Fun With Age Curves


A thought exercise.  Let's say that you're Brian Agler, the coach and GM of the Seattle Storm.  You're doing very very well in the WNBA in 2010, when all of a sudden you get a phone call from Marynell Meadors, the coach and GM of the Atlanta Dream.

"Brian, this is Marynell," you hear.  "I have a trade proposal for you.  I will trade you Angel McCoughtry for Lauren Jackson - straight up.  What do you say?  Get back to me."

At first, you think this is a no-brainer and Meadors is pulling your leg.  Jackson is probably one of the greatest players in basketball history.  McCoughtry is great, but not Jackson-level great...not yet, anyway.  Jackson has three MVPs and is probably going to have a fourth one someday, if not this year, then the year following.  You're very tempted to call up Meadors and thank her for calling...but that she should try to palm that one on someone else.

Then, as you pick up the phone, you begin to have doubts.  Yes, Jackson is a great player...but she's also 29 years old.  How many more years is Jackson going to play?  What's her future like?  If she's reached her physical peak, then we're hitting the decline years of Jackson.  Angel McCoughtry, on the other hand, is 23 years old, fresh and free from injury.  She's an MVP caliber player, so who's to say that she won't have three MVPs someday?  She hasn't reached her peak yet, and she's just going to get better and better until she does reach it.  Didn't Branch Rickey say something like, "better to trade a player too early, than too late?"

What do you do?

It would be a great thing if we knew how much "future value" a player had.  If someone could give us a peek at the future stats of McCoughtry and Jackson from now until retirement, it might be an easy decision.  This is why being a GM is hard; ofttimes you find yourself on the wrong side of history.  Either decision could be a foolish one.  McCoughtry might never be an MVP player. Jackson could decline as a player starting...tomorrow. 

Age curves and other predictive metrics are attempts to get on the "right side" of history.  All sorts of attempt have been made by basketball statheads to predict how much value a player has earned of their total value, based on age.  Some of these metrics are very simple ones, others are very complex.  Some stat people like Kevin Pelton have given season-per-season progression a great deal of thought, down to how individual stats (field goal percentage, turnovers, rebounds) change over time.

The problem turns out to be a very complex one.  Players simply don't age the same.  The learning curve of the WNBA is a very steep one.  Some young players come into the league with a weakness, and after a week of play, it seems that every other player in the league knows that weakness and tries to exploit it.  Some players are driven out of the league after three years, the flaws in their game exposed.  Other players never seem to age at all, pumping out high-volume year after high-volume year even after their traditional peak years.  Lisa Leslie could still be playing in this league if she desired to.  The process of averaging destroys the distinctions.

Even so, let's make an attempt.  What we need is some way to determine a player's cumulative value.  I'll use a metric called adjusted wins score, which is a linear metric.  It can be used to assign value to the individual season of a player or the player's entire career. 

The next step is to determine the total adjusted wins score for players at particular ages.  I've created a tool that can give me a player's career stats by age:  if I want to know what Lisa Leslie's stat line was at age 25 or age 26, I can do that. 

The final step is to create an average career adjusted wins score by age.  In other words, if we followed all players in the WNBA only up to year 24, what would be their average career adjusted wins score?  How about for age 25?  How about for age 26?

Since this is a cumulative metric, we'd expect the numbers to increase with increasing ages.  We continue to process to age 50 - Nancy Lieberman's final year - and then examine the results.


Age    Pool Size    Avg Adj WS

19    4    3.30
20    12    9.98
21    97    3.65
22    317    5.46
23    412    11.44
24    456    18.32
25    505    24.01
26    536    28.34
27    560    33.68
28    582    37.26
29    596    40.30
30    615    42.38
31    629    44.35
32    638    46.19
33    643    48.54
34    651    50.28
35    651    51.89
36    652    52.77
37    653    53.40
38    655    53.47
39    656    53.35
40    656    53.37
       
50    656    53.37

We see that there are a few glitches in the system.  Average career adjusted win score fluctuates in a negative direction for that rare group of players that starts at age 19 and 20.  In order for a player to start at that age, they are most likely a very good international player.  What happens is that this cohort of players is linked with an average group of college players coming into the WNBA at age 21, and the average career adjusted win score decreases.

However, the career number goes up...until age 39, when it regresses slightly.  The two problems are that adjusted win score can be a negative value, and that 38 year old players have earned virtually all of their value.  By 37, most players are pretty much used up.

