Table of Contents

Wednesday, December 12, 2007

Fishing for Bedard: how much is too much?

The Reds are in a remarkable position right now in that they currently have 4 prospects who are considered by many to be ~Grade A prospects: Jay Bruce, Joey Votto, Homer Bailey, and Johnny Cueto. They also have another player in Josh Hamilton who, while entering his age-27 year, is similar to these players in that he has a high ceiling, some significant risk, and still has many more years until free agency. Given that several of these players keep popping up in trade discussions, especially with respect to Erik Bedard (right), it's worth it to try to quantify how much the Reds should get in return for their prospects should they decide to trade them.

In the recently-published August '07 edition of the SABR newsletter, there's a good study by Victor Wang investigating the value of prospects. He makes the important point that as free agent salaries increase, the relative value of a prospect also increases, because the performance of those prospects costs so much less than that of a free agent or near-free agent. I thought I'd summarize his findings and then try to apply it to the Bedard situation.

Breakdown of his methods
  • You can probably skim this part unless you get hung up below.
  • Wang estimated the total value of the prospect as the player's actual production plus the monetary savings that the team gets by using the cheap young player instead of a free agent for that production.
    • Player Production Estimate:
      • He looked at hitters and pitchers separately, and followed those ranked as 1-10 prospects, and those ranked as 11-25 prospects by Baseball America from 1990-1999. Therefore, this study only investigate the value of elite prospects.
      • He then quantified their contributions by WARP (Wins Above Replacement Player from Baseball Prospects). The use of WARP creates some problems for translation to actual wins, as WARP uses a much lower baseline than any other replacement stat I know of. But as long as we stick to WARP numbers when applying the findings of this study, we'll be fine.
    • Monetary Savings:
      • The idea here is that the performance that players contribute during their first six years costs the teams less than the same performance by free agents. So if you have two teams with identical payrolls, but one is composed exclusively of free agents, and the other is composed of 50% league-minimum players and 50% free agents, the latter team will perform better because the performance of those young players is much more inexpensive.
      • To estimate financial value, Wang essentially took the difference between player salary during their first six years in baseball and the free agent cost for that level of performance.
      • He then converted that dollar figure into a WARP figure using average free agent $/WARP values ($1.69 million per 1 WARP). This is essentially the additional production that you can buy on the free agent market if you use a young player instead of an equivalent free agent player, and yet keep the payroll the same. So, if a young player makes an average of $1 million a year over six years, but produces at the same level as a $4 million/yr free agent, then you essentially can spend an additional $3 million/yr on another player if you employ the young player.
    • Total Value
      • By summing the WARP value of the six-year production + 6-year monetary savings (converted to WARP by average WARP per $), you get the total average value of a prospect type. This is the total value that you should demand in a trade for such a prospect, extended over the number of years you can expect to control the acquired player(s).
Wang's findings:
  • Hitters
    • Top-10 prospects averaged 24 WARP in their first six years, or ~4 WARP/yr. This performance came at a savings of $5 million/yr relative to how much you'd spend on an equivalent free agent, which was the equivalent of ~3 WARP/yr of free production.
      • The total trade value of a top-10 hitting prospect therefore came to 24 + 3*6 yrs = ~42 WARP.
    • 11-25 prospects averaged 19.3 WARP in the first six years, or ~3.2 WARP/yr. This performance came at a savings of ~$4.1 million/yr relative to a free agent, which was the equivalent of ~2.4 WARP/yr of free production.
      • The total trade value of an 11-25 hitting prospect therefore came to 19 + 2.4*6 yrs = ~34 WARP.
  • Pitchers
    • Top-10 prospects averaged 12.9 WARP in their first six years, or ~2.2 WARP/yr. This performance came at a savings of $2.7 million/yr relative to how much you'd spend on an equivalent free agent, which was the equivalent of ~1.6 WARP/yr of free production.
      • The total trade value of a top-10 hitting prospect therefore came to 19 + 1.6*6 yrs = ~22 WARP.
    • 11-25 prospects averaged 11.1 WARP in the first six years, or ~1.9 WARP/yr. This performance came at a savings of ~$2.3 million/yr relative to a free agent, which was the equivalent of ~1.4 WARP/yr of free production.
      • The total trade value of an 11-25 hitting prospect therefore came to 11 + 1.4*6 yrs = ~19 WARP.
Clearly, pitchers were less valuable than hitters, which was largely due to pitchers' high "bust" rates. Wang found that an alarming 54% of top-10 pitching prospects turned out to be "busts" (meaning that they contribute less than 2 WARP/yr over their first six years) compared to just 21% of top-10 hitting prospects. But I think what is more impressive is how valuable even the average 11-25 pitching prospects tended to be, despite their risk (61% bust rate). 19 WARP over six years is the equivalent of a $32/6 million contract, using Wang's $1.69/WARP conversion. Top hitting prospects, on the other hand, are valued the equivalent of a 6 yr/$71 million free agent. That's the average, not just the ones who pan out!!

Application to the hypothetical Bedard trade

So, what does this mean for the Bedard trade we keep hearing about? Well, Bedard's a phenomenal pitcher, with a WARP value over the past two years of 7.1 and 8.0. This means that he netted the Orioles ~8 wins above a hypothetical replacement-level pitcher last year, which is the difference between them going 69-93 (0.426) and going 61-101 (0.377)--an enormous difference (again, WARP probably overestimates this value, but my guess is not by more than a win or two). Bedard has two years remaining on his contract, and has stated that he very much intends to test the free agent market, which means that any team acquiring him can really only count on controlling him for two more years. This is a key point that seems to be missing from a lot of the discussions I've seen regarding Bedard.

Now, in terms of future value, I think Bedard's likely to regress slightly from his outstanding performance rates in '07, but counteracting that, he missed some time when the Orioles very cautiously shut him down early last season, reducing his total value to the team. So it seems reasonable to predict that he will produce between 7 and 9 WARP each of the next two seasons, for a total performance value of 14-18 WARP. Obviously, he could perform well below that if he gets injured or something (and he does have some history with injuries), but 14-18 WARP over two years seems like a reasonable optimistic performance forecast.

Also, he's not yet making free agent money, as he's just now entering his 5th year. So given that, we probably need to give him some bonus value to match up . Tom Tango estimates that players make 40%, 60%, and 80% of free agent value in their 4th, 5th, and 6th years in MLB (their arbitration-eligible years). So, as a very rough approximation, let's add 40% and 20% to Bedard's value over the next two years to his extra monetary value, which puts his approximate "trade value" at 18-23 WARP.

Ok, let's now compare his value to some of the Reds prospects:
  • Jay Bruce - a 1-10 prospect as a hitter, total value of 42 WARP. Note, he's really a top-2 or top-3 hitting prospect, which probably should have a higher value, but we'll run with this for now.
  • Joey Votto - a 11-25 prospect as a hitter, total value of 34 WARP.
  • Homer Bailey and Johnny Cueto - I'm going to be slightly conservative and peg them as 11-25 prospects as pitchers, which gives them a total value of 19 WARP. But either could probably be a top-10 prospect depending on who you ask, which would bump up their value to 22 WARP.
  • Josh Hamilton - As a quick'n'dirty estimate, I'm going to rank him as equivalent to Votto, but only over 5 years instead of six, so 28 WARP. My feeling is that this is conservative, but probably not by more than 5 wins or so given the uncertainty surrounding his health.
So, if Bedard's value is 18-23 WARP over two years, he would make a reasonable one-for-one trade for Bailey or Cueto, with perhaps an additional lower-tier prospect or two thrown in. You might also be able to justify a one-for-one trade for Hamilton or Votto if you give Bedard's value an additional bonus because his performance will happen sooner rather than later. But that's assuming that the Reds are going all-in over the next two years, and I don't think the club is at the point that they should be doing that, as much of their best talent is still young.

Nevertheless, what this analysis indicates to me is that a package of any two of the Reds' prospects would be severely overpaying for two years of Bedard. Now, Bedard's trade value could be greatly improved if you could extend Bedard beyond the 2010 season. But the potential for such an extension seems questionable given Bedard's comments about wanting to test free agency. Furthermore, pitchers don't tend to make particularly good investments in the long term because of how unreliable even great pitchers tend to be past age 30.

Given that a one-for-one trade of any of the Reds' prospects for Bedard is apparently very unlikely, I have to say that I'm really hoping the Reds do not end up making this deal. So good luck to the Dodgers, Mariners, and anyone else who might want to step in and try to outbid Krivsky.


