When should you draft an injured player?

Baseball players get hurt. It happens to every player at some point. They'll miss time due to the injury, and even after they return they won't likely be performing at their full capacity right away, if they even get back there at all during the season.

When a good player gets hurt before the season, a player you may want on your fantasy team, the question then becomes when they should be drafted. Obviously, they shouldn't be drafted as if they were healthy, because they will not give you production equal to the value of that draft spot. You have to assess the value they will give you during the season, and draft accordingly.

There's an inherent uncertainty to this, since information on a) when the player will return, and b) how the player will produce when he does return is wholly imperfect. There may be a timetable for return, but the player may race ahead of or fall behind that projection. Similarly, a player is likely to return before he is 100% healthy, but how much that affects production is an open question.

Take, for example, Chase Utley. Before his knee issues cropped up, he was generally considered one of the top three second basemen available. Now that he'll be out for an indeterminate period of time, and his production when he does return is in question, his value has dropped. So how far should he fall in the draft before he is worth a pick?

The first determination you have to make when assessing an injured player is when he'll be healthy enough to start for your fantasy team. A player may get back into his actual team's lineup when he's "70% healthy," but this may not be enough production to start him on your team. Assuming that a phrase such as "70% healthy" roughly translates to "will perform at 70% of his expected pre-injury production," then he isn't worth starting until "X% healthy" has a value of X= 1/(1+VORP). At that point, he'll be performing at exactly the level of a replacement player. In this case, since a player is missing time, VORP cannot be assessed in terms of total season points; instead it should be assessed in terms of production rate. The best measure for this would be either points per game or points per PA.

Using Bernie's Bombers scoring, Utley's xPts/PA is 0.9524, which gives him an xPts/PA VORP of 0.101. This means he shouldn't be in your lineup until he's "90% healthy," since 1/1.101 = 0.908.

Next, we have to make an assumption as to when Utley will be 90% healthy. The outlook on his knee isn't so good, so let's assume he won't be back in action and worth starting on a fantasy team until right after the All-Star Break. Further, let's assume he increases production by 1% per week. That would mean his first week back on your roster he's at 90%, then 91% the following week, 92% the week after that, etc. And further, let's assume he hits a plateau at 95% capacity, since the injury is a) irreversible damage to knee cartilage, b) knee injuries affect all aspects of a player's game, and c) actually playing won't help the knee heal.

As you can see, that's a lot of assumptions. That's what makes drafting injured players so difficult, and why most people try to stay away as much as possible. But let's press on.

Up until the All-Star Break, you have to play a different second baseman. Chances are, that second baseman will be at or around replacement level. A full-season projection for a replacement-level second baseman is 523.25 points. For the first 14 weeks of the season, that's your expected prorated production. The season is 25 weeks long, so for the first 14 weeks your 2B production will be 14*(523.25/25) = 293 points, or about 21 points per week. During Utley's first week back (week 15) he'll also be at replacement, so he'll net you 21 points. The next week (week 16) he'll be at 91%, or 21.04 points, then 21.27 during week 17, 21.5 during week 18, 21.74 during week 19, and then 22 points per week for weeks 20-25.

That puts your expected 2B production over the course of the season at the sum of your expected pre-All-Star Break production from a replacement player plus Utley's expected weekly post-return production, or 531.55 points. Essentially, drafting Utley as your primary 2B is equivalent to drafting a 2B with an xPts value of 531.55 points.

Using this value, we can then calculate adj PAR for your 2B spot. Using the adj PAR formula of ((xPts^2)-(xPts*rPts))/rPts, you have ((531.55^2)-(531.55*523.25))/523.25, which is 8.432. That yields rankings for your expected 2B production at #80 for xPts and #146 for adj PAR. The average of those two (113) puts Utley at #100 overall, or roughly the end of the 11th round.

So, under these assumptions, Chase Utley should fall from the 2nd round to somewhere in the range of the 11th-12th round due to lost production. That makes him roughly the #9 second baseman, below Ian Kinsler and Brian Roberts but above Kelly Johnson and Aaron Hill. Obviously, Roberts has injury concerns of his own, so perhaps Utley is the #8 second baseman.

Now, these calculations are made under a number of assumptions about playing time, post-injury production, etc, any or all of which may (actually, will) be wrong to varying degrees. Utley may miss more or less than 14 weeks, and (as a player who is known for toughness) he may produce at up to 100% production at some point after he gets back, and perhaps fairly soon after he returns. It also assumes you draft essentially a replacement-level player and not a player whose production is significantly below replacement.

The point isn't the specific numbers on Utley, the point is that this is how you go about discounting players who have a preseason injury. You make assumptions about return date and post-return efficacy, and follow these steps.