We come up with the final cumulative age value curve based on a 22 year old player:

22    10.24%
23    21.43%
24    34.33%
25    44.99%
26    53.10%
27    63.12%
28    69.82%
29    75.51%
30    79.42%
31    83.11%
32    86.55%
33    90.96%
34    94.21%
35    97.23%
36    98.88%
37    100.00%
38    100.00%
39    100.00%
40    100.00%

In short, at the end of the average player's first season, she's earned 10.2 percent of her total career value.  At the end of her second, she's earned 21.4 percent and so on.  Her value has reached its half-way point at the end of the season in which she turns 26 years old.

Now, let's look at the case of McCoughtry and Jackson again.

McCoughtry earned 74.5 AWS points at the end of her first season as a 22 year old.  That's 10.2 percent of her value.  This implies that McCoughtry will earn 727.5 AWS points over her career, and that she has 653 more AWS points to go.

Jackson has earned 1284.5 points during her career, and Jackson was 28 at the end of the 2009 season.  She should have earned 69.82 percent of her value.  This implies that Jackson will earn 1839.7 AWS points over her career, giving her 555.2 more AWS points to go.

So if you follow these assumptions - and oh, boy, there is a lot you're taking on faith here - if you're Brian Agler you welcome Angel McCoughtry to the Storm and break a lot of hearts in the process.

Let's count the assumptions.  All players don't age the same.  Jackson might never decline, pumping out consistent value until she reaches the upper limits of the age curve.  Furthermore, the further back you go in age the more volatile the projection becomes.  Can you really predict a player's entire career based on a single year?  Let's factor in outside forces such as injuries and personality issues (maybe McCoughtry will become a missionary) and the simple fact that some players are better fits for coaching styles than other players are.

Add the admission that single-number metrics can't encapsulate everything there is about a player - the little details that coaches and others who can really evaluate the small components of a player's game - and it seems to be an exercise in futility.  But, in a crunch, it might provide some illumination about a player's future prospects and it could be a simple tool used to think about trades.

What about Plenette Pierson for Tiffany Jackson?

Pierson:  12.9 career AWS to age 27, 20.4 projected career AWS, 7.5 AWS points to go
T. Jackson:  42.6 career AWS to age 24, 124.3 projected career AWS, 81.7 AWS points to go.

Nolan Richardson hates Plenette Pierson, and because adjusted wins score as a linear metric also hates Plenette Pierson, Jackson wins in a walk.  (Why can't Plenette Pierson get any love?)

Okay.  That was a freak evaluation.  Let's take the biggest trade of the year:

Liberty:  gets Cappie Pondexter and Kelly Mazzante, gives up Shameka Christon and Cathrine Kraayeveld
Sky:  gets Shameka Christon and Cathrine Kraayeveld, gives up Candice Dupree
Mercury: gets Candice Dupree, gives up Pondexter and Mazzante

The unearned career AWS of each player in question:

Pondexter:  248.7 AWS
Mazzante:  67.5 AWS
Christon:  34.5 AWS
Kraayveld:  79.5 AWS
Dupree:  556.3 AWS

Liberty:  248.7 + 67.5 - 34.5 - 79.5 = 202.2
Sky:  34.5 + 79.5 - 556.3 = -442.3
Mercury:  556.3 - 248.7 - 67.5  = 240.1

Result:  the winner is Phoenix, simply because they got a young player of Candice Dupree's caliber - but New York comes off well too in that they get Pondexter.  The big loser is the Sky.  Adjusted wins score thinks better of Kraayeveld than it does Christon, but even put together they don't match Dupree's overall unearned future value.

As you can tell, the above hinges on yet another assumption - that adjusted wins score is an accurate value of worth.  Suppose you don't like AWS.  You could go to wins score which is adjusted wins score's predecessor.  You could find a way to turn John Hollinger's PER into some sort of cumulative metric - Plenette Pierson has a higher career PER than Tiffany Jackson, so PER might make more sense that AWS. You could even use cumulative box scores value, or some other metric.

Even if you choose a different metric you will be building the assumptions that come with that metric into the model.  Some metrics like certain kinds of players and some metrics hate certain kinds of players.  Ask Plenette Pierson and Shameka Christon.

And in the end, it all comes down to a lot more than a statline.  What kinds of players bring value to a team?  What kind of value?   Do you think of present-day value or future value?  Answering these kinds of questions can give many a stathead - much less many a WNBA GM - present-day conniptions.

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