Last week, the Red Sox announced that they would be retiring Wade Boggs’ number 26. This will be the 9th retired number in the Red Sox organization (10 if you include the league-wide retirement of Jackie Robinson’s #42), and the 5th retirement since 2000. With that, two questions are begged: 1) Are MLB teams retiring numbers more than they had historically? and 2) When will every team run out of numbers to use?

We’ll take a look at each question separately. First, are MLB teams retiring numbers more than they have historically? The answer: it depends. Certainly the rate of retirements is increased from 2010 compared to 1950, but it’s hard to say that the numbers in the 2000s are dramatically higher than those in the 1980s. Don’t believe me? Here’s a chart with the quantity of retired MLB uniform numbers over time. I have excluded the one-time league-wide retirement of Jackie Robinson’s #42 in 1997 because it is a one-time event that would otherwise skew the numbers.

As you can see, there’s a sharp increase that begins in around the 1970s and continues upward. “That corresponds with MLB expansion quite nicely,” you may note, but when we remove teams that did not exist in 1940, we get the following chart:

Overall the numbers are pretty similar. So what it seems is that the answer to our first question is “kinda sorta yes.” MLB teams are retiring numbers at accelerating rates. The chart resembles the old distance-velocity-acceleration chart anyone who took high school physics has probably already forgotten. As time increases, the curve increases in an exponential fashion. We’ve established that we are in real danger of running out of uniform numbers.

That, however, is on the aggregate level. As we look at individual teams, we see an even more dramatic story. Take the New York Yankees. In 1965, the team had merely 3 retired numbers. In 1980 they had 7. In 1990? 13. Today, they have 20 numbers retired, eliminating the possibility of almost one out of every five uniform numbers from being used by active players. Here’s how the Yankees look over time.

Using these graphs and running a regression, we can start to forecast when every MLB team will run out of individual uniform numbers, answering the second question posed above. Before I show you the dates, I’ll include some notes about the data:

1) I’ve assumed that uniforms can have 2 numbers maximum, and that 0 and 00 are considered “different numbers” (given that 16 players have worn 0 and 20 have worn 00), however single digit numbers preceded by a 0 are not included (e.g. 03 is not permitted). This gives 101 possible uniform number combinations (0-99 + 00).

2) I have included Jackie Robinson’s league-wide retirement of 42, but removed double counts of other teams who have retired the number 42. The Cardinals, Dodgers, and Yankees have also retired 42, so that was not counted twice.

3) Similarly, if a team retired one number for two players, it counted as only one retirement. This one should be obvious, but the Yankees number 8 was retired for Yogi Berra and Bill Dickey, it counts as only one number retirement.

4) The line of best fit used a quadratic (ax^2+bx+c) equation where the data could support it, otherwise a linear line of best fit was used. The longer a team has retired numbers, the more data that exists, and the more reasonable it is to forecast an exponential type growth of number retirements. For teams that have not retired many numbers, a linear function was used as it will be a more reasonable estimate.

5) I have obviously ignored any unretirements or “releases” of uniform numbers. I am, for the purposes of this, assuming that the teams will ust be surprised one day when they don’t have enough numbers, and that no “counter measures” will be used. We all know this is unlikely, unless we add a third digit to uniforms or start using letters.

6) I have included the number when the teams cannot fill a 40 man roster, a 25 man roster, and all numbers will be gone. I also included the line of best fit, plus the r^2 value so you can see how well the line fits with the current data.

Without further ado, the numbers: