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Tuesday, October 29, 2002

Adjusted Average Age

Paul examines the effects of team age.

I got the idea to analyze team performance in the context of team
age when I was flipping through Bill James’ Win Shares, and I came across
an essay amongst his “Random Essays” in which he uses Win Shares to
calculate a Team Age and does a little analysis of his method. In the
analysis, he says, “it would be a fairly simple matter?to figure
the “team age” for every team in baseball history, to track the
movement up and down for teams”

href="#_edn1" title="">

[1]
As part of this analysis, he says team age functioned as a indicator
of future performance of a team. So I got interested in seeing whether
it did, and whether team age could tell us anything about playoff
teams and World Series teams.

First things first, I need to describe my methods. Now, not having the Win Shares numbers in a convenient fashion (and having some philosophical issues with James’ method[2]), I decided to use a different formula to arrive at Team Age[3].  It’s pretty simple and fairly easy to compute quickly (well, with the help of a computer, anyway). For each hitter, multiply his baseball age for that season by his plate appearances. This gives you BatterAgeContribution. Then divide the sum of these for all players who played with a team in that season by that teams’ total PA to get AverageHitterAge. Do the same for pitchers, except to substitute IP for PA. Then, to combine the two, count the number of different hitters and pitchers to appear. The final average for the team is then arrived at by multiplying AvgHitterAge by the number of hitters, and AvgPitcherAge by the number of pitchers, adding the two and dividing by the total number of players[4].  Now, we have what I will refer to as Adjusted Average Age.

So, now with all these Adjusted Average Ages computed for all teams since 1903[5], I decide to just look around at the numbers. For the course of the 98 seasons (1903-2001 inclusive), the average team age was 29.32 years. The chart that follows is the average age by decade[6]:

 

 

Decade

Average AAA

1900s

29.34521974

1910s

28.34762986

1920s

29.66943974

1930s

29.62352342

1940s

29.74471631

1950s

29.30669317

1960s

28.65316602

1970s

28.69564495

1980s

29.63620964

1990s

29.74402794

2000s

29.60578844




The average age has stayed pretty steady across baseball history. It dipped in the 1960s and 1970s, and was pretty low in the teens. I can’t think of any particular reason for this. Perhaps the 1960s and the 1970s were eras predicated around speed, a “young player’s skill”, as opposed to the 90’s and 00’s which are largely power and walks, “old player’s skills”. That doesn’t explain the 1980’s though. Here’s a chart that shows team age movement by year:

There’s a huge dip at the end of the first decade, and a rise in the postwar era that gave the 5 “oldest” seasons in history. I cannot, however, explain the huge drop-off last year. There WAS a influx of young talent playing last year, but I didn’t think it was substantial enough to be reflected in the average team age.  There was also a steady climb starting in the late 1970s that pushed the average team age up over 29.5 for most of the 1980s and 1990s. So the next natural question to ask is, “What effect does this have on team performance? Are older teams better? Are younger teams worse?” Well, that’s three questions.

I looked first at the correlations between team age and winning percentage. For the period studied, there was an overall correlation of .213. There’s a slight upward trend to the data, but nothing that jumps out at you on first glance.  Here’s another graph, the year to year correlation of team age to winning percentage:

As you can see, it’s a mess. There’s no clear patterns or relationships emerging. The data fluctuates from a .7 correlation (for two consecutive years in the late 1970s) to a -.4 correlation in the mid 1930s. I think it’s more a small sample size issue than anything else (one team can influence the numbers in a drastic fashion). So let’s look at the numbers, in table form, of correlations by decade:

 

Decade

Correlation

1900s

0.244216294

1910s

0.176273996

1920s

0.130905471

1930s

0.078346905

1940s

0.206078334

1950s

0.318256377

1960s

0.217011218

1970s

0.470670632

1980s

0.229530774

1990s

0.322559471

2000s

0.307169506



Excepting the 1980’s, there’s a trend in the free agent era towards older teams being better (I should rephrase that, older teams being better than their historical counterparts). Of course, medical science may also have something to do with that phenomenon as well. So now I’m going to focus on extreme teams: the oldest and the youngest teams in history.

