Adding Value

Free agency started 10 hours ago, and as of today, teams are free to spend money in the market to upgrade their rosters. A lot of teams will do just that, selecting from the available pool of free agents to fill holes on their roster or replace players that don’t live up to their standards. This is the traditional way of improving the organization’s odds of winning – get better players than you already have. It’s generally a really good strategy if you can pull it off.

However, I think there’s an alternate path that may see some gains in popularity as teams attempt to keep their costs down during a tough economy. Rather than focusing purely on maximizing the potential positives, there is value to be had in minimizing the potential negatives. Let me use pictures to explain this better.

Here’s a sample win curve of the probable outcomes for a +1.8 win (roughly league average) player – the probabilities are made up to demonstrate the theory, though I’d bet they’re in the neighborhood of reality.


You’ll notice that this is not a normal distribution. The chance of injury make a disappointing outcome more likely than a breakout, so its not a traditional bell curve, but there are possible outcomes on both sides of the player’s actual talent level. The traditional replace-with-a-better-player method would lead a team to look for a guy who is closer to a +3 or +4 win player, pushing the entire curve to the right. However, +3 to +4 win players are expensive, and if you already have a +1.8 win guy on the roster, the marginal cost is probably going to outweigh the marginal benefit. In turn, you will not be willing to pay full price for those extra wins, and that good player will go sign with a team that has a giant hole at the position, thus receiving the full benefit of their talent level.

But there are a decent amount of teams that don’t have glaring holes on their roster, yet still want to improve their chances of winning. Rather than paying full price to upgrade from a +1.8 to a +3.5 win player, only netting +1.7 marginal wins in the process, perhaps there’s a more efficient way of buying wins, focusing on minimizing risk rather than maximizing return. Or, in graph form, doing this.


Rather than replacing the average player with a superior option, this new graph represents the result of simply having more options. This is a strategy to pursue depth rather than premium talent. It is the baseball version of diversification. Rather than pursuing a single, high-end player with a big contract that still leaves them vulnerable to total loss in case of an injury or inexplicable drop in performance, pairing different types of players can offer similar upside and risk at a reduced cost.

At 5 pm, we’ll look at some teams that may be in the position to do just that this winter

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Dave is a co-founder of and contributes to the Wall Street Journal.

35 Responses to “Adding Value”

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  1. Snapper says:

    I’m interested to see how you handle this. It is a very complex optimization with playing time a key constraint.

    Injury is the conceptually easy part, but what is less clear is how much depth protects you from bad performance. It is not clear to me that you can replace the 2.0 WAR player having a 0.5 WAR year with the 1.5 WAR player in any sort of systematic way. You don’t want to over react to slumps and hot streaks, but if you wait too long, the damage is already done.

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  2. Simmy says:

    Scenario 1:
    Spend on a 3.5 player to replace a 1.8 player
    Scenario 2:
    Spend on an additional 1.8 player

    While scenario 1 carries injury risk which could render your expensive purchase worthless, keep in mind that scenario 2 carries the opposite risk. If player #1 never gets hurt and plays all season, then player #2 becomes just like player #1 of scenario 1: someone who never plays.

    The question teams would need to weigh between choosing between those 2 options would be which is greater:
    The value of the upside of the purchased player (3.5 over 1.8) – The injury risk that the expensive player gets hurt
    The actual cash savings – The health risk that the retained player never gets hurt in the depth purchase.

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  3. The A Team says:

    Snapper brings up good points. A key to maximizing a depth strategy is the ability to get your depth guys regular playing time in AAA so that it’s easier to determine how the depth player compares to the guy on the current roster.

    I think your graph understates the value of depth on the upper end. A larger number of available players should ostensibly increase your chance of finding Ben Zobrist (a breakout player). Your graph shows depth decreasing this chance. Sure it’s tricky figuring out who’s actually breaking out and who is having a string of 80 strong PA’s, but I have trouble believing having say…five 1.5 WAR players decreases your chance of find a breakout performer against a single player.

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  4. Garrett says:

    Very interesting stuff, Dave. Looking forward to reading more on this. I have to think a few teams could be Minnesota, San Francisco.

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  5. Rich in NJ says:

    The strategy would seem to make more sense with pitchers than position players because of the increased risk of injury to the former, but beyond that, it also demonstrates that large revenue teams have an edge because they are can more easily compensate for taking a risk on more expensive players with a greater upside.

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  6. Bubba says:

    I don’t think your second graph represents what you’re saying. The red line does not show minimized risk, but rather more volatility. The probabilities for both poor and great performances go up, the probability for expected performance goes down.

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  7. jimbo says:

    Would this be why Adrian Gonzalez is being discussed? Teams seem to be figuring it out that the earlier you trade inexpensive, high WAR players, the more you get to increase depth.

    It makes sense. If you know he’s going to get expensive well before there’s a solid team around him, why wait and decrease return? Really wonder how many teams are looking at data like this.

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  8. Everett says:

    Looking at the curves, can you tell us what the different integrals would be? Is the goal here to show that each approach gives the same number of marginal wins, just with different approaches, or that the minimizing risk actually appears to offer slightly higher marginal wins? Just eyeballing it, it appears that the minimizing risk has a larger integral than the standard approach.

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    • Everett says:

      Scratch that – integral isn’t quite what I’m looking for, as whether the area under the curve is above the 1 or above the 3 will give the same integral. My question about value remains though.

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    • Dave Cameron says:

      The point is that you can increase your expected wins by minimizing risk as well as maximizing potential, though the latter is the far more traditional strategy.

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  9. brian recca says:

    Perhaps what Dave is suggesting is more platoons around the league? I saw a lot of situations last year where platoons could have worked but just didn’t happen. The Rays were able to use one effectively with Gross and Kapler.

