|David Ortiz, who destroyed a dugout phone during|
a 2013 ejection, is MLB's resident veteran hothead.
To answer such a question, we consider a metric known as Ejection Rate: It's a fairly simple calculation of Games Played divided by Ejections. For instance, if Player A has 10 career games under his belt and was ejected one time, his Ejection Rate would be 10, or one ejection per 10 games played. If he was ejected twice over the 10-game span, his ejection rate would be five, or one ejection for every five games played.
Taking into account our veteran players, defined by those active with a minimum 2000 games played, we see 13 names from A-Rod to Aramis. They are listed below ranked by games played (G) and with career ejections listed thereafter:
Alex Rodriguez - 2624 G - 5 Ejections
Adrian Beltre - 2476 G - 2 Ejections
Bobby Abreu (still listed as a free agent) - 2425 G - 5 Ejections
Torii Hunter - 2287 G - 9 Ejections
Ichiro Suzuki - 2260 G - 1 Ejection
Carlos Beltran - 2222 G - 4 Ejections
Andruw Jones (still a free agent) - 2196 G - 0 Ejections
Albert Pujols - 2173 G - 6 Ejections
Miguel Tejada (FA) - 2171 G - 0 Ejections
David Ortiz - 2163 G - 11 Ejections
Raul Ibanez (FA) - 2161 G - 1 Ejection
Jimmy Rollins - 2150 G - 2 Ejections
Aramis Ramirez - 2106 G - 5 Ejections
Sorting the players by ejection rate, we can answer the question of which veteran is most prone to ejection:
1. David Ortiz - One ejection per 197 Games Played
2. Torii Hunter - 254 G
3. Albert Pujols - 362 G
4. Aramis Ramirez - 421 G
5. Bobby Abreu - 485 G
6. Alex Rodriguez - 525 G
7. Carlos Beltran - 556 G
8. Jimmy Rollins - 1075 G
9. Adrian Beltre - 1238 G
10. Raul Ibanez - 2161 G
11. Ichiro Suzuki - 2260 G
12. Miguel Tejada - (Null)
12. Andruw Jones - (Null)
The average ejection rate of these players with 2000+ G is 930, or one ejection for every 930 games played. David Ortiz, whose one ejection per 197 games is nearly five times as frequent, is therefore MLB's resident veteran hothead as defined by ejection rate, with Torii Hunter not far behind. And speaking of Milton Bradley, MB was ejected 19 times over 1042 games played, for an ejection rate of once every 55 games played, which is followed by Gary Sheffield's one-per-78 statistic. Bradley, thus, would be baseball's generational hothead player. And since I know you're curious, AJ Pierzynski's nine ejections over 1865 games is a rate of one-per-207, which makes him more ejection prone than Torii Hunter, but less than Big Papi.
The most ejection-prone player in the league today, however, is Bryce Harper, whose five ejections over 416 games played is a one-in-83 rate, albeit with the small sample size ratio of 5/416. Matt Kemp is not far behind with 11 ejections over 1177 games, or one-in-107.
As an aside, umpires have this statistic, too, and since 2005, Marty Foster has ruled this category with 53 ejections from 2005-2014 over 1260 games officiated for a rate of one ejection for every 23.8 (make it 24) games officiated. Joe West also had 53 ejections over this span, but worked 1306 games, for a rate of one ejection for every 24.6 (make it 27) games officiated.