1 Albert Pujols > 2 Casey Blakes (Or, All Wins Are Not Created Equal)
by pacgnosis on Oct 12, 2009 9:20 PM EDT
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I'm a big believer in WAR, but something about it has been nagging at my brain for a while. The WAR leaderboard tells us that Albert Pujols was worth 8.4 WAR ($38 million) in 2009, and that Casey Blake was worth 4.3 WAR ($19.2 million). So let's say you're John Mozeliak. The devil comes to you and offers you the following proposal: In 2010, you can replace Albert Pujols with Casey Blake and his identically skilled twin, Blake Casey. Under the terms of the deal, Pujols and Blake (and Blake's twin) will perform exactly as they did in 2009. The combined salary of Casey Blake and Blake Casey will be the same as Pujols' salary. Which do you choose?
Even without accounting for fan reaction, the answer seems obvious: Pujols. For one thing, he only takes up one position and one roster spot, allowing you more roster and lineup flexibility. The Blake twins may provide the same total WAR as Pujols, but this value is mitigated by the loss of potential WAR from other spots. Having that value concentrated in one player allows you to add another player to your lineup; provided you have another above-replacement-level player available, who wouldn't prefer that? In essence, the comparison here isn't so much 1 Pujols vs. 2 Casey Blakes as it is Pujols and say, Skip Schumaker vs. the 2 Blakes.
An even larger problem is that of scarcity. Think of a major league player as a diamond (the gem, not the infield), and WAR as the carat count of the diamond. All else being equal, a 1-carat diamond will always be worth much more than twice a 0.5-carat diamond. Why? Because the relationship between carat count and rarity is non-linear. It is exponentially harder to find a 1-carat diamond than it is to find a 0.5-carat diamond. Thus, a 1-carat diamond is worth exponentially more than a 0.5-carat diamond.
Similarly, an 8-WAR player is much, much rarer than a 4-WAR player:
The preceding graph is compiled from FanGraphs WAR data (position players and pitchers) for the past 3 seasons. The exponential relationship is clear. Over the last 3 seasons, there have been an average of 4 8+ WAR players and over 68 4+ WAR players per season. In these seasons, an 8-WAR player has been about 8.5 times harder to find than a 4-WAR player. 4-WAR players are (comparatively, anyway) a dime a dozen.
Shouldn't the 8-WAR player be much more valuable than two 4-WAR players, then? I'm not arguing that Pujols is worth 8.5 Blakes, but certainly he's worth more than 2 Blakes, based on the scarcity of his skill set.
There are (at least) two ways of resolving this. The first would be to make an exponentially-scaled WAR, or an alternative WAR to dollars conversion that incorporates this relationship. I don't want to replace the current, linear model, which does a good job of measuring the market value of a given performance. What I would like is a market-independent valuation that can be used to figure out what portion of MLB's salary resources a player's performance should command in a perfectly rational, performance-based economy (yeah, I know, that'll never happen, but still...).
The other solution would be to find a way to compare 1 player to 2 players (or 3 players; or 2 players to 3 players, etc.) that accounts for the added value of performance being concentrated in fewer players. In other words, we'd need a scale that could convert the combined performance of a number of players into an equivalent, 1-player value. This would be a particularly useful tool for evaluating multi-player trades.
Has anyone worked on anything like this already? Does anyone have ideas for how to do so? Am I crazy, or missing some key element? If you disagree, please enlighten me; I'd be interested in hearing any arguments for the Blake twins. Thanks for reading.
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It all depends on who you have as a replacement
Remember, just because something is rarer doesn’t mean it is necessarily more valuable. 8 WAR is 8 WAR, and it really doesn’t matter if two players are worth 8 WAR or one player is. If you do have a Skip Schumaker, who is solidly above replacement level, then yes, it would make sense to have Pujols. If you have a guy like Neifi Perez, than it would make sense to have the Blakes.
by vivaelpujols on Oct 12, 2009 9:25 PM EDT reply actions 0 recs
That doesn't make sense.
You’re statement above implies that 2 4-WAR players are more valuable than 1 8-WAR and 1 0-WAR player. (I’m assuming Perez is 0 WAR based upon the tenets of the argument, I don’t actually know the player).
My opinion would be that having 1 8-WAR player allows for the potential to have another above replacement level player; while 2 4-WAR players does not. As such, the 8-WAR player is more valuable as it is 8 + y / 2 WAR per player, where y is your additional player, as compared to a 4 WAR per player. So long as y >= 0 (replacement level or better), then the 8-WAR player is better.
If you assume that replacement level is freely and readily available (therefore, you should never have worse than replacement level), then the 8-WAR player is, at worst, equal to the 2 4-WAR players.
by Trickman on Oct 13, 2009 3:10 PM EDT up reply actions 0 recs
You just said exactly what he said, only wordier.
by seanbergmanrules on Oct 13, 2009 7:05 PM EDT up reply actions 0 recs
uh yeah
BTW, Neifi Perez is a player who is actually below replacement level.
by vivaelpujols on Oct 13, 2009 8:11 PM EDT up reply actions 0 recs
Yeah
and this is a risk you take when you use “replacement level” players. Replacement level players are, on average, replacement level. But sometimes they overperform and sometimes they underperform. Its a bad assumption to think that you will never get below replacement level production.
by lookatthosetwins on Oct 13, 2009 10:24 PM EDT up reply actions 0 recs
All players have risk
Some will over perform, some will under perform — that’s why we talk in expectations.
The minimum expected production from Pujols and a replacement level player would be 8, with there being a possibility of being lower or higher. The maximum expected production; however, is limited only by the available free agents and the amount of payroll available for filling the spot through free agency.
With the two Casey Blakes, the minimum expected value equals the maximum expected value of 8, so you are limiting your upside without any real reduction of low-end risk.
Again, this isn’t necessarily a realistic scenario as few teams are going to have 25 man rosters where consolidation of WAR becomes truly beneficial.
by Trickman on Oct 14, 2009 9:10 AM EDT up reply actions 0 recs
Another consideration is injury
If you lose the 8 WAR player you are down 8 WAR vice 4 if one of the Casey Blakes goes down.
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by Jeff Zimmerman (TucsonRoyal) on Oct 12, 2009 9:46 PM EDT reply actions 0 recs
Yeah, but the Blakes are playing twice as many minutes and are twice as likely to get injured
That’s not a convincing argument.
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by PaulThomas on Oct 13, 2009 2:39 PM EDT up reply actions 0 recs
Let’s say there’s a 15% chance that your typical MLB player loses a substantial portion of the season to injury. (That number is a TOTAL FABRICATION for illustration purposes only.)
That means a 15% chance of losing Pujols for a season but a 2% chance of losing both Blakes.
by cwyers on Oct 13, 2009 2:55 PM EDT up reply actions 0 recs
Using this 15% chance...
You’re now giving value to variance.
The E[ WAR ] in both cases is 6.8 WAR (8 at 85%, 0 at 15%) or (8 at 72.25%, 4 at 25.5%, 0 at 2.25%).
The V[ WAR ] in each case is 8.16 in the case of Pujols, and 4.08 in the case of the Blakes, suggesting that decreased variance carries with it additional value (which, I would agree with).
However — how does this account for the issue I brought out above where you have 1 less roster spot in exchange for the lesser variance?
(8 + Y) , Y >= 0 is always atleast as good as (4 + 4) — which implies that adding a replacement level player to Pujols is, at worst, equivalent to two Casey Blakes.
by Trickman on Oct 13, 2009 3:16 PM EDT up reply actions 0 recs
Just as an additional note...
Under realistic scenarios — I would certainly go with the 2 Casey Blakes due to the decreased variance, as the benefit of consolidating WAR only becomes necessary and beneficial when all roster spots contain above-replacement level players.
I think this would hold more true for trading 4 “average” players for Pujols, as now you’re talking about 4 2-WAR players as compared to 1 8-WAR player.
by Trickman on Oct 13, 2009 3:21 PM EDT up reply actions 0 recs
Variance can be a good thing
If you are a fringe contender, you might as well take chances, because you’ll need a few things to break right. Instead of going with the more stable Casey Blakes, you’d want to take a chance that Pujols stays healthy and produces the 8 WAR.
by lookatthosetwins on Oct 14, 2009 12:46 AM EDT up reply actions 0 recs
I would pay a small premium to consolidate my WAR into fewer players if I had a large payroll.
Yes, there are a limited number of spots that contribute to your team, but surprisingly few teams run out of space.
Dave happened to write about this today: http://ussmariner.com/2009/10/12/roster-construction-theor/
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by Sky Kalkman on Oct 12, 2009 10:45 PM EDT reply actions 0 recs
Basically.
There is a finite number of teams that derive any value from the combining of roster spots like that. At one end of the spectrum you have really bad teams, where you could sign one 8-WAR player or two 4-WAR players or four 2-WAR players and end up at the same place, because you probably do have four positions where you’re pretty close to replacement. In the middle you have average teams, who again probably get the same benefit out of two 4-WAR players are they would one 8-WAR player.
You do have a handful of teams (right around two, in case you were wondering) that are stacked enough to get surplus value from an 8-WAR player compared to two 4-WAR players. But, unless those two teams are directly competing for ALL the same free agents, there’s no incentive for either of them to pay that premium; their competition is the average team, which has little to no incentive to offer the “consolidation” premium. You don’t have to pay that player what he’s worth to YