlike most other columns, reaction to
the column was sharply split, as evidenced by the following two reactions:

N.J. wrote:


Thanks. Outstanding article. By the way, you and BP do a terrific job.


D.S. wrote:


Very surprising to see such crap from such a respected source. GIGO.


This week, I’ll review and respond to some of the other comments:

T.D. wrote:


It was charitable of you to answer N.J., but you’ve done more harm than good
by indulging him. You’ve created the Game-Winning RBI on andro and attached
your name (and BP’s) to it! How is this new freak stat any better for
evaluating hitters than "Wins" and "Saves" are for
pitchers? Yee-uck!


I agree that Contribution is not much better than Wins or Saves as a
player-evaluation metric. However–and I think this gets to the crux of the
negative reaction to the column–Contribution is not, and should not be used
as, a player-evaluation metric. If you recognize that the question being
asked is "How should credit for team wins be divided?" rather than
"How good was this player’s performance?," then the resulting
answer that Contribution gives us, while still imperfect, may not bother you
as much.

The Contribution exercise is based on a team-outcome valuation system, which
runs contrary to the context-independent player-outcome systems
predominantly used in sabermetrics. However, I believe it’s worthwhile to
occasionally break out of the box and examine how the baseball world looks
through other lenses.

B.S. wrote:


The problem with context-based evaluation, of course, is that the context is
variable within the game itself. A hit by player A that contributes to a
lead in the fifth inning is suddenly rendered "valueless" in such
a system when the starter fades in the sixth inning and the team falls
behind. And of course, when some other player on the team hits a two-run
homer in the eighth, player A’s hit is suddenly a positive contribution again
(as long as the closer doesn’t blow the save).

In other words, this "Contribution" system means that a player’s
evaluation is completely independent of his actual performance, and instead
is dependent on the performance of his teammates. Sammy Sosa had a
great game…unless the bullpen blows it, in which case Sammy Sosa’s game is
worthless!


B.S. has correctly identified one of the main issues with using the system I
presented as a player-evaluation metric, although calling contribution
"completely independent" is not accurate. Contribution is a
post-hoc division of credit based on team results. Until the team has
created something of value–a win–there’s no way to assess who was most
responsible for creating it.


B.W. wrote:


How could you publish your most recent piece on "win
contributions?!!" Given that there is no statistical evidence for an
ability (year-to-year correlation) to hit above one’s average in situations
that "contribute" more to a win, your metric measures luck (both
the luck of being on a good team and the luck of getting one’s hits in close
games).

[.]

My point is to warn you against publishing false stats that ignorant fans
can use to bolster their inane positions (like that Luis Gonzalez
should be the NL MVP). Knowledge in the wrong hands is, as the saying goes,
a dangerous thing. If more people were to write articles similar to yours,
Barry Bonds‘s MVP hopes might fade substantially, creating a
disastrous situation where one of the best single-season performances ever
goes unrecognized just because Bonds didn’t "contribute" enough.


I don’t believe that something shouldn’t be written because someone might
misunderstand or misuse what it says. Contribution is absolutely a measure
of luck, in combination with player skill, teammate skill, in-game
interactions, strength of schedule, park factors, and a slew of other
factors. It’s a descriptive metric–a record of what happened (weighting
certain events deemed critical more heavily than others), rather than an
predictive one to determine the likelihood of a repeat performance, or an
analytical attempt to measure the relative isolated value of an individual
performance. And as such, the lack of evidence for consistent year-to-year
ability isn’t a factor because we do not require such a characteristic.

James Kushner wrote:


Your article "Making Statheads Cringe" is a fun bit of research
[.] Perhaps we should extend the logic involved…

Since the purpose of a run is to help a team achieve a win, what is the
purpose of a win? To help the team reach the postseason, of course. This
means that, at season’s end, the contributions of Bret Boone,
Ichiro, et al should be discounted because of all the superfluous
wins achieved by the Mariners. If they win 115, but only need 95 to reach
the postseason, then each Mariner’s contribution should be multiplied by
95/115 to account for their "true" value.

[.]

Making each player bear the entire brunt of his team’s success or failure,
even on the single-game level, is just plain silly.


James has taken the Contribution idea to its logical (some would say
logically absurd) conclusion, and we could in fact apply the margin of
victory for the divisional races or wild card as well as the in-game score
differential. The level of granularity is different, but the concept is the
same. Runs are tactical goals towards the strategy of winning the game. Wins
are the tactical goals towards the strategy of winning the division.

In a perverse way, this approach would defuse the often contradictory MVP
arguments about whether it’s "more valuable" to win a race by a
large margin. For example, we often hear the argument that Mo Vaughn
was the MVP in 1995 over Albert Belle because the Red Sox wouldn’t
have made the playoffs without him, while the Indians won their division
handily. Conversely, you also hear that Ichiro is the AL MVP this year
because he was the spark plug for the record-setting Mariners, which ignores
that Seattle won by such a large margin that removing any one player would
not have cost them anything in the final standings.

A.P. wrote:


The idea that the MVP award should go to the "most valuable" and
not necessarily the best player seems reasonable to me. I was wondering if
we might extend the state beyond just wins. The purpose of winning games in
the regular season is to make the playoffs, so would it be possible to
adjust the games won by how close the race turns out to be? That is, can we
measure the player who was most important to his team in the regular season?
Off the cuff, it seems like this adjustment would put Juan Gonzalez
in a commanding lead over Bret Boone.


A couple of people wrote in with the same idea, and the following table is
thanks to A.A., who did the leg work for me when he wrote in:


Here are your results, but sorted by Contribution/Win which, I think, is a
better indication of value. Granted you lose some of the importance that the
player may play in winning more games for his team, I think this is
outweighed by the exclusion of his team’s pitchers, i.e., they play a role
in the win total and so they help someone like Boone, while hurting someone
like Brian Giles or Todd Helton.


American League

Player Team W RP Cont Cont/Win BP Rank New Rank Juan Gonzalez CLE 80 118.5 56.3 0.70 2 1 Alex Rodriguez TEX 70 128.0 47.5 0.68 7 2 Corey Koskie MIN 74 96.5 49.0 0.66 4 3 Garret Anderson ANA 74 94.0 48.6 0.66 5 4 Troy Glaus ANA 74 95.5 42.3 0.57 14 5 Jim Thome CLE 84 110.0 47.9 0.57 6 6 Manny Ramirez BOS 69 108.0 38.8 0.56 20 7 Bernie Williams NYA 84 89.5 47.0 0.56 10 8 Bret Boone SEA 107 122.0 59.4 0.56 1 9 Paul Konerko CHA 76 91.0 41.9 0.55 15 10 Roberto Alomar CLE 86 104.5 46.8 0.54 11 11 Edgar Martinez SEA 87 93.5 47.1 0.54 9 12 Magglio Ordonez CHA 76 98.5 41.1 0.54 16 13 Tino Martinez NYA 88 98.5 45.9 0.52 12 14 Derek Jeter NYA 81 86.0 40.9 0.51 17 15 Jason Giambi OAK 87 104.0 42.8 0.49 13 16 Mike Cameron SEA 99 99.0 47.1 0.48 8 17 Ichiro Suzuki SEA 105 93.5 49.2 0.47 3 18 Eric Chavez OAK 85 94.0 39.1 0.46 19 19 Miguel Tejada OAK 93 100.0 40.6 0.44 18 20

National League

Todd Helton COL 66 131.5 54.7 0.83 2 1 Larry Walker COL 58 110.5 43.1 0.74 16 2 Ryan Klesko SDN 67 103.0 49.1 0.73 6 3 Barry Bonds SFN 76 122.0 53.9 0.71 3 4 Jeff Bagwell HOU 89 120.5 57.9 0.65 1 5 Vladi Guerrero MON 64 101.0 40.8 0.64 19 6 Shawn Green LAN 81 116.0 51.3 0.63 4 7 Mike Piazza NYN 67 82.0 42.3 0.63 18 8 Gary Sheffield LAN 69 89.5 43.1 0.62 15 9 Sammy Sosa CHN 79 139.5 48.5 0.61 7 10 Phil Nevin SDN 71 101.5 43.1 0.61 14 11 Chipper Jones ATL 79 99.0 46.1 0.58 10 12 Rich Aurilia SFN 80 99.0 46.2 0.58 9 13 Scott Rolen PHI 77 95.0 44.2 0.57 12 14 Albert Pujols SLN 86 115.5 49.3 0.57 5 15 Luis Gonzalez ARI 84 125.0 47.1 0.56 8 16 Bobby Abreu PHI 80 105.5 44.0 0.55 13 17 Moises Alou HOU 77 89.5 42.3 0.55 17 18 Lance Berkman HOU 84 113.0 46.0 0.55 11 19 Craig Biggio HOU 85 86.5 40.0 0.47 20 20


Shawn Weaver wrote:


Nice article on importance and Contribution. However, I wonder why we attach
importance to runs only in wins? Isn’t it important for a player to
contribute to effort, even if his teammates fall short? I think an
examination of situations such as "late and close" might add some
insight. Of course, "late" to me is not as important as
"close," because if you score more runs than the other team by the
third inning, you still win.


The basic assumption behind Contribution is that we’re trying to allocate
credit for a successful team outcome– the win. One could compute the
fraction of run scoring a player should be credited with in a loss, but
scaling that fraction by the number of wins the team had in that loss yields
zero in all cases. This is a top-down approach towards awarding credit
(starting with the team’s value created and figuring out who is
proportionally responsible), versus the bottom-up approach of a context-free
model, in which each outcome a player creates has some fractional win value
which can be aggregated across a season.

Roy White wrote:


I don’t see any reason to cringe at the idea of evaluating a player’s
performance according to its significance within a game; we don’t get into
the miry slough of clutch hitting unless we carelessly ascribe performance
in a given context to clutch ability.


Roy has made the same point I tried to make above (and probably said it
better). Contribution is not a measure of clutch ability, it is a measure of
significance to the ultimate game outcome (with the caveat that we’re
looking at offense only, not pitching, of course).

M.S. wrote:


Although I have been firmly in the sabermetric camp, I think you have
stumbled onto something. You have captured what goes on in the right brain
when thinking about the MVP: runs that win games. The method even devalues
runs scored by teams with good pitching.


Jason D. Scott wrote:


Nice job on the "Aim for the Head" this week. I understand the
frustration that a lot of sabermetricians have with this type of analysis,
but for years (although I love the work that BP does) there have simply been
times when hardcore stat analysis just doesn’t add up to the lived
experience of watching a player contribute to a team’s wins.

Tops on my list for this is Garret Anderson. I KNOW that his overall
numbers aren’t very good, I KNOW he can’t walk to save his life, and I KNOW
he’s going to go 0-for-4 or 1-for-5 more often than not. I also know that it
seems like every time I see an Angels’ win, there’s G.A. getting a
game-winning or game-tying hit or in the middle of a two-out rally. Any
attempt to assess the context of a player’s performance–though flawed–is
quite welcome and refreshing.


Both of these previous comments touch on the difference between potential
results and actual outcomes. At the risk of annoying the physicists among
our readers (or losing the interest of the non-physicists), I’m reminded a
bit of the principle of superposition–each player in the game produces a
contribution that has an effect on the probability of winning, somewhat
analogous to a wave function. Add up these "wave functions" for
each team, and you get a result that expresses how likely the team is to win
with these particular sets of contributions, yet at this point it’s still
unknown whether the team actually wins (much like the fate of Schrodinger’s
cat inside the box). However, the wave function only collapses to the actual
result when the game is played (or the box containing the cat is opened).

While this has been a fun diversion down a path not often
travelled by most baseball analysts, I don’t expect to revisit
Contribution on a regular basis. It is not useful for the primary goal of most
sabermetric inquiry — the assessment of player ability to help teams win
games. It’s inferior to various measures that to attempt to describe
such abilities in several ways (including those mentioned by the readers
quoted in today’s column), and thus there’s no reason to prefer it as an
analytical tool (despite some correlation with context-independent value
measures). It’s in the same category as an "analysis" of who had the most
Hall of Famers as teammates — a way of looking backward at what has
happened, and categorizing events in some interesting, but not necessarily
predictive, way.

Keith Woolner is an author of Baseball Prospectus. You can contact him by
clicking here.