So How Many Starters Does a Team Need, Then?

Watching the Braves rotation grab appendages has been tough this spring. Kris Medlen has ligament damage in his elbow, Brandon Beachy has biceps soreness, and Mike Minor survived a scarred urethra only to encounter shoulder soreness. None of the three is a lock to make the opening day rotation. And this is a team that brought two veteran free agents in for depth and had extra youth at the back end of their rotation. They might be fine without Ervin Santana, but yet that team does inspire a question. How many major-league ready starting pitchers should a competitive team field in a given year?

Starting from a theoretical angle, the answer seems almost easy. Any given starter has a 40% chance of hitting the disabled list at any given time, so if they all happen to hit the disabled list at the same time, you’ll want nine starting pitchers — .4 times eight is 3.2 missing starters and we’re talking worst-case scenarios here. You might have a young team. Younger pitchers can have as little as a 35% chance of hitting the DL in a given year (every year adds 1%) — a young rotation might only need eight. Both of those numbers feel like a lot. It also seems very unlikely that one team would see three guys go down at one time, to say nothing about 3.2 or 2.4 guys.

Well, how about that likelihood of multiple injuries at once then. Thanks to Jeff Zimmerman’s excellent work, we know that teams averaged 360 days lost to the DL from their starters, in six trips. Knowing that there will be six trips to the DL that average 60 days long, can we find out how likely it is that two (or more) starters will be on the DL at one time? Matt Murphy helped slice the data, and it looks like the following things are true of the average team in a given year, given the information above:

* There’s an 11% likelihood that two starters will be injured at the same time.
* There’s a 4% likelihood that three starters will be injured at the same time.
* Teams will need to use an eighth starter for a six games a season, on average.
* There’s even a 1% likelihood that *four* starters will be injured at the same time.
* Even if a team only suffers four 60-day DL stints, that team will only have a complete opening day rotation for 36 games (22% of the season).

Apparently I can’t read! The above is the case if only two starters are injured on a given team!! Here’s what the average team (six DL stints, 360 days) will suffer:

*10% likelihood that 4+ starters will be hurt at the same time (.082+.016+.001)
*32% likelihood that 3+ starters will be hurt (0.22 for exactly 3, plus the 4+ injured pitchers above)
*65% likelihood that at least 2 starters will be hurt at any given point in the season (105 games)

But we also know that year-long absences are skewing the data on some level. One 180-day stint from one pitcher is not the same as three 60-day stints. How about an empirical, retrospective angle?

We know from Jeff Sullivan’s excellent work that teams need about 32 starts from pitchers that weren’t in their top five. But how many people filled those posts? Answer: a lot. Since 2011, the average team has seen ten different pitchers start a game for them over the course of a single season.

The Rockies have needed 13 pitchers a season over the last three seasons, but they did try some different things with their rotation, so maybe they are an extreme case. It’s even more/less impressive that the Orioles have gone with a five-man rotation and needed more than 12 pitchers a year since the beginning of the 2011 season. But that might be about trying to find something that worked more than dealing with injury or depth concerns.

But it’s the Jays that show us a worst-case scenario when it comes to an injury-riddled staff. We know how many days they’ve lost to injury, and how they ranked in baseball last year, and now we know that they’ve needed, on average, 12.3 pitchers a year over the past three years.

The Braves had Mike Minor, Julio Teheran, Brandon Beachy, Kris Medlen, Alex Wood, David Hale, Gavin Floyd and Freddy Garcia lined up on their depth chart this year and it seemed like enough. Now it looks like it might not have been enough, even in a normal year where all the injuries didn’t happen at exactly the same time.