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Six Six Six - A Numerical Repudiation of the Six Man Rotation

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I've seen some commenters, here and elsewhere, discuss the idea of a six-man rotation should the Cardinals sign Roy Oswalt. What follows is a set of tables that should illustrate why this is a bad idea. The best way I can put the argument in simple terms is that a six man rotation gives fewer starts to better pitchers in exchange for worse pitchers. There's no real evidence that this keeps pitchers healthier but that is the argued advantage. There's some evidence that high pitch counts in individual games are dangerous to pitchers but less evidence that a high number of games are dangerous if the pitcher stays on their rotation.

The claims are difficult to refute because there is a lack of hard evidence since no team has had a six man rotation. What we can do is run the numbers on run prevention using projections like ZiPS to estimate pitcher talent and scale the number of innings each pitcher would get accordingly. So I admit that some of the claimed advantages of a six man rotation are difficult to refute but that is primarily because they can't be proven either. They are simply unfalsifiable. What I can show is that more innings to worse pitchers is a bad idea.

A few notes:

  • FIP is being calculated from peripherals in Dan Szymborski's ZiPS projection system using a 3.2 league modifier.
  • All starters are assumed to make 30 starts in a 5 man rotation with the remaining 12 starts going to a replacement pitcher (Lance Lynn in this case). Starters make 26 starts in a 6 man rotation with a replacement pitcher getting 6 starts.
  • The bullpen is considered to be used the same under both circumstances with a replacement level reliever (Kyle McClellan) picking up any additional innings created in these scenarios. You can simplify this consideration by assuming that the innings per start for both Oswalt & Westbrook are equivalent. If you do the run totals don't effectively change since Westbrook's FIP projects the same as a middle reliever and he bumps a better reliever out of the bullpen. Literally nothing changes in that scenario, I've simply chosen to project Westbrook for fewer IP/GS than Oswalt.
  • Innings per start are a combination of my judgment and ZiPS projected innings per start.

You can certainly argue with these caveats but, in order to get a six man rotation to be advantageous, you have to make some radically different assumptions about pitcher effectiveness and playing time.

The first scenario is if the Cardinals stick with a five man rotation and don't sign Oswalt (BO5 = Before Oswalt 5 Starters).

Player Innings - BO5 ZiPS FIP Runs Scored - BO50
Adam Wainwright 195 3.20 69
Chris Carpenter 210 3.45 80
Jaime Garcia 180 3.50 70
Kyle Lohse 180 4.20 84
Jake Westbrook 165 4.35 79
Roy Oswalt 0 3.65 0
Replacements (Lynn) 60 3.85 25

That is a total of 990 innings across 162 starts. We'll see later that 30 starts from a five man rotation that includes Roy Oswalt is going to pitch 15 additional innings in this hypothetical example but we'll assign those to Kyle McClellan our default middle reliever. Remember that when we're adding innings to the bullpen, it's likely that the good relievers are already pitching as frequently as they can so the lesser relievers will be taking on the additional starter's innings.

Player Innings - BO5 ZiPS FIP Runs Scored - BO50
Reliever (McClellan) 15 4.5 7

This set of starters will allow a total of 407 runs plus 7 runs coming from middle relief. That is 414 runs in a total of 1005 innings. Now lets look at the same set of starts if we put Roy Oswalt in and use a 6 man rotation. They will pitch 992 innings in this scenario and leave a middle reliever with 13 innings.

Player Innings - AO6 ZiPS FIP Runs Scored - AO6
Adam Wainwright 169 3.20 60
Chris Carpenter 182 3.45 69
Jaime Garcia 156 3.50 60
Kyle Lohse 156 4.20 72
Jake Westbrook 143 4.35 69
Roy Oswalt 156 3.65 63
Replacements (Lynn) 30 3.85 12
Reliever (McClellan) 13 4.50 6

That is a total of 411 runs allowed. So if you sign Roy Oswalt and play a six man rotation you are essentially paying his entire salary for a 3 run upgrade. That's a hefty rate for less than half a win. The last scenario is after an Oswalt signing with a 5 man rotation (Jake Westbrook fades quietly into the night) and the rotation will accumulate 1005 innings so there will not be any additional middle reliever innings to account for.

Player Innings - AO5 ZiPS FIP Runs Scored - AO5
Adam Wainwright 195 3.2 69
Chris Carpenter 210 3.45 80
Jaime Garcia 180 3.5 70
Kyle Lohse 180 4.2 84
Jake Westbrook 0 4.35 0
Roy Oswalt 180 3.65 73
Replacements (Lynn) 60 3.85 25

This rotation yields 401 runs over 1005 innings. This is essentially a swap of Jake Westbook and Roy Oswalt. So we're talking about a 13 run upgrade.

(4.35-3.65) / 9 * 180 = 1.4

Take out the rounding errors and what we're seeing is that Roy Oswalt is a little more than a 1 win upgrade over Jake Westbrook. A six man rotation is not demonstrably better than a five man rotation with this set of pitchers. Additionally, this set of pitchers is something of a best case scenario for advocates of a six man rotation since all of the pitchers are above replacement level. For those teams with pitchers below replacement level (or just with worse pitchers in general) the penalty is far heavier since the gap between their pitchers talent level is greater than that between Adam Wainwright/Chris Carpenter/Jaime Garcia and Jake Westbrook.

As I'm filing this earlier and will be out of town for the remainder of the weekend, I won't have a chance to update this post if there is an actual Oswalt signing. I hope this serves as a dampener, however, to the idea of a six man rotation. The burden of proof resides with you to give some logical rationale or concrete numbers as to why the Cardinals would benefit from more starters.

A quick plug for Future Redbirds: Tomorrow will feature a question and answer session from John Vuch. Make sure and stop by.