First, let’s look at the teams that fall into each category. The oldest and youngest:

 

 
Oldest

Year

Team

AdjAvgAge

1982

CAL

33.52645

2001

ARI

33.33641

1983

CAL

33.26014

1998

BAL

33.25511

1983

PHI

32.98651

1945

WSH

32.89529

1945

CHW

32.87507

1981

PHI

32.78644

1988

DET

32.71679

1984

CAL

32.64627

1999

NYM

32.64073

2000

NYY

32.59633

1973

DET

32.5928

1992

OAK

32.5476

1925

BRO

32.50979

1982

PHI

32.49734

1999

BAL

32.49677

1988

NYY

32.49377

1960

CHW

32.45555

1908

CHW

32.39534

1983

KCR

32.39181

2000

ARI

32.3707

1997

BAL

32.36089

1928

BRO

32.34923

1905

BOS

32.2661

1924

BRO

32.23617

1994

DET

32.19873

1926

BRO

32.19565

2000

BAL

32.15342

1945

DET

32.12004

1961

CHW

32.09632

1999

NYY

32.07253

2000

NYM

32.06782

1927

SLB

32.04941

1998

SFG

32.03924

2001

NYM

32.02887

1945

CHC

32.02298

       
Youngest

Year

Team

AdjAvgAge

2001

  MIN

24.68653

1968

  OAK

25.19833

1967

  KCA

25.22759

1915

  CLE

25.38217

1972

  SDP

25.67735

1973

  SDP

25.69204

1966

  KCA

25.85157

1911

  BOS

25.89829

1914

  BOS

26.08875

1910

  BOS

26.19722

1975

  SFG

26.22196

1920

  PHA

26.23189

1917

  PHA

26.25241

1921

  PHA

26.2578

1915

  PHA

26.28432

1974

  SFG

26.29043

1982

  MIN

26.31308

1916

  PHA

26.40419

1998

FLA

26.40946

1956

  PIT

26.45037

1914

  WSH

26.47231

1975

  MON

26.50808

1969

  OAK

26.51672

1918

  PHA

26.51714

1919

  PHA

26.54129

1913

  BOS

26.62545

1969

  KCR

26.64716

1970

  CIN

26.65286

1969

  SDP

26.6568

1912

  STL

26.65722

1973

  MIL

26.67076

1999

FLA

26.69395

1911

  STL

26.69417

1914

  PHA

26.70571

1998

  MON

26.72785

1917

  PIT

26.74288

2001

FLA

26.74482

 

        As you can see, there’s a lot of expected teams on these lists. The recent Jeffrey Loria debacles rank as some of the youngest, while the “Geezerbacks” of last year rank as one of the oldest. These old teams as a whole posted a .528 winning percentage, while the young teams posted a .431 winning percentage. You can begin to see that having an old team is not a recipe for success, but having a young one is definitely inviting failure. This becomes more apparent when we examine division placement, grouped the young and old teams:

 

Finishes   (Young)

Times

Place

1st

2

2nd

3

3rd

2

4th

5

5th or   greater

25

 

 Finishes   (Old)

Times

Place

1st

7

2nd

8

3rd

6

4th

5

5th or greater

11

 

        The younger teams routinely finished amongst the weaker teams, whereas the older teams finishes were more evenly distributed. The two “young” first place finishers were the 1970 Cincinnati Reds, who lost in the World Series to the Orioles, and were the 28th youngest team ever; and the 1914 Philadelphia A’s, who were swept out of the WS by the Boston Braves. The Orioles were a full three years “older” than the Reds, the Braves barely missed the youth cutoff[7] themselves by about .05 of a year. The seven old pennant winners are the 1945 Chicago Cubs, who lost to one of the other “old” pennant winners, the 1945 Detroit Tigers in the WS; the 1982 California Angels, who lost to Harvey’s Wallbangers in the ALCS; the 1983 Philadelphia Phillies, the so-called “Wheeze Kids”, who lost to Cal Ripken’s Baltimore team; the 1992 Oakland A’s, the end of their late 80’s/early 90’s run, who fell to the Toronto Blue Jays in the ALCS; the 1997 Baltimore Orioles, also at the apex of a run, went as far as the ALCS; the 1999 New York Yankees, who went all the way to the top; the 2000 edition who also took home the crown; and finally, last year’s WS champion, the Arizona Diamondbacks. So this made me wonder, “Are World Series winners ?older’ than average?”

        It turns out that they are. Of the course of all the World Series that have been played so far, the average World Series champion is 29.322 years old, and averages being 0.36 years older than that team’s average, a 1.21% increase. Here’s a table of the “oldest” WS winners, listed by Difference From League Average:

 

 

Year

Team

AdjAvgAge

LeagueAvgAAA

Diff

2001

ARI

33.33641

29.20895

4.127457

2000

NYY

32.59633

29.9894

2.606934

1980

PHI

31.85207

29.37446

2.477605

1999

NYY

32.07253

29.97275

2.09978

1978

NYY

30.8195

28.8543

1.965195

1977

NYY

30.3757

28.65075

1.724947

1950

NYY

31.05481

29.44972

1.605089

1931

STL

31.25857

29.77191

1.486667

1998

NYY

31.38951

29.95613

1.433383

1947

NYY

31.62508

30.23501

1.390074

1909

PIT

29.91819

28.63266

1.285532

1941

BRO

30.57114

29.30777

1.263373

1979

PIT

30.3205

29.14479

1.175712

1970

BAL

29.73455

28.56579

1.168766

1945

DET

32.12004

31.02198

1.098051

 

        Notice a trend? Three of the top four champions are the last three WS winners, last year’s “Geezerbacks”, who were a whopping 4.1 years “older” than the league average, and the NY Yankees of 1999 and 2000, as all mentioned in the previous section. (For reference, last year’s Yankee team wouldn’t have placed on this list, only creeping in at +.03). Let’s look at the youngest teams to take the top prize:

 

Year

Team

AdjAvgAge

LeagueAvgAAA

Diff

1942

STL

27.42344

29.2846

-1.86116

1946

STL

28.88784

30.48132

-1.59348

1944

STL

29.05509

30.58663

-1.53154

1990

CIN

28.09558

29.5413

-1.44572

1914

BSN

26.79353

28.20022

-1.40669

1926

STL

28.52405

29.889

-1.36495

1915

BOS

27.0891

28.26245

-1.17336

1912

BOS

26.77972

27.94587

-1.16615

1986

NYM

28.57121

29.68371

-1.1125

1969

NYM

27.27775

28.37284

-1.09509

1995

ATL

28.53735

29.62609

-1.08874

1966

BAL

27.41014

28.3972

-0.98705

1916

BOS

27.4077

28.26167

-0.85397

1982

STL

29.14826

29.79205

-0.64379

1959

LAD

28.84579

29.44098

-0.59519

 

        Both NY Met championships are on here (hint, hint Steve Phillips). One that surprises me is the 1995 Atlanta Braves.  That’s probably colored by my perception of them now, for back in 1995 the Three Aces were still in their 20s. The only entries on here in the last twenty years are that team, the surprise 1990 Cincinnati Reds team, the Buckner Mets, and 1982’s St. Louis team that relied on speed, speed, and speed (they hit less HRs as a team that year than Barry Bonds did last year). Since there’s obviously a range of WS winners, let me get back to the original questions: “Do old teams sink? Do young teams rise?”

Taking our young group, they averaged 0.006 improvement on their winning percentages in their next season. So it doesn’t seem like young teams necessarily have to improve. Players may not pan out, injuries, and inconsistent play may do these growing teams in. The older group averaged a loss of 0.025 percentage points in the following season. This is a lot more significant, but still not very significant. It may make the difference between winning your division and some good golfing in October, though. Part of the problem is the old teams already are up high in the standings for the most part, and thus are more likely to fall instead of improve, whereas the young teams tend to be distributed more towards the bottom making it easier to move up. The overall correlation between age and next year’s performance is -0.158, and here’s the numbers by decade:

 

Decade

Correlation

1900s

-0.23707

1910s

-0.12591

1920s

-0.18686

1930s

-0.06989

1940s

-0.08596

1950s

-0.14612

1960s

-0.20734

1970s

-0.22002

1980s

-0.18413

1990s

-0.23588

Note I left 2000 off the chart. There’s only one season pair, so I decided to do without it. Bill James, in the section of Win Shares that I mentioned at the beginning, says he noticed this correlation during the period he was doing his Abstracts. Interestingly enough, the correlation was fairly low in the 1980s, only to swing back higher in the 1990s.

