Understanding the "injury prone" roster

In the Fake Teams Dynasty league, I drafted Jose Reyes, Josh Hamilton, Joe Mauer, Chase Utley, Brett Anderson, Jake Peavy, Francisco Liriano, Erik Bedard, and Jason Bay at some point throughout the draft. These are all players that made trips to the disabled list in 2011. At first glance, this looks like an awful decision, as these "injury prone" players are more likely to get injured than other players.

I won't argue that point, because the probably that Jose Reyes gets a hamstring injury is higher than Starlin Castro, or Chase Utley getting a knee injury over Robinson Cano. For that same reason, Chase Utley is drafted way below Robinson Cano when they offer similar true talent levels. Cano has the age advantage but Utley would still be considered a first or second round talent if he didn't have these injury riddled seasons.

So why exactly would I draft these types of players?

Creating a perfect stat to identify the risk involved with drafting an injury prone player is as close to impossible as it gets. Every injury is different, every player reacts different to injuries, That isn't to say however, that we can't approximate injuries based on what we know. According to a study done by, Babson College about 400 players hit the DL every year. There are 1280 players that will be on a team's 40 man roster at any given point in the season. Some of these players still qualify for the minor league disabled list however. We are looking at a 1/3 to 1/4 chance of a player hitting the DL. Position matters in this case however, as pitchers are obviously much more volatile. Catchers are also much riskier than the average position player, which has a lot to do with why catchers never live up to the draft hype. Pitchers also tend to spend longer on the DL as the number of minor pitching injuries is relatively small.

Let's dive into the pitchers. Jeff Zimmerman of Fangraphs and Rotographs came up with a formula to figure out the likelihood of a pitcher hitting the DL, and it can be found here. Let's compare a couple pitchers.

Jake Peavy is one of the most injury prone pitchers in the business. He hasn't been healthy in one hell of a long time. He is the ultimate case. The likelihood that Jake Peavy hits the DL in 2012 is somewhere in the neighbourhood of 65%. Looking at this alone, it seems like an awful investment to make. When healthy, however, Peavy is capable of dominance, and his 3.21 FIP shows just that. That's the same range as Tim Lincecum. Am I saying he is that good? No, but he is more than capable of pitching like an ace.

Tim Lincecum, a relatively healthy pitcher who hasn't spent any time on the DL in recent seasons is still at risk to get injured, and probably more than you think. About 40% of healthy pitchers will get hurt in a given season.

The difference? Jake Peavy went in the 14th round for $2, Tim Lincecum went in 2nd round for $12. Seeing as the amount of minor injuries that pitchers get is so minuscule in comparison to the major injuries, the days spent on the DL would be rather similar.

Jake Peavy has top 4 round upside, but is discounted so severely for his injury prone label that he drops down to the 14th round. Tim Lincecum is being drafted exactly where his upside is. He is much more likely to reach his upside than Peavy is, but he is also much more likely to provide value less than his draft position. You can call the Peavy, Liriano, Anderson and Bedard investments risky if you wish, but they aren't the true risky investments. If they get injured or perform poorly because of their injury past, the investment is minimal where as a pitcher drafted when healthy provides insane amounts of downside. There is no where to go but down for these pitchers. In 2 years, there is a 60% chance my pitchers are injured, and there is a greater chance they are ineffective. In two years time, Tim Lincecum has a 40% chance of getting hurt, and there is also a greater chance that he is ineffective. It's easy to point at my pitchers and say it's because they were injury prone and poor investments, but what would you call the 40% chance that Lincecum has? Bad luck or a poor investment?

Enough about pitchers, we already know they get hurt. Batters provide much of the same risk however. Josh Hamilton is a perennial injury victim. Last season, he was drafted as a top 10 player, and rightfully so. He is one of the most talented hitters in baseball. Surprise surprise, he got hurt and missed a total of 41 games last season. He of course, did not provide top 10 value, but still put up solid numbers across the board, enough to warrant a selection in the 4th or 5th round. So why exactly, is Hamilton lasting so long in drafts? I managed to pick him up with the 49th pick, two picks after Hunter Pence. What is the probability that Hamilton plays 160 games? Less than 5%. What is the probability he plays more than 120 games? More than 50%. If he plays 120 games, he fulfills his draft value and puts up similar stats to Hunter Pence. If he plays more than 120 games, he puts up numbers that exceed his draft value. If he plays less than 120 games, he puts up numbers that fall well below his draft value. This in turn, ends up looking like a normal curve.

via www.tushar-mehta.com

10 is his draft value, 18 is first round value, 2 is less than 20 games played. Hunter Pence on the other hand, looks like the left side of this normal curve. 10 is his draft value, 10 is his upside, and 2 is less than 20 games played. Both players are able to put up 4th round value, except one of the two is able to put up first round value. Josh Hamilton is the prospect everyone drafts, but instead of having a high probability of being ineffective, he has a higher probability of being hurt, but he still has that massive upside we all seek.

Let's use the values listed above in the graph as a way to calculate expected probability. The 10 represents their draft value. Hunter Pence is rarely injured, so he is more likely to hit his true talent level than Hamilton is. Let's give him a 50% chance of hitting it. This is fairly generous considering only half of first round picks are able to maintain their draft status, 4th rounders are much more volatile. Let's give him a 10% of exceeding his potential draft slot, as once again, this is generous considering his performance history. That leaves 40%. 20% chance he performs well, but not quite up to his draft slot, 5% chance he is the victim of poor luck and a 15% chance he gets injured or is ineffective.

That gives us:

E(X) = (.50)(10)+(.10)(12)+(.20)(8)+(.05)(6)+(.15)(4)

E(X) = 8.7

Let's do the same for Hamilton. 50% chance he plays 120 games at his draft slot. 5% chance he plays 160 game at first round value, 5% chance he gets injured for the entire season and give's you no value, 20% chance he plays 140 games, 5% chance he is the victim of poor luck AND only play 120 games, 10% chance he is more injured for more than 40 games and 5% chance he is ineffective.

That gives us:

E(X) = (.50)(10)+(.05)(18)+(.05)(0)+(.2)(12)+(.05)(6)+(.10)(8)+(.05)(4)

E(X) = 9.6

Again, this is being generous towards Hunter Pence as I totally discounted the possibility that he misses an entire season due to a large injury. Is this an exact science? Hell no, but if this was, baseball would be too easy. I was accused of not using numbers in the same way I do with my other drafting and managing philosophies, so I thought I would prove that it was an incorrect assumption.

Chase Utley is in the exact same boat. He was an 8th round draft pick. His true talent suggests that he is a first or second round player, but his injuries have limited the numbers of games played over the past few seasons. If he plays another season while injured and dealing with the lingering effects of his knee surgery, he performs at 8th round value, while having the upside to do much better. Joe Mauer and Jason Bay are once again, in the same boat.

The biggest issue here lies within the fact that people discount injury prone players for the possibility of being injured or ineffective but do not make the same assumption for healthy players. No one is saying Chase Utley is healthier than Robinson Cano, but to assume that Cano is not at risk of injury because of his past is absurdly foolish.

What did this mean for you? Your draft strategy should include tons of upside late in drafts, and where people chase prospects, chase the "injury prone" players. You aren't paying for them assuming they will stay healthy, so there is no risk of losing a large investment involved. For seasonal leagues, it could bite you in the ass, but in dynasty leagues and keeper leagues, you should be all over this. Your roster will not look the same in three years, I guarantee it. You don't win the league by having people perform at their draft slot, you win because of players like Ellsbury who come off injured seasons to become superstars. Add the surplus value you receive from the injury prone players to your proven stars and you can dominate a league.