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    • The Hit Dog says:

      Right, but don’t forget that in many situations, platoons actually decrease depth. As in, if you have a straight R/L platoon split in LF, you are carrying 2 players to fill 1 25-man roster spot, leaving 1 less spot for a bench player/extra arm out of the pen.

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  10. JH says:

    Seems like the Rays are the best model of what this kind of team looks like. They got pretty unlucky in 2009, but they came into the season with a quality backup at every single position except catcher.

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  11. Choo says:

    Add the Mariners to that list. Jack-Z wasted little time accumulating low-cost platoon options at 3B (Jack Hannahan + Bill Hall), 1B (Mike Carp + RH Scrap Heap 1B to be named) and LF (Ryan Langerhans/Michael Saunders + Bill Hall).

    With these contingency plans already in place, the Mariners aren’t jumping into FA “needing a 1B” or “needing a 3B.” They have the flexibility to shop aggressively and get the most bang for their buck – even if that means spending the bulk of their budget on pitching.

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  12. Does anyone know why that first graph picks back up just a little bit at the end?

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  13. Robbie says:

    I find this interesting because this is very much a football concept. Anyone that follows football with the kind of passion most of us analyze baseball with knows and talks about constantly the concept of building depth, often speaking of it as more important than adding stars.

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  14. Judy says:

    I think a 25 man roster limit makes it really difficult to do this unless more than a few of your options are, well, optionable.

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    • Dave Cameron says:

      I’d argue that almost every major league team wastes at least one roster spot on a fairly useless player – generally a 12th or 13th pitcher that just isn’t needed.

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      • Rodney King says:

        Great article- I’ve been thinking about similar points in roster construction recently, essentially that middle relievers should all come from your farm system if possible, and can be shuttled up and down as necessary to keep enough decent arms in the mix. Most teams have several guys who can provide decent enough innings in these spots, and their WAR is more or less going to depend entirely on their luck. So why would you ever sign FAs to fill these roles? (this is particularly pertinent because I’m a Cubs fan and of course they violate this thinking every single year, most recently with the Grabow “deal”.)

        Platooning wherever possible seems like a good way to pick up cheap WAR- LF, 1B, 2B seem like they have a lot of potential options for such a platoon. Perhaps I only think this about 2B due to the Cubs having Fontenot, but a lot of the switch-hitting 2B’s are only good at one side of the plate anyway, and there are so few true stars that a team might be better off trying to platoon a AAAA guy in this situation. It would be awesome if a team could find two good-fielding SS’s who can fill both halves of a platoon with good hitting, but it seems like these guys are rare, and are probably already starting at SS no matter how bad they are against same-side pitchers.

        Most teams probably have a couple roster spots they’d easily get better use of, not only the 12-13th reliever (which, is there anything more infuriating than a 13th reliever? i think not.) but also a lot of the 24-25th man bench guys serve no discernible purpose except playing garbage time in blowouts; these guys should be brought up from the minors if needed, but otherwise should see their spots filled by players who have some actual purpose.

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  15. CaseStreet says:

    I think I was just arguing for this.

    The Mets are rumored to be trying to move Castillo and probably will have to take on some of his contract to do so (maybe $4M). Or they’ll have to overpay for a guy like Millwood ($12M) when they could get a better pitcher like Wolf for $8M.

    What if to improve defense they signed a guy like Polanco (at $4M) who shouldn’t be as expensive as Lopez or some of these other guys available?

    If they put Castillo to backup Polanco, and Polanco to backup Reyes. They essentially have a bench player with high OBP and would be better than any other middle infield bench player and they have depth.

    All for the same amount of money.

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  16. Judy says:

    Plus, a free agent is most likely going to prefer to sign with a team that doesn’t have an incumbent starter at his position still on the roster, if given a choice.

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  17. Ashley says:

    It’s a little different, but this strategy works in deep fantasy leagues, too.

    I’m in a 30 team league with full minors. I built my roster around depth rather than star talent. It paid off and I made the championship series this year.

    Practically speaking, having that depth means not only injury protection, but stabilization of performance. You’re not likely to ride as high as a team with a streaking superstar, but you won’t fall as low as a team with a slumping superstar. At any given point, some of your solid guys will be on while others are off their game.

    That adds a secondary benefit in terms of evaluation. As the beginning of a season unfolds, a balanced team built on depth has a truer understanding of where the team is than a team built on one or two studs. If the team is contending or close to it, they can acquire the necessary pieces, increasing cost at the correct time to maximize potential success.

    A team built on one or two pieces may be swayed by a unique performance. They may buy heavy based on an unsustainable hot streak and waste cash that way. On the other hand, they may sell off useful pieces necessary for a playoff run based on a cold streak that is bound to turn.

    Thus, depth can increase a small market team’s ability to time runs correctly.

    Maybe I’m just Captain Obvious…

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  18. Logan says:

    Great. Article. Dave.

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  19. John C says:

    …..not a normal distribution?!?!??! BUT I TOOK AP STATS, WHATS HAPPENING?!?!?!?!??!

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  20. maqman says:

    This seems to elevate the value of good WAR level players who can play multiple positions, such as Figgins and DeRosa. They can step in and reduce the teams fall-off in performance when a high WAR position player goes down. A player such as that is surely worth more than the teams 12th best pitcher.

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    • Rodney King says:

      Well, they’re already worth way more than a 12th pitcher…I think any multi-positional bonus which might exist is currently negated by using these players in sub-optimal positions for no other reason than “versatility”, while better players sit or are DHd. While I understand the need to rest your players, there is often no rhyme or reason why teams decide to shift around their lineup- for example DeRosa played 1B from time to time with the Cubs…this was obviously not a good idea. Figgins playing CF while Hunter sits would be another situation like this.

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