I.  Explaining the Method

              First we have to establish "What is normal expectation for a rookie?" 

              This is a Win Shares Study, and it is a study only of NON-pitchers.  No pitchers allowed.  If pitchers WERE allowed they would completely dominate the disappointing post-rookies list, but that’s not why they’re not allowed.   They’re just different.  They’re in a different data file.  Didn’t use them.

              I start by defining the data set.  It is (a) all rookies (b) who had 200 or more plate appearances in a season (c) from 1920 to 2005.   "Rookies" as defined by playing time and by modern rules; I don’t care whether the guy had spent 50 days on the major league roster or was not considered a rookie at the time.    I didn’t use players pre-1920 because the game was so different then it loses some relevance, and we have plenty of data anyway, and I didn’t use post-2005 because this involves players still in mid-career, thus with currently misleading totals.   We still got a couple of active players in the study, like Albert Pujols, but that’s a minimal distortion, of no real impact.

 This creates a file of 2,640 rookies. We start with five pieces of information about each player: 

1)      Age

2)      Games Played

3)      Plate Appearances

4)      Win Shares as a Rookie

5)      Career Win Shares total 

Then we combine the Games Played and Plate Appearances into a "Game Equivalent", by the method explained last week.   Mis-explained; the formula is actually Plate Appearances, plus 4.3 times games played, the sum divided by 8.6.  Or Plate Appearances divided by 4.3, plus Games, the total divided by two.   Or Games divided by two, plus Plate Appearances divided by 8.6. . . any of those work and get the same total; everything works except the formula I wrote last week.  Games Equivalent is usually about the same as Games Played.   It’s only really different when you have a weird situation where a player plays 130 games and has 240 plate appearances or something.  It’s just better in principle to use a broader base of information.  Also, it is better in principle to give a version of the formula that actually works. 

So now we have four pieces of information about each player, rather than five—Age, Game Equivalents, Win Shares as a Rookie, and Career Win Shares total. 

Next we move to Playing Time Adjusted Win Shares.  Why do we adjust the Win Shares for the Playing Time?   Well. . .Willie McCovey, 1959.   McCovey, called to the majors in late July, hit .354 with 13 bombs in two months, posting a 1.085 OPS.   He had only 12 Win Shares, but his FUTURE Win Shares are more predicted by the quality of his play, rather than the quantity.  Frank Thomas in 1990 is kind of the same; he hit really well in 60 games as a rookie, and Jeff Francoeur in 2005 played extremely well in 70 games. 

I adjusted everybody to a 145-game basis.  Why 145 games?  It doesn’t matter; 145, 150, 155, 162 games. . . the players are the same relative to one another, so one number will work as well as another; it just makes some formula later on a little different if we use a different base. 145 games just seemed like a reasonable representation of a rookie regular’s playing time.  

I adjusted everyone to 145 games, but not entirely.  I adjusted each player 75% of the way toward 145 games. 

Why 75% of the way to 145 games, rather than all the way?   Willie McCovey.   McCovey played fantastically well in 52 games, but doing that in 52 games is not the same as doing it in a full season.  You have to make SOME adjustment for playing time.  You have to give the rookie who plays in 160 games SOME advantage over a rookie who plays equally well in 80 games, because you can’t assume that the part-time rookie can sustain the same level of performance over more playing time.   A ¾ adjustment for playing time just seems about right.  There’s no science behind it, no research; it just seems reasonable. 

So now we have THREE pieces of information about each rookie:  His Playing-Time Adjusted Win Shares, his age, and his Career Win Shares.   Willie McCovey, 1959, had 12 Win Shares in 51.465 Game Equivalents, which adjusts to 28.36 Playing-Time Adjusted Win Shares.  This is a very high total, one of the highest of all time; it’s just not as high as it would have been if he had done the same thing all season. 

The question which faces us now is; what is the player’s EXPECTED career Win Shares total.  Actually, that was the question that faced us at the start of this article; we’ve just now reached the point of being able to address it.   McCovey is now a 21-year-old player who has 28.36 Playing-Time Adjusted Win Shares, and that is all he is to us; we don’t know if he is 7 foot tall or 5 foot, a first baseman or a shortstop, a left-handed hitter or a part-time poet; he’s just a 21-year-old player who has 28.36 Playing-Time-Adjusted Win Shares. 

