Draft strategy: Injury risks can lead to big rewards (Part 2)

On Monday, I talked about why high-upside players make good late round draft picks and began to discuss why I prefer injury risks to players who have skills upside. Today, I’d like to finish giving you my thoughts on this matter.

This is actually a topic I haven’t discussed since I was writing at my original blog — an article I’m sure most of you have never seen. A recent discussion with Mike Podhorzer of Fantasy Pros 911, though, made me realize that I’ve never brought it up at THT before. Thanks, Mike!

Changing the way we think about draft picks

When most fantasy owners think about drafting, they think about each selection as picking a player. While this is what appears to be happening on the surface, what you’re actually doing with each selection is filling a roster spot. When you select Alex Rodriguez, you aren’t selecting Alex Rodriguez. You are selecting a set of stats, which will occupy the “3B” spot on your roster.

What happens, though, if A-Rod sustains a season-ending injury in the first game of the year? 0 at-bats, 0 hits, zeroes across the board. Did you just spend a first round pick on those stats, those zeroes? Not unless you leave A-Rod sit in the “3B” spot all season. More likely, you’ll drop him and pick up a replacement level third baseman.

We need to think about that first round pick as being spent on the “3B” spot, not on A-Rod. That “3B” spot will be filled by the combination of whoever was orginally selected to fill the “3B” spot — in this case, A-Rod — and whoever you pick up to replace him. You’re drafting a comprehensive “asset,” not a single player.

Real-life example

By now, some of you can probably see where I’m going with this. While the above example is an extreme one, let’s now look at one that’s more realistic.

Rickie Weeks is a guy whose underlying skills I really like, but he can never manage to stay healthy for a full-season. As such, we must dock his stats. Marcels has him projected for 450 ABs, and we can assume that the missing at-bats can be accounted for by his usual time on the DL. Are those 450 at-bats of production all we’d be paying for, though?

If you’ve followed my logic thus far, you’ll be shaking your head “no” right about now. Are you going to let Weeks sit in your “2B” spot while he sits on the DL, or are you going to put him on your DL and pick up someone to replace him? The latter, I would hope.

Below is a chart listing the THT projected value of Weeks, extrapolated to 450 at-bats. I’ve also listed Mark Ellis, a replacement level player who you could pick up off waivers once Weeks gets hurt, extrapolated to 150 at-bats (the name of the player is unimportant — again, it’s the stats that matter). The third line gives their combined totals.

| LAST        | AB  | BA   | HR | RBI | R   | SB | $    |
| Weeks       | 450 | .251 | 15 |  44 |  81 | 19 |  $ 7 |
| Mark Ellis  | 150 | .253 |  4 |  15 |  21 |  3 | -$20 |
| Weeks+Ellis | 600 | .252 | 19 |  59 | 102 | 22 |  $17 |

Over 450 at-bats, Weeks would be worth just $7. Over 150 at-bats, Ellis would be worth -$20. But because the selection of Weeks isn’t the selection of just those 450 at-bats, we combine them with 150 replacement level at-bats and, ta-da! His value jumps ten dollars! While Weeks himself is worth just $7, selecting him is akin to selecting an asset that is worth $17 to fill your “2B” spot.

Helping to understand

I understand that this may be a very difficult concept to wrap your head around at first. After all, we’ve always been taught that a replacement level player is such because he has zero marginal value (for some discussion on replacement level, if you’re not familiar, check out Paul Singman’s article here). This player is available to all teams at no cost, and therefore, provides no advantage whatsoever.

So how can you combine his -$20 value with Week’s $7 value and get $17? How can you take a $7 player and combine him with just a portion of a replacement level player and have that $7 actually rise? Again, very difficult to comprehend.

To help understand why this occurs, we must first understand that projected value is extremely reliant upon playing time. Look at the below chart, which shows how the value of Rickie Weeks and Mark Ellis would change based on the number of at-bats accrued.


And it’s like this for every player in baseball. The more at-bats, the higher the value. As you can see, though, it takes quite a few at-bats before a player even starts having positive value, which is why a 150 at-bat Mark Ellis is worth -$20. It’s also why those first 150 at-bats don’t appear to be very valuable, but once you are in the positive range, simply adding at-bats — even a small amount of replacement-level at-bats — causes that value to rise a good amount.

The dark blue line represents Ellis’s line affixed to Weeks’s line at the 450 at-bat level. While the line, from that point forward, isn’t as good as Weeks’s, it still adds a good amount of value (just as our tables above showed).

Back to the injury risk vs. skills upside question

Relating this back to our discussion from Monday, we can clearly see, now, that an injury risk is much more valuable than a player with skills upside because he is tying up fewer of his roster slot’s at-bats, even if their surface value is identical. He does not have to take a single step toward fulfilling his upside in order for you to receive more value than he alone is worth (and more than the player with skills upside is worth). And if you’re lucky, he will fulfill that potential and you’ll get even more value out of the deal:

A Hardball Times Update
Goodbye for now.
| LAST        | AB  | BA   | HR | RBI | R   | SB | $    |
| Weeks       | 600 | .251 | 20 |  58 | 109 | 25 |  $20 |

As you can see, if Weeks were to stay healthy and get 600 at-bats, he would be worth $20 — more than the Weeks/replacement level combo but not so much that you’ll be terribly disappointed if he never reaches this level… if you understand this concept, anyway.

Finally, we must consider that when we draft a $7 skills upside player, he needs to see a legitimate skills/production increase of $13 in order to reach his $20 upside. For a $7 Rickie Weeks to reach his $20 upside, though, he only need gain $3 in value because selecting by selecting a $7 Weeks you’re actually selecting a $17 “2B” asset.

All else being equal, the injury risk is the far, far better choice.

Concluding thoughts

As this article ran longer than anticipated, I’ll be posting a third part in the coming days discussing some of the players who would be worth targeting if you’re planning on using this strategy.

And as always, if you have any questions, comments, ideas, whatever, feel free to post a comment or e-mail me.

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Connecticut Mike
14 years ago

In a vacuum this seems fine and good, but I’ve never played in a league where there are an unlimited number of DL spots.  I understand that the value of the injured player is derived from tying up fewer of his team’s at-bats, but what if he is occupying an active roster spot that could be used for an uninjured players? 

If I play in a 15 team league with 20 roster spots and one DL spot, how would that change this analysis?  In my experience having a bunch of bench spots occupied by players on the DL is an absolute team-killer, and as a result I try to stay away from injury risks in all but the late rounds of a draft. 

Keep up the good work, I enjoy your articles.

Mike Ketchen
14 years ago


Everytime I think I find a new edge to exploit it appears you are writing about it within a week. Please stop! Lol keep up the good work man.

Donald Trump
14 years ago

I agree that the piece you are missing is that there might now be unlimited DL spots.  Maybe more importantly, weeks misses a lot of time but does not always go on the DL, thus you get a real life zero from him during these times, or maybe worse, you have to drop someone of value to pick up ellis to use for just a week.  There is real value lost when you have to do this.  Lastly, Weeks doesn’t just get injured and go on the DL on the same day, so you always lose some games due to the time it takes the team to put him on the DL.  This is especially costly in weekly leagues.

14 years ago

Didn’t know you’d have to spell it out like this—seemed like common sense that a baseline 150 ABs plus an above average 450 ABs would result in a player who was significantly above the margin.

The problem is that it assumes production in those limits ABs. Drafting a guy like Weeks could leave you holding the bag waiting for him to have that “one big week” where he turns it all around. Still, I’d much rather take a flier on a guy like Weeks than start a guy like Freddy Sanchez all season…

14 years ago

It all depends on

1 – depth of league

2 – DL spots available

3 – Transactions limits and frequency

I have always felt that injury risk players are never factored with their replacements numbers in mind..

It’s as simple as A + B = C

14 years ago

“In my experience having a bunch of bench spots occupied by players on the DL is an absolute team-killer…”

He is not advocating a team full of injury risk players, this is a bottom half strategy were you have marginal choices left for specific slots.

I don’t agree with the base arguement against this approach. Any player on the bench is giving you zero value. They have the “potential” to create value and they are not available to provide value to your competetition, but as long as they do not occupy a roster slot they provide zero stats. If I fill that spot with a DL for a few weeks what is the difference? The entire league will be dealing with the same DL limitations and this should help you maximize your returns from the bench.

Ed Schwehm
14 years ago

Derek, great point. I’ve never mentioned this to friends because of competitive advantage, but bravo for an excellent explanation.

They key point is that “projected value is extremely reliant upon playing time.” That’s what most people miss. A $7 player projected for 700PA is worth far less than a $7 player projected for 400PA.

Keep up the good writing!

14 years ago

Yeah, interesting thought.

There was a very similar point made yesterday at this website. Definitely worth reading:


14 years ago

How does this change in deep leagues?  AL or NL only or 16-20 teams?  Since the Replacement Players value is much lower, does that make this strategy not work?  Or does it still work because a large part of every roster is lower, so who cares if replacement player is lower?

Ed Schwehm
14 years ago

@neoforce: Since the replacement level is lower, the replacement stats will be worse (instead of Mark Ellis, you might be using Marco Scutaro). The combo might end up a few bucks less then, $14 instead of $17 (or something like that). So it still works, just not as well.

14 years ago

Longish post, so here is my point in a more succinct manner – This strategy should be modified in really deep leagues.  Because a replacement-level player is so bad in a deep league, it is probably better to actually grab the injury-prone player’s actual replacment early in the season (via late-round draft pick, early free agent pickup, or $1 at the auction), rather than grabbing a replacment-level player once the guy gets injured.

I don’t think the strategy works in deep leagues.  The shallower the league, the better the replacement level.  I play in a 15 team NL-only league with 11 active hitters (that also has a small minor league roster for each team). 

The replacement level player in that kind of league is a guy who gets 8 at-bats a week as a pinch hitter and defensive replacement. 

Or to put it another way, there is not really a free agent available that has any value as a starter for a couple weeks.  The only way I see the strategy working in a really deep league is if you actually draft, pick-up, or buy (at auction) Weeks’ replacment (Alcides Escobar?) to have him on stand-by for the expected injury.  Because I promise that in a really deep league, the backups for these guys are usually already sitting on some manager’s bench.  Better make it yours!

The strategy can work, but the replacement level is so pitiful at that point that instead of $17 in value (using the Weeks example), you probably get $8 or $9 in value (going back to your Weeks example). 

Best guess at Weeks’ replacment on the Brewers is Alcides Escobar, so if you get Weeks and Escobar on your team for $10 combined, then you have a decent chance at getting positive value.  But if you have Weeks and someone else has Escobar, the actual replacement level player you grab when Weeks goes down will be virtually worthless.

14 years ago

Having one DL spot is like having a free option, so it always has value and should be filled even with a marginal player (assuming no transaction limits – otherwise this needs to be factored in). 

I haven’t seen this analysis done using Black-Scholes option pricing models but if you could quantify risk of recovery time as a proxy for volatility (i.e., higher if actual recovery time is harder to predict based on type of injury) and use est. return date for option expiration date, you could theoretically convert the player’s full-season price into an option value and bid more precisely than just prorating the numbers for projected ABs. 

For example, the expected value of holding a stock for 3 months is NOT the same as the price of a 3 month option at a given strike price because it does not account for volatility.  This would suggest that injured players are systematically undervalued (even if values factor in projected playing time) since most people don’t do this analysis, although it would be hard to say by how much.

Risk-free interest rate needed for Black-Scholes formula would need to be estimated using value of replacement player. 

This would produce a more efficient market for injured players and trades.  The bad news: it would take a lot to build a reasonable database and robust set of assumptions to capture this, but as a rule of thumb, I place higher values than most on DL players and have been pretty happy with the returns.

14 years ago

The DL spot can be treated like any other roster spot: it’s value equal the value of the guy you have in it minus the value of the best guy you don’t have in it because of the better guy you have. Your DL spot has a replacement level too. Of course, you don’t actually score points for the guy in your DL slot, but you can think of the value as the future opportunity. For example, while I have Weeks on the DL, his value in that slot is equal to his projected future at bats minus the value of the same number of at bats from Ellis. However, if I also own Chipper Jones and Jones gets injured, Weeks value should be compared with Jones value as a DL stashee. Let’s assume Jones is the greater of the two; then we should keep Jones and release Weeks. However, Jones value is effectively diminished to the value of Jones minus Weeks, not Jones minus Jones replacement at 3B, and the marginal value of Jones is thus smaller.

Taking several injury risk players is just what the name implies: risky.

14 years ago

I can’t agree enough how much projected AB/PA plays a role in preseason player estimation.  I think Derek’s strategy makes a lot of sense for picks in the 2nd half of the draft where there’s a decent chance that the ‘safe’ pick is no better than replacement value anyway – e.g., gamble on Weeks vs. Ellis.  But I agree w/ others that limited DL slots make this a strategy that you can’t make up and down your roster.

14 years ago

While I agree with the main thrust of the article, I’m not buying Weeks plus replacement level player is worth $17.  My assumption is you arrived at that figure by comparing Weeks plus replacement player to other 2B whose stats do not take into account a replacement level player for time they miss.

Derek Carty
14 years ago

This would make a difference, Mike, but how many other 2B after Weeks are being projected to miss time due to injury?  I don’t think it’s enough to change that value too drastically.