Some conclusions: having a veteran laden team isn’t a recipe for success, but completely lacking any veterans is dangerous for your team’s health, the game is getting older[8], and last year’s Diamondbacks were truly a “historical” team, in more than one sense of the word.[9]


[1] James, Win Shares, pg. 233

[2] James’ methodology multiplies WS by Age. I feel that we shouldn’t be looking at performance as measure of team contribution in this sense; rather, I felt that measures of playing time were more appropriate.

[3] It turns out my method is similar to the method used by Sean Forman in calculating Team Ages on baseballreference.com. His method differs from mine, in that he keeps hitter and pitcher averages separate, and the formulas used, although the batting formula is very similar, to arrive at these team ages. I was unaware of this method when I started my work. His weighted averages can be found here.

[4] Yes, pitchers in non-DH leagues are double counted under this method. They are counted for their PAs and IPs. I originally took out their hitting contributions, but I feel more comfortable leaving them in.

[5] Spotty DOB information caused problems doing calculations for any season before this.  Besides, it happily coincides with the first year the World Series was played.

[6] 1900s=1903-1909, 2000s=2000 and 2001.

[7] Two standard deviations less than the all time average. For older teams it was the top 37 to match the fact that were 37 “young” teams.

[8] As noted by Clay Davenport in his essay, “Graying the Game”, printed in Baseball Prospectus 2002.

[9] A quick acknowledgement to Sean Lahman, for his wonderful database, which I used in all these calculations.

 

 

 

Paul Mazurkiewicz Posted: October 29, 2002 at 06:00 AM | 11 comment(s) Login to Bookmark
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   1. Sean Forman Posted: October 30, 2002 at 01:59 AM (#606972)
The baby boom explains the dip in the 60's and 70's. The population at that time was much younger, so there is a reasonable expectation that more 20-year-olds would lead to more good young players able to make their way into the major leagues. They pushed out players from generations that were more competitive.

I know a guy who believes the baby boom is the main explanation for the pitching performances of the sixties and early 70's. With fewer prospective players the top athletes want to be batters. When the competition is higher some of them "settle" for being pitchers in order to get opportunities to play. He believes this starts in little league and high school.
   2. Dave Till Posted: October 30, 2002 at 01:59 AM (#606973)
The thought that occurred to me when I read this was that older players tend, on average, to be better than younger players because the poorer older players have already been weeded out. If a player is 23, and isn't very good, there's a chance he might improve; if a player is 33, and isn't very good, he will be out of baseball.

Bad teams tend to be younger teams for this reason: if you don't have any good veterans, there's no point in stocking up on poorer veterans, as Orioles fans well know. It's better to play a bunch of kids and hope that some of them will improve.
   3. Charles Saeger Posted: October 30, 2002 at 01:59 AM (#606974)
Interesting, but some questions remain:

* How well does team age make a forecast of later wins? Young teams win few games and old teams win many games. If young teams become better teams the next year and old teams become worse, this may be one of the reasons teams always regress to .500.

To look at this right, you must look at all teams in a winning percentage group, say all teams with winning percentages between .400 and .450. Look at how many games each team won the next year, and see how many games young teams and old teams won.

* I guess you know about Don Malcolm's look at age in the 2000 BBBA. What Don's showed was the span of age. The 1991 Texas Rangers had the young Ivan Rodriguez and the old Nolan Ryan. As Bobby Bragan would say, the mean shows that team as in the middle, but it is the mean of two outliers. Do these teams win more or fewer games than other teams of the same mean age?
   4. Lujack Posted: October 30, 2002 at 01:59 AM (#606975)
Is baseball age the players age as of a certain day in the season or his age at debut (i.e. 24 years, 34 days)?

If the former is true, then aren't there only two significant digits in your calculations?
   5. Ned Garvin: Male Prostitute Posted: October 30, 2002 at 01:59 AM (#606978)
Excellent study. I was quite surprised that there wasn't a clear change when free agency came about. Maybe I shouldn't have been.

