October 24, 2001

Aim For The Head

They Cringed

by Keith Woolner

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.

Keith Woolner is an author of Baseball Prospectus. 
Click here to see Keith's other articles. You can contact Keith by clicking here