# Win Shares and the parabolic course of baseball lives.

In his book entitled Win Shares, Bill James undertakes a preliminary analysis of "aging patterns" by studying position players who earned at least 280 win shares during their careers. (1) He remarks, "If you want a 'clean' study of aging patterns among baseball players, the only guys you can really study are the great players" because "great players are the only players who have 'clean' careers with a full opportunity." He goes on to say, "Studying aging in baseball players is a complicated, messy business because, for one thing, the cast of characters changes so much. If you study all 23-year-old major league players, and then you study all 33-year-old major league players,you'll find that you are looking at different groups of men. Most of the guys who play the majors at 23 are gone long before age 33, and many or most of the players who are in the majors at 33 weren't there when they were 23."

There is a way to circumvent this problem, one that allows the careers of unchanging groups of players to be followed throughout their baseball lifetimes. This will be described below as Method 1. But first I wish to introduce the idea that the level of baseball performance tends to follow a parabolic course, as it rises and then falls over the span of a player's career in such a way that the longer a career, the greater a player's peak performance is likely to be. This concept is illustrated schematically in Figure 1, which depicts a parabolic curve where win shares (per season) is plotted for a span 20 seasons, reaching a peak of about 25 win shares before descending symmetrically to zero. There are three additional sets of axes on the chart. Each of these defines a shorter career length that is fitted into the basic parabola; spans of 5, 10, 15, and 20 years are indicated. The distance from each horizontal axis to the peak of the parabola (indicated by the lengths of the arrows) determines the magnitude of a player's peak contribution.

[FIGURE 1 OMITTED]

WIN SHARES

When my copy of the eighth edition of Total Baseball arrived during the summer of 2004, I was delighted to discover that win shares had been calculated for every player in the book. (2) Because I consider win shares to afford the best overall index of baseball performance yet devised, I decided to make use of these numbers.

For a particular player during a major league season, win shares relates to the fraction of his team's victories that are attributed to that player. Win shares is not a rate statistic like batting average, but rather a counting one, like RBI or the number of home runs. Therefore, other things being equal, the more playing time a player has, the higher will be his win share value.

To illustrate how the system works, consider two teams from the 2001 National League season, Atlanta and San Diego. Team win shares are divided as follows:
```            Hitting:   Fielding   Pitching   Total

Atlanta       104.1      46.4       113.5     264
San Diego     147.9      28.3        60.8     237
```

To create units of a convenient size, James decreed that a team would be credited with three win shares for each victory during its major league season. (From this, in can be deduced that Atlanta won 88 games, San Diego, 79.) Win shares for each team have been divided among all players who won at least one win share--33 Atlanta Braves and 38 San Diego Padres. Here is how the top ten players on these teams were ranked by the win shares statistic:
```Atlanta Braves (264)

C. Jones 3B     29
A. Jones OF     22
B. Jordan OF    19
J. Burkett SP   17
T. Glavine SP   16
J. Lopez C      13
B. Surhoff 0F   12
R. Furcal SS     9
M. Giles 2B      9

P. Nevin 3B       31
R. Klesko 1B      29
B. Trammel 0F     17
M. Kotsay 0F      16
B. Davis C        15
R. Henderson 0F   12
D, Jackson 2B     11
T. Hoffman RP      9
D. Jiminez SS      8
M. Darr 0F         7
```

Note how pitchers and position players are intermingled; this is a unique feature of the win shares rating system. Three starting pitchers are on the Atlanta list, whereas closer Trevor Hoffman is the only San Diego pitcher to make the top ten. Despite playing on a poorer team, Phil Nevin was able to garner two more win shares than (:hipper Jones, the Atlanta leader. In this example, Jones won 11 percent of Atlanta's 264 win shares whereas Nevin earned 13 percent of San Diego's 237.

CAUSES

Although it is my purpose to document the rise and decline of baseball performance, rather than to speculate about why it happens, a few words about likely causes are in order. Until the age of about 28, there seems to be an increase in physical strength and agility, bolstered by the fruits of experience. After age 30 or so, physical abilities decline. For many activities, such as golf or bowling, this would hardly be noticed, but playing baseball at the major league level is a very demanding business. As the aging process continues, very few, even among this highly select group, are able to remain on a major league roster beyond age 40. Most are gone long before that.

Baseball players are plagued by injuries, mostly minor ones. The more time a player spends on the disabled list, the less he can contribute to his team. Younger players are less likely to be injured than older ones, and they probably heal faster. Over the years, injuries take their toll as eyesight dims, bat speed slows, and the eye-hand coordination of youth is compromised by the normal aging process.

