Many of us have been frustrated at times this year with Kevin Cash pulling starters and particular Chris Archer earlier than maybe expected in games and in result having the Rays using the most bullpen innings in baseball. I've read around twitter and in comments about him being scared of the 3rd time through the order and that is kind of right, but it is actually the 4th time through the order that Cash and more than likely Rays management want nothing to do with.
Here is a breakdown of the starters so far this year and when they've been pulled seems to have nothing to do with inning, effectiveness, or pitch count.
Batters Faced (multiples will be in parentheses)
Chris Archer -19,21,22,24(4),25,26(5),27(2),29,30
Jake Odorizzi -18(injury),22,24,25,26,27(4),28(2),29
Alex Colome - 15(2),18,20(3),22,23,26(2),29,30
Nathan Karns -18,19,21,22(2),23,24,25(2),26,27,29,30
Erasmo Ramirez -17,20(2),21,22,23,24,27(2)
Drew Smyly - 18,22,23
Matt Andriese -15,16,17,19,20,24
Andriese seems to be more in line with the 3rd time mark but everyone else is right at the 4th time cut-off. only 13% of the time (10 out of 77 not counting Geltz) has a pitcher been allowed to see an order for the 4th time with a max of 30 BF.
Here are the PC for the game over 27 BF
30 BF 97 PC 6 IP 5 ER
29 BF 99 PC 6 IP 11 ER
29 BF 100 PC 8 IP 2 R (1 ER)
30 BF 105 PC 8 IP 1 ER
7 other times Archer has thrown 105 or more pitches in a start, all with 27 or less batters faced.
28 BF 98 PC 6 IP 4 ER
28 BF 98 PC 6.1 IP 4 ER
29 BF 103 PC 8 IP 1 ER
3 times Odorizzi has thrown more than 103 pitches with 27 or less BF
28 BF 99 PC 6 IP 2 ER
30 BF 106 PC 5.2 IP 5 R (4 ER)
29 BF 108 PC 6 IP 5 ER
As you can see 6 of the 10 outings involved more than 4 runs being scored and only 3 times has a pitcher gone more than 6.1 while facing this many batters. I don't believe I like this strategy but it is working so far for Cash and Co. but I think it is safe to say that as we near the halfway point in the season he has a pretty strong cut off point for his starters and we should all but take the idea of starters getting complete games out of our mindset.
FWIW as a comparison, Chris Archer's biggest competition possibly for All-Star game starter Dallas Kuechel alone as 12 starts in which he has face 28 or more batters and former Rays Cy Young winner David Price has 10.