"Millionaires vs Billionaires" (Part 2: What Percentage Of MLB Players Reach Free Agency?)

I asked the SABR-L community: "What Percentage Of MLB Players Reach Free Agency?" I wondered how many major league players last long enough to put themselves on the "open market".

Two responses came in today:

Pete Ridges wrote:

Or, Do most players have short careers?

1) Let's start by looking at all the position players whose last game was in 2012, say. I count 98 players.

86 of 98 played at least 10 games in their career.

60 of 98 played at least 100 games.

21 of 98 played at least 1000 games.

 7 of 98 played at least 2000 games.

 1 of 98 (Omar Vizquel) played 2968 games.

The median was 170 games, but the mean is 492 games. Players around the median include Mike McCoy, Jason Donald, Jeff Clement, Scott Moore...if you can recognise half of the names on the list, you must have been paying very close attention.

2) But if, instead, you pick a random box score from 10 or 20 years ago, you may well recognise most of the names. You may well find that all (not just 60%) of the position players in that game played at least 100 career games, and that about half played over 1000 games.

On the list of 98 players, Omar Vizquel and Eddy Rodriguez [Padres catcher, 2 games] count the same: each is one of the 98. But if you pick a box score, you are far more likely to come across Vizquel than Rodriguez. The top 12 players on that list had a total of 24,454 games: the other 86 players totalled only 23,717 games. In fact, the 49 players below the median totalled 2611 games, which is fewer than Vizquel alone. So, picking a random game, you are slightly more likely to pick a box score containing Omar Vizquel than a game with even one player who was below the median.

So, which question are we interested in? The percentage of all the players in the encyclopedia, or the percentage of players in a typical game?

Finally, note that the number of players with single-digit career games depends partly on transaction rules, such as September roster sizes and how many options a player has. These rules may not be relevant to other discussions.

Sean Lahman wrote:

Talent is not normally distributed at the MLB level, as Bill James pointed out in his abstracts, because big league players represent the far right end of the bell curve. It's important to remember this when looking at salaries or career lengths.

There aren't any public data sets (afaik) that track service time, but we can approximate that by looking at games played, at least for batters. I looked at the 763 players who made their debut from 2005-2012, and here's how their careers panned out. I used 125 games as a proxy to measure a full season in the big leagues.

Sixty percent of players played less than three seasons, which means they didn't play long enough to become eligible for arbitration. 25% of players made it to six seasons, which is the threshold for free agency. Roughly 10% of players made it to 10 seasons. Raw data is below. I think any methodology would produce a similar shape.

Career Games Played
 Pct       Games    Cum. %
39.3%      1-125
12.1%    126-250   (51.4%)
 8.6%    251-375   (60.0%)
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 7.1%    376-500   (67.1%)
 4.6%    501-625   (71.7%)
 3.3%    626-750   (75.0%)
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 4.6%    751-875   (79.6%)
 3.6%    876-1000  (83.2%)
 3.6%   1001-1125  (86.8%)
 3.1%   1126-1250  (89.9%)
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