METHOD 1

There is a way to get around the messy problem described by James. Using Total Baseball as my data source, and win shares as the measure of performance, I examined 120 position players (40 in each of three groups) whose careers lasted exactly 10, 15, or 20 years. The 10- and 15-year players were, in each case, the first 40 listed alphabetically (3) in Total Baseball. Because there have been fewer than 40 players whose careers lasted exactly 20 years, this group was supplemented by adding a few who played for 21, with the final year (usually carrying a very small win-shares value) ignored.

I also studied 110 pitchers. As with the position players, there were 40 in each of the groups who had played for exactly 10 or 15 seasons. However, because I exhausted the supply of 2D-year pitchers, I added data from some who played for 19 and 21 years. For the 19-year players I assumed a value of zero for year 20, and I lopped off the last year for those in 21-year group. Even so, I decided to quit with a group of only 30 rather than to extend the age range any further.

RESULTS: METHOD 1

Figure 2 shows how average win shares rise and fall as the seasons progress. Although the membership of each of the six groups is stable, the ages of the players differ depending upon players' ages during their debut seasons.

[FIGURE 2 OMITTED]

The smooth curves drawn through the 10- and 15-year data are best-fitting parabolas. The fit for both 10-year groups is excellent and for the 15-year groups it is not too bad. However, parabolas fit the data of the 20-year players very poorly; the smooth curves are instead best-fitting fifth-order polynomials.

The performance of the 20-year players begins to follow a parabolic course, rising to great heights as expected, but at about the eighth season, near the peak year for 15-year players, the 20-year curves decline only gradually for the next seven or eight years, so that the inevitable final decline is postponed.

After only two or three seasons, the 20-year players are already garnering win shares faster than the players in the 20-year group, and by their fourth season they have eclipsed the peak performance of the 15-year players. Fifteen years after their debuts, the 20-year position players, though heading downhill, are still performing at or better than the peak level of the 15-year players.

Overall, the position players accrued about 25 percent more win shares than their pitching counterparts. Average lifetime win shares for the six groups are as follows:
```Group                    Win Shares

Position players 10 yr       67
Position players 15 yr      177
Position players 20 yr      312
Total                       556

Pitchers 10 yr               68
Pitchers 15 yr              127
Pitchers 20 yr              248
Total                       443
```

None of the extra Win Shares for Position Players derive from the 10-year group. If the win share statistic discriminates against pitchers, one would expect it to do so for the 10-year group as well. Therefore it seems likely that position players with long careers actually do contribute more to their teams' wins than do their pitching counterparts.

The major limitation of the Method 1 is the considerable variation in the ages of the players during their careers. The 10-year players debuted over a range from ages 20 to 27; the 15-year players, from 17 to 26; and the 20-year players from 18 to 24. This means last players to retire for the three groups did so at ages 37, 41, and 44.

METHOD 2: RESULTS

When the data are plotted as a function of chronological age (4) (the "messy" procedure discussed by James) the curves of Figure 3 result. A scan of Table 1 reveals that (1) position players tend to debut earlier than pitchers, (2) many more pitchers than position players are active after age 40 (all in the 20-year group), and (3) almost all players are active at ages 27, 28, and 29.

[FIGURE 3 OMITTED]

The data are "messy" because win share values derive from the contributions of a variable number of players at various ages. Consequently the 10-year average curve covers about 15 years, that of the 15-year players more than 20, and the 20-year group more than 25. These curves therefore cannot be matched by any real players.

SOME INDIVIDUAL DATA

Figure 4 plots win shares vs. chronological age for a tiny selection of the 230 pitchers and position players in this study. Total lifetime win shares are shown for each. These plots provide a takeoff point for a very preliminary look at individual player performance, a subject that deserves a thorough investigation but is beyond the scope of this paper. All of these players (except Ruth) are in the 20-year group of position players having an average lifetime total of 312 win shares.

[FIGURE 4 OMITTED]

The graphs are ordered according to the total lifetime win shares accumulated by each player (values shown on graphs). Although Babe Ruth was not included in the group of 40 position players studied (he played too many years) I have included his graph anyway: his total of 756 lifetime win shares is the all-time record, one that is not likely to be broken soon. (Cobb 722, Wagner 655, Aaron 643, and Mays 642 are next on the lifetime win shares list.) Also, Ruth's 55 win shares at age 26 is second only to Honus Wagner's 59 at age 34. (Walter Johnson and Barry Bonds are next on this list, tied at 54.)

Manny Mota started late, leveled off after a few years, then dropped precipitously after age 34 with fewer than 70 at-bats each season, mostly as a pinch-hitter. Jay Johnstone is an example of severe up-and-down performance variations and an array of win-share seasons that are almost all below the average curve.

Doc Cramer was another late starter who peaked at a venerable 39 and lasted until age 43. Jimmy Dykes's career more or less follows an average course except for a somewhat late start and miscellaneous fluctuations. Except for a few bad years, Brian Downing improved until age 38 before drifting downward, still remarkably productive during his last season at age 42. Sam (not Jim) Rice took off like a rocket and rose spectacularly before being sidelined with only seven at-bats during his third season. After that, Rice was a steady, outstanding performer all the way to age 40, still contributing at age 44.

With ups and downs (where even the "downs" represent good seasons) Willie Stargell peaked at age 33, declined rapidly but then had very good years at ages 38 and 39 before suffering a final rapid descent. Cal Ripken had only 39 at-bats during his inaugural season, insufficient even to earn a single win share that year, but his total rose spectacularly during the next season when he started playing regularly. Even his poorer seasons are close to the average curve. Ripken's win shares descended slowly after age 32, yet he was still playing above average at age 40 during his last season.

Babe Ruth? His record speaks for itself. Following his difficult season in 1925 at age 30 some people thought that he might be on his way out. How wrong they were! Although this is an extreme case, temporary mid-career dips are quite common. Trying to predict what a player will do, based on his prior win-share record, is no easier than trying to predict the weather: there are simply too many variables involved. Nor is it easy to forecast the length of a player's career based on his age during his first season. What does seem to be almost universally true is that, once given a chance to play regularly, the win shares of players who will become stars take off very rapidly.

SUMMARY

This study has used win shares as an index of baseball performance across major league seasons. By analyzing groups of ballplayers who have played for exactly 10, 15, or 20 years, stable groups of players can be followed as their seasons progress, although their ages differ. This is preferable to comparing players of the same age whose careers are at various stages, especially because not all players are represented at all ages--what Bill James described as a "messy" situation.

Results for pitchers and position players are virtually identical for the 10-year players. For the 15- and 20-year groups, position players accrue significantly more win shares than pitchers. This is probably not an artifact of the win shares system.

For the 10- and 15-year career players, the average win share data are reasonably well described by a parabola, rising during the early years, reaching a peak around age 28, then descending symmetrically toward retirement. Star players in the 20-year group exhibit unusual mid-career "staying power."

The data support the idea that the length of a baseball career depends upon the basic ability of the player. The great ones are already performing at a superior level by their third season, and they play for a long time.

Notes

(1.) James, Bill, and Jim Henzler. Win Shares. Morton Grove, IL: STATS Inc., 2002. Although Henzler is listed as co-author, the writing is vintage James. The section on "Aging Patterns Among Great Players" (pp. 199-202) is one of 413 "Random Essays" in Section IM of the book.

(2.) Thorn, John, Phil Birnbaum, and Bill Deane, eds. Total Baseball. Wilmington DE: Sports Media Publishing, 2004.

(3.) This method is essentially equivalent to a random selection. In the Player and Pitcher Registers, there is for each player a final line of summary statistics with the number of years of a career indicated just to the right of the word "Total" at the far left. Win shares are listed in the second column from the right under the heading "WS." Players active in 1993 or who appeared in any games before 1901 have been excluded.

(4.) Age is defined as the difference between the season of play and birth year, without regard to month, as if all players were born on January 1 of their birth years.

Following BOB BOYNTON's retirement from academe (UCSD) in 1991, he turned full time to baseball writing. This is his 16th baseball publication, seven of them in SABR journals.
```Table 1. Players Active at Various Ages in Each Group

Position Players        Pitchers

Age   10yr   15yr   20yr   10yr   15yr   20yr

17    --     --      2     --     --     --
18     1      2      7     --      1      1
19     2      3     13     --      2      3
20     5      7     22      5      6      6
21     8     13     33      9     12      7
22    12     22     38     16     19     14
23    18     32     40     28     30     24
24    28     36     40     30     32     28
25    34     38     40     36     27     29
26    37     39     40     39     40     30
27    39     40     40     40     40     30
28    38     40     40     40     40     30
29    38     40     40     40     40     30
30    35     40     40     36     40     30
31    32     40     40     32     40     30
32    27     40     40     24     40     30
33    21     38     40     12     39     30
34    12     37     40     11     38     30
35     7     33     40      5     34     30
36     3     28     40      1     30     30
37     1     19     38     --     20     30
38     1      7     34     --     11     29
39    --      4     27     --      8     27
40    --      2     18     --      3     24
41    --      1      5     --     --     24
42    --      1      1     --     --     14
43    --     --      1     --     --      7
44    --     --      1     --     --      2
```
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