  1. I think that system you used in the article severely overrates prospects and am actually pretty astonished that it places such a high value on them. Isn't one of the rules of economics that you don't factor in sunken costs (I'd consider your payroll a sunken cost since most teams have a general idea of what they are going to spend and will spend it either way)? Most MLB clubs will have a mix of youth and veterans anyhow so even if you dealt a Homer Bailey and a couple more prospects for Bedard, it will even out when you look at the organization as a whole.

    Plus you are assuming that the prospect will have no injuries in 6 full years as well as no hiccups along their way and we all know that is one heck of a stretch (minor league stats don't necessarily translate over no matter how high the prospect is rated). Now I know baseball fans that follow prospects get overly attached and it's easy to get caught up in the hype but one of the core uses for the farm is to help supply the MLB team with MLB talent. I think you are kidding yourself if you really think Bailey for Bedard straight up is borderline over paying and anything more would be drastically over paying. Now I'm not saying the package is or isn't but that line of logic seems extremely dangerous to me if you plan putting a competitive team on the field for more than a couple years out of every decade.

  2. I wouldn't say he's assuming no hiccups because he's basically taking an average of similarly ranked prospects over a given time period. Injuries and adjustment periods are factored into those numbers based on that, unless of course Wang's sample just happened to contain an inordinate amount of prospects that hit the ground running.

    Justin, I'll admit to not following the details of the study closely, but has the bust-rate been factored into the WARP numbers outside of just being included in the averages? What I mean is, part of the reason a Bailey for Bedard trade doesn't make sense from the Orioles perspective is because there's such a large chance that he could be a bust. The reason that the Reds would need to include another prospect is to mitigate some of that risk. So while 19 WARP might be a decent estimate of his future value, he could also have a 50% chance of 0 WARP compared to Bedard who may only have a 10% chance at 0 WARP (just guessing at the numbers). Do you see what I'm saying?

  3. The average is the average. The standard deviation is of course higher for the prospects. It's about your risk aversity. If you could buy a lottery ticket that gives you a 10% chance at 100$, 40% chance at 10$, and 50% chance at nothing, how much would you pay for that lottery ticket? The expected value is 14$. A broker taking an action of 14$ per bet will breakeven over the longhaul. If you would only place a bet at 10$, good luck finding someone who will take your action. You are too risk averse for this game.

    The only way for a broker to take your action is if he really really needs 10$ right now, and is willing to pay out, if he loses, a few years down the road.


    WARP overestimates pitchers by AT LEAST 0.1 wins per 9IP. So, a 216 IP pitcher will be overestimated by at least 2.4 wins. It's closer to 3.0 wins. Study the issue, and you'll end up with my conclusions.

  4. Looks like the questions have been answered already, but to reiterate:

    @Anonymous: the values reported here are the averages of all players in Wang's sample. Some of them were absolute disasters, some drastically outperformed those estimates. Also, remember, the key point is that the Reds would only get Bedard for two years. If they had him for longer (e.g. via an extension), he'd be a much more valuable commodity.

    Also, a big part of the prospect values listed above is the monetary savings/efficiency of young player performance. And that part of prospect value gets higher and higher each year as free agent salaries get higher and higher. This means that prospects are, in fact, much more valuable than they were 10 or 20 years ago.

    One thing that might be interesting to do, though, would be to look at median performance instead of mean performance. I'd have to look at the data again, but it could be that the star players in the sample are pulling up the average when you measure it via the mean. There's also, as Joel pointed out, an issue of sample size here. But these findings aren't inconsistent with those from other studies.

    @Joel, as Tango said, the issue is one of risk. Bedard's more reliable than Bailey over the two years the Reds would control him. So yes, it's possible that Bailey might never amount to a hill of beans. But it also entirely possible that Bailey would go to Baltimore and be every bit as good as Bedard for six full years. That'd be an enormously lopsided trade. See Haren for Mulder, for example--even if Mulder had kept it up, it'd be a lopsided trade favoring Oakland). So yes, as I said, I think a one-for-one trade of Bailey for Bedard is pretty reasonable, with perhaps an extra C+ish prospect or two tossed in to even things out.

    @Tango, I have no doubt that you're right, and wasn't trying to say otherwise. In that sentence to which I think you're referring, was just trying to emphasize that WARP was properly recognizing that Bedard is a phenomenal pitcher to deflect criticisms that I wasn't giving him enough value. I tried to stay within WARP in the rest of the writeup to further misinterpretations. -j

  5. The risk issue is really what matters here I think. Even a statistically disinclined person would understand the basic concept that a 2 or 3 for 1 deal sees the prospect receiving getting the higher value ceiling with less certainty and the star receiving team getting a higher floor with more certainty.

    Of course, if you are an 85 win team trying to both win and build a winning culture, adding 6 or 7 "certain" wins might be more valuable both financially and on the field than risking the lower extreme of prospect failure.

    I think the specifics of the Reds current circumstance add to the argument supporting a trading for a Bedard or Haren. That said, I think Bailey, Hamilton, and say, Wood, is the upper end of what I'd feel comfortable offering. Bruce would be untouchable in this circumstance and I would not part with both Bailey and Cueto.

    I'd actually prefer a move for Chris Capuano, who still represents a significant upgrade over the 5th starter chaff, which would only require some bit players - Freel and Roenicke maybe - without touching the 4+1. But that's another story.

  6. Interesting rumor about Danny Haren. Let's repeat the above analysis on him.

    BPro has him at ~8 WARP last season, essentially the same as Bedard. For the sake of argument, let's assume he'll keep that up from '08-'10. That puts him at 24 WARP over three years.

    He apparently has three years remaining on his contract for what looks like absurdly low cost. If David's numbers are correct, he'll be earning ~50% less than his free agent value over the next three years (probably more, but let's run with that number). So, again as a very rough approximation, we'll double his value to 48 WARP. That third year helps a great deal...

    That would make a Votto + Bailey deal, or 34+19=53 WARP, seem pretty reasonable to me.

  7. @RMR, Capuano could be a fabulous pickup. Much better than our current #5 starter (a replacement player), and a guy who has the potential to be a #4 guy.

    All depends, of course, on who they'd have to send in return, but it seems like a very good "buy low" trade. -j

  8. I'd be interested on your take on the Astros' Tejada deal. Not knowing much about WARP's and all of that (I though a warp was 1X the speed of light), it appears to me as if the Astros literally gave away the farm.

  9. I haven't had time to sit down with this one. Thing is, I'm not sure if any of the prospects traded are even in the 11-25 prospect category from Wang's study (I have no idea who any of them are aside from Luke Scott), so I might not be able to say much. Wang's study really only deals with elite prospect value.

    Tango's blog is the place to be for this kind of analysis, of course. Tango sees this as a great deal for the O's, just in terms of a pure salary dump, and not even thinking about the players acquired. But Rally sees Tejada about a half-win higher per year, which would make his salary about dead-on. So the question then comes to exchanging 2 years of Tejada's market-value production for the production of a bunch of young players. My guess is that the O's come out ahead, but I'm not sure. I'm probably just going to follow along with those guys on this one. :)

  10. Bailey, Hamilton and Wood for Bedard would be close to a fleecing of the Reds.

    As Tango suggests, Bedard's value is reasonably closer to 10-12 wins above replacement over the next two seasons.

    The suggestion that the Reds are an 85 win team as currently constructed really needs justification in my mind...

  11. The suggestion that the Reds are an 85 win team as currently constructed really needs justification in my mind...

    I'm not sure that RMR was actually making that claim, though maybe he was...

    That said, I think the Reds *COULD* win 85 games next year if a lot goes right. But a lot would have to go right. 0.500 is probably a more reasonable optimistic estimate, and even that's assuming that quite a bit goes right.

  12. Jojo, I was not making that claim in the least. IF we add one of those arms, I think we're an 85 win team. If we were already at that level, a trade like this makes a lot more sense.

  13. Rick,

    Sorry to put words into your mouth, and I agree with what you're saying.

    I just think that if Bailey/Hamilton+something potentially useful (i.e. top ten near-ready pitching prospect + 3 win major league talent with upside + lower prospect) is the market for quality starters, then the Reds really should be trying to trade Harang and Arroyo rather than trying to pay the price.


  14. I like the analysis, but I think your system completely over estimates the value of prospects based on their salary. By this type of model the Marlins would be absolutely awesome.

    Trading Harang and Arroyo is a retarded idea. If we are going to win we need to stop thinking about the future and start thinking about the now. We are a LOSING team, seven years running, and if we are going to win we need to get PROVEN players.

  15. The Marlins have a great deal of value in their players. The caveat is that this system assumes that teams will continue to invest the money they save from the young players in additional talent. That's not what the Marlins are doing, of course. If they continued to at least post a league-average payroll, they'd be a dangerous team over the next 6 years.

    I don't see this as a problem with the valuation system. It's a problem with how the Marlins are being managed. Their payroll will be about equivalent to what the Marlins get from MLBAM next year, which means that the ownership is banking all other forms of revenue. Their statement that they had to trade Cabrera for economic reasons is absolute fabrication. Baseball reasons, maybe, but not economic reasons.

  16. My only concern with the analysis is that the prospects have 6 years to produce and Bedard only has 2. To me, it seems like the anlaysis assumes the Reds can't find somebody in the future to replace the production of the prospects and they will be replaced with a RP. I don't think that is entirely accurate due to being able to find other talent (through the draft, free agency, trades).

    I completely understand that I may not understand something, I would just appreciate a little explanation. Just seems like the prospects value is overrated due to their time under team control.

  17. One thing that this analysis doesn't consider is that Hamilton and Bruce are both outfielders, and there is talk that Votto may be eventually used there as well. We currently have Dunn, Griffey, Hoppper, and Freel. When looking at their WARP, it should be considered that they will be replacing some very good players. Bedard on the other hand would be replacing, in effect, our #5 starter. I do agree that we shouldn't be so quick to give up these prospects.

    Also, I notice some have argued with the value of these prospects due to injury risk. I would say that giving up several players for one player increases your injury risk. I don't think Bedard is necessairily any more of an injury risk than any of the players you named, but he's no less. If you assume Bedard is of equal value to three prospects, the odds of him getting injured is greater than the odds of all three of them getting injured.

  18. @Alex, I think I see your point, I'm just not sure that I agree that it's a flaw in the analysis. Prospects are valuable because a) they are under control for six years once they break in, and b) any production they provide comes at a drastically lower cost than the same production by a free agent. I don't see any problem with those statements.

    Essentially, what I think you're actually saying is that Bedard is undervalued here because after he leaves he can be replaced by a free agent. I won't disagree that it's possible to replace at least part of his production via free agency, at market rates. But I have a hard time understanding how that fact should actually increase his value...


    So you're saying that we should discount our outfielders' value because we have too many of them? I certainly understand the justification for trying to trade those parts, but I still think we should try to get market value for them in return. That's what I'm talking about here.

    With respect to your injury comment, I think you're right--the injury risk is greater to the team that gets fewer players in a deal. However, prospects also have a risk of just not developing as projected, which is another part of their risk. That risk, of course, is factored into Wang's estimates.

  19. I posted this at Redleg Nation in response to David's comments. I thought it was worth re-posting here so that I can find it later on. :)
    @David, this is kind of a long post, but I wanted to run your projection on Bailey through this analysis to see what happens.

    If we assume 4.50 ERA (~4.8 RA, since R/9 is usually ~0.3 higher than ERA) over 175 IP, and we assume that replacement level is 5.9 RA (which is about right), that's the equivalent to ~21 RAR per season (calculation: [4.8-5.9]/27outs*175In*3out/In = 21 RAR), or ~2.1 WAR (wins above replacement) per season. Times six years, that's a total of ~126 RAR, or 12.6 WAR.

    Bailey adds to his value by being inexpensive. A 2 WAR player, according to Tom Tango's salary scale, is worth ~$8.8 million/year, or $53 million over six years if purchased as a free agent. If Bailey makes 400k each of the next three years, then makes 40%, 60%, and 80% of his value, then he'll make 400k*3 + 3.6m + 5.4m + 7.2m, for a total of $17.4 million. That's a difference in cost of $35 million. Assuming $4.4 million WAR (Tango's number), that money saved on Bailey could be invested for an expected 8 WAR over six years.

    So, 12.6 WAR + 8 WAR = 20 WAR over six years. That's Bailey's total trade value, using your projection--which actually is pretty close to the average predicted performance of a pitcher in Wang's study.

    Ok, now comparing to Bedard: last season, he had an RA of 3.3 over 182 IP. Let's be really optimistic and say that over the next two years, he gives up 3.3 R/9 over 200 IP per season. That comes to 57 RAR ([5.9 - 3.3]/27*200*3=57 RAR), or 5.7 WAR per season. Times two years, that's 11.4 WAR total.

    We should also factor in his salary. 5.7 WAR, at $4.4m/WAR, is worth ~$25 million/year (wow), or $50 million over two years. So if he makes 60% and 80% of his true salary in '08 & '09, that puts him at $15 million in '08 and $20 million in '09, for a total of $35 million, $15 less than he's worth as a free agent. $15 million savings could be invested in free agents worth 3.4 WAR, which brings his total two-year value to 11.4 WAR + 3.4 WAR = 14.8 WAR. The salary estimates are probably a bit high (he won't be considered a 5.7 WAR pitcher in arbitration this year, as that was a big jump up for him from the previous years), but even doubling that part of his value brings up to 18.2 WAR, or just about the same as Bailey.

    Again, as I said in my piece, I think a 1 for 1 swap of Bailey for Bedard is a pretty fair trade. Higher risk for the Orioles, but potentially as good of a pitcher over six instead of just two years. But any two of the Reds' 4+1 prospects seems like too much to me.

    [Technical note: the reason my WAR numbers differ from the WARP values is that WARP uses an absurdly low baseline for replacement level, which really limits its usefulness.]

  20. Justin,

    I posted this in the redleg nation thread but I thought it more pertinent and likely for you to see here.

    How do you feel about comparing WARP numbers across season like in your analysis? Or more simply, are 6 years of a 2 WARP player really equal to 2 years of a 6 WARP player? It’d be pretty hard to do an analysis of such having to include division races, the wild card, opponents and newer prospects, but intuitively it doesn’t seem to me that it’d be a linear relationship.

    All else being equal, say your team missed the playoffs by three games each of the six seasons with the 2 WARP player. Would you rather make the playoffs two of those six having the 6 WARP player? It’s an extreme example and perhaps a linear assumption works well enough in practice, but I could still see as something to consider.

  21. I had the same thoughts as several on here, all of which are qualified by the fact that I don't understand anything:

    - the linearity question Neuge poses.

    - the 2 vs. 6 year question (doesn't this analysis assume that Bedard will be replaced by a replacement-level player in year 3? Not sure that's realistic.

    - the Marlins example. I know Justin understands the "real world" application of this analysis, but the system itself flawed, by ignoring the fact that at some point you have to actually compete and not just amass the most underpriced talent.

    I'm not sure where that point is, but (going back to Dave's point), where can we be certain that the Reds aren't there?

    - Does the system recognize the non-linear distribution of talent? (i.e, there's only one Barry Bonds, but there are 50 Norris Hoppers).

    This all ties together, in that you only have 25 roster spots and 162*9 IP -- having 25 cheap-and-slighty-above-average guys just results in a very cheap 83-win team.

    - I think the model ignores the premium on certainty. In a mathematical sense, 2 50% chances to win $100 are worth the same as $50 in cash, but that's no longer true to the person who absolutely, positively needs $50.

    - Practicality: By this model, shouldn't the Reds be trading Harang, Arroyo, Dunn, and Griffey for prospects?

    - Billy Beane may well have done this sort of analysis in trading Haren.

  22. BTW: I know a lot of my points have already been addressed, and most (all?) of the others are ignorant. So no need to address them if you don't want.

  23. Hi guys, I thought I’d try to answer some of the questions posted:

    Linearity problem:
    You guys are correct in saying that all else being equal, you’d rather have an all star season now rather than 3 years later. I changed the WARP figures to discount future WARP and future savings all to present value. These were the numbers I got:
    Top 10 Hitters- from 41.84 WARP to 31.93 WARP
    Top 10 Pitchers- from 22.45 WARP to 17.11 WARP
    11-25 Hitters- from 33.85 WARP to 25.77 WARP
    11-25 Pitchers- from 19.16 WARP to 14.58 WARP

    2 yr vs. 6 yr problem
    The analysis assumes that all FA WARP that is purchased is fairly priced. Ex- if a prospect produces 4 WARP, it assumes that if the team were to replace that 4 WARP, it would have to purchase 4 WARP on the free agent market for the going rate.

    Marlins Example

    Not sure how this would affect the model, please explain more.

    Certainty on Premium
    The breakeven figures are expected value figures. In the long run, going by expected value will give you the best chances of fielding the best team. Of course, GMs may not be able to have enough time to go by expected value all the time. Some times they may need to give future value up for greater certainty now.

    If the Reds are a 75 win team, wouldn’t you guys agree it would be smarter for them to trade away the aforementioned players? However, if they are an 85 win team, I’m sure most of you guys would support trading for Bedard. A team’s spot on the win curve is essential to evaluating prospect trades. I mention this at the end of my article, if you’ve read it. Any boost on the win curve should be factored in to the value a team gets back in a trade. For example, say the Reds are an 83 win team without Votto and Bailey and they acquire Bedard, whom we’ll say is a 7 win player for Votto and Bailey. Without factoring in the win curve yet, we find that Votto and Bailey are worth 40.35 WARP. Let’s say that Bedard is worth 23 WARP over the next 2 years, counting his surplus value. However, Bedard takes the Reds from an 83 win team to a 90 win team. This increases the Red’s chances of going to the playoffs from about 20% to 55%. Let’s say that a playoff appearance is worth an extra $25 million in revenue.
    ((.55*25)- (.2*25))*2= $17.5 million/$1.69/WARP= 10.36 WARP+23 WARP= 33.36 WARP

    Now, the difference in value between Bedard and Votto and Bailey is much closer. Factor in draft picks gained from Bedard, and it becomes an even tougher decision.

    Remember, this is only a model, it is not perfect and it has its flaws. A lot of variables need to be taken into account and that leaves a lot of margin for error. However, this still provides a starting point to see the value and risk prospects bring.

    - Victor Wang

  24. Forgot to put to look at what Justin said given the Marlin's example.

  25. Also, some recommended reading for a team's spot on the win curve, subscription required:

  26. @Everyone, thanks for all your comments. I think Victor addressed most of them, and I (mostly) agree with his responses.

    The one thing I wanted to add was the Marlins comparison. Let's say the Marlins payroll is $25 million next season (I'm not sure what it will be, frankly). Now, let's say that there are two ways to fill out that roster. One can fill it out with free agents, or one can fill it out with a mixture of free agents and talented young players. Which approach is likely to result in greater production? Obviously, it's the team that uses young players, because those players will produce more runs per dollar spent than the team of free agents. Neither team is going to be very good, but the team that includes young players will probably be a heck of a lot better than the free agent team if they have the same overall payroll.

    That's precisely that additional value that we're trying to identify in this analysis. The question before most teams is, given a particular payroll, how much production can you get from your players? Usually, it's going to be through a combination of talented young players, as well as appropriately-priced free agents. Teams that don't have young players, or have free agent players that are priced above market rates for their production, will tend to do poorly at a given payroll level.

    @Victor -- Thanks for stopping by. I'd be interested to hear how exactly you did the discounting--i.e. how did you determine how much to discount production two years vs. 6 years from now. Also, are you planning to devise a way to include draft pick value into the return on a prospect? I think those data can be pulled from Jazayerli's study, and I may look at that in the future, but I doubt I'll get to it anytime soon unless the Reds compel me to do so via some blockbuster trade. :)

  27. Victor,

    Your comments on the win curve are more or less what I was referring to with the nonlinearity stuff.

    Let's assume a straight up Bailey for Bedard trade. Again, let's say the Reds are an 85 win team for each of the 6 years of Bailey's contract and an 89 win team for 2 years when he's replaced with Bedard. If the NL central or wild card winner is at 88 wins, monetary considerations aside, you would obviously, IMO, want to make the trade. Making the playoffs 2/6 years instead of 0/6 years is an improvement.

    What that means is 6 years of a 2 WARP player is not the same as 2 years of a 6 WARP player, or WARP comparisons across seasons are not necessarily comparable, or, nonlinear.

    I'll throw out an even more extreme, and obviously impossible, example. Would you trade, again monetary considerations aside, 162 seasons of a 1 WARP player for one season of a 162 WARP player? I'm pretty sure I would.

  28. #26- Justin, I used an 8% discount rate that Jazayerli proposes in his BP draft study. I believe Nate Silver did a study a few years ago on the dollar values of a draft pick. I suppose that could be factored in as well, but that might be a little tricky. Factoring in draft picks is on the lower end of my priorities with the system right now, though.

    #27- Neuge, yes true. That is why I added the discount rates for the prospect production.