I also wonder what the win-age correlation would be if one omitted teams such as the recent Marlins, who have clearly and purposely gotten young and bad. Of course there are non-competetive teams at all points in history, and I suspect those teams may comprise a significant fraction of that positive correlation shown.
   6. Paul Mazurkiewicz Posted: October 30, 2002 at 01:59 AM (#606980)
Thanks for all for reading. I wrote this a while ago, and need to reread it myself to fully appreciate the comments, but here goes so far:

Sean--that's an interesting theory about the pitching (I know it's not yours). It's hard to prove--although maybe with the multitude of options in sports today, this explains the hitter binge we had?

Charles--you caught me, I am not familiar with Malcolm's work...that's interesting stuff to look at. And the groupings by WINPCT are a good idea...I'm disappointed I didn't think of it myself.

Lujack--my team ages are as of July 1st of the season. My knowledge of significant digits is lacking right now...someone who remembers can please help me with this. I could go back and rewrite queries to calculate a more precise age...although at first blush I'd be worried about cutoff dates and making assumptions about season length/start.
   7. jeff angus Posted: October 31, 2002 at 01:59 AM (#606981)
Interesting work, and appreciate the footnotes.

A quick note on presentation. The first table would read better (and mean just as much), with just two digits after the decimal (hundredths of years).

Suspect the 1917-19 seasons and 1942-46 seasons should be out of the study because of demographic skew arising from factors external to baseball. Maybe that would have no effect on the trends, but it's worth considering anyway..

I think the age dip is, as Sean Forman suggests, a big uptick in the players available. He cites the baby-boom phenomenon, but I'd like to suggest racial integration <u>might</u> be as significant a difference-maker as the baby-boom. I think there's even a way to track it, which is to chart the average age of *assumed-white* ballplayers from '50- about '73 (i proffer '73 because it's the 15th season of full integration since the last Jim Crow major-league team integrated in '59).

Also think Saeger's suggestion is important. My memory of James' age study (though maybe a later add-on of the original) was he had a shape for age distribution based on 'young', 'prime years', and 'old'. Maybe you could consider creating clusters and having the computer assign teams to those clusters and see if that clarifies both "success" and "direction".
   8. Cris E Posted: October 31, 2002 at 02:00 AM (#606994)
I agree with the suggestion that race is an important factor in the drop in ages during the 60s. It would add to Sean's point about increased competition for jobs driving some older players out.

The increase starting in the 70s is most likely due to the DH.

The drop in the 90s may be due to the MIN/MON philosophy of not competing on the field for financial reasons, and running cheap kids out there instead. There were a lot of seasons of AA players in some of the "small markets" that would have done a lot to offset the normal, older, rosters.
   9. Lujack Posted: October 31, 2002 at 02:00 AM (#606998)
Right Scott S.

My point about the significant digits was that the difference in comparing decades seems to be less than a year in most cases and by using only two significant digits any number that you report as 28.3 may actually be closer to 28.8 in reality.
   10. Charles Saeger Posted: October 31, 2002 at 02:00 AM (#607001)
Some more thoughts:

* You might want to run the Win Share age means to see the differences. I do not think there will be large differences, but I think there might be some, and it may be worthwhile to look at those teams.

* As I see it, there are three main ways to weigh it: opportunity (PA/BFP), stolen opportunity (Outs/IP), and success (Win Shares or some way like it). As I said above, I wonder if any teams have huge differences in the three ways, who they are and what happened to them.

* Are there differences between young and old hitters and young and old pitchers? I guess age means less for pitchers, but I do not know.

* I know Bill James looked at matched pairs of young and old teams in an old Baseball Abstract.
   11. Vardibidian Posted: November 05, 2002 at 02:01 AM (#607065)
I'm curious whether and how teams age (using this number). That is, do old teams tend to age up to a certain point, and then get younger? Do they do so suddenly or gradually? Similarly, do young teams age slowly or suddenly? And does that have any correlation with success?

I suspect that old teams get young quickly, with a correlating drop in success (as the older stars get dumped or retire and are replaced with kids), while young teams age slowly (roster stays the same, with everybody one year older and one or two veterans added) and improve slowly. But that's a casual-fan observation, and I'd be curious to see if it is supported by the stats.

Thank you,
-Vardibidian.

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