There is some sort of predictable relationship between a player’s age, his Win Shares as a rookie, and his career Win Shares, but what is that relationship?   I studied the relationship both ways:  based on age, and based on Playing-Time Adjusted Win Shares.   There were 184 21-year-old rookies in my study.  Those 184 players had 2,616.7 Playing-Time Adjusted Win Shares as rookies, and 31,571 actual Win Shares in their careers.  That’s a ratio of 12.07 to 1.   We could figure that if McCovey has 28.36 Playing Time Adjusted Win Shares as a rookie, he should have about 340 Win Shares in his career.   We could figure that, but we’re not done with the process yet.  That’s a marginal Hall-of-Fame type number.   This chart gives the age-to-expected production data for each age group:

In that chart, what reads as "Age 19" is actually "19 and under", and what reads as "Age 32" is actually "32 and over."   You can see that the number of rookies peaks at age 24 (465 rookies) and that the ratio of Rookie to Career production decreases in a fairly predictable fashion. 

Fairly predictable, but I need a formula.  I don’t want to say that the ratio if 3.51 at age 27 and 3.22 at age 28; I want some predictable formula.  The formula that works is:

.60, plus

33 minus age, divided by two, plus

25.5 minus age, for players younger than 26, plus

22.5 minus age, for players younger than 23. 

The formula says that a player should have 2.1-to-1 ratio at age 30; the data says 1.75, but the data is based on only 43 players, so you wouldn’t want to trust that too far.   At age 27 the ratio should be 3.6 to 1; the data says 3.51, but we’re going with 3.6.  At age 24 the formula says 6.6 to one and the data says 6.66 to one, but that’s the Devil’s Number so I would never use that. 

At age 21 the data says 12.07 but the formulas says 12.60—by far the largest raw discrepancy between the data and the formula at any age, although it’s only 4 to 5%.  In any case we’re going with the formula, which I think is more likely to be accurate than the data, based on only 184 rookies.   Not that 184 is a SMALL sample; it’s just not a large sample.  It’s about the number of at bats than McCovey had as a rookie—meaningful, but not reliable. 

But would this ratio be the same for Willie McCovey that it would be for.  . . .Joe Lovitto in 1972?  Lovitto was also 21 years old in 1972.  He had more playing time than McCovey, but he hit .224 with 1 home run.  That tends to impact how long you can stay in the majors.  

To study that, I stated Playing Time Adjusted Win Shares (PTA in the chart below) as integers, and then figured the ratio for each level:

You can see that as the players get better, the length of their career stretches out, as you would expect that it would.   Below a Win Share level of 10, it works the other way.   This is just the way math works; as the denominator Y heads toward zero, the outcome of X / Y tends to zoom off toward infinity.  It turns out that there is an easy fix for that, which is to just treat all players with less than 10 Playing Time Adjusted Win Shares as if they had 10.   If you eyeball the data you can see why this would work. 

OK, how do we put together the information in the first chart above with the information in the second chart?  Well, first we have to reduce the data in the second chart to a prediction formula.  That formula is:

5.4 plus

Playing Time Adjusted Win Shares minus 10, divided by 4. 

That formula works at 12 and above; for 11 and below we just assume that the ratio is Six to One. 

We’ll call those Figure 1 (F1), the one derived from the age chart, and Figure 2 (F2), the one derived from the productivity chart.   Then I experimented with different formulas, trying to find the most accurate formula to predict Career Win Shares from Playing Time Adjusted Win Shares as a Rookie, F1 and F2.   Abbreviating Playing Time Adjusted Whatever as P, that formula is:

P * F1 * F2 /6.91. 

Remembering that P is always assumed to be at least 10. 

So for Willie McCovey, P is 28.36, F1 is 12.6 and F2 is 9.9.  That makes:

28.36 * 12.6 * 9.9 / 6.91

And so we conclude that Willie McCovey has a career expectation of 512 Win Shares, which is a huge, huge number, an obvious-Hall-of-Famer number.  It’s actually the fourth-highest prediction for any player in the study, behind Ted Williams, Stan Musial and Dick Allen. 

There is also a special rule, which applies to only a few players, that a player’s expected Career Win Shares must be at least one Win Share larger than his Rookie Season Win Shares, if the player had 200 plate appearances as a rookie, as all of these players did. 

Let’s do a few more players.   Willie Mays, 1951, has a P (Playing Time Adjusted Win Shares) of 21.78 and was 20 years old, which makes 21.78 * 15.1 * 8.4 / 6.91, which makes 400.   Frank Thomas and Scott Rolen also have predicted career Win Shares of 400, as rookies. 

Gil McDougald and Willie Mays were the 1951 Rookies of the Year.  McDougald has a P of 26.51 and was 23 years old, which makes 26.51 * 8.1 * 9.7 / 6.91, which works out to 300. 

Greg Luzinski, 1972 has a P of 15.91 and was 21 years old, which makes 15.91 * 12.6 * 6.9 / 6.91, which works out to 200. 

Jesus Alou, 1964, has a P of 11.57 and was 22 years old, which makes 11.57 * 10.1 * 5.91 / 6.91, which works out to 100. 

So that’s how you get each rookie’s Expected Win Shares for his career, based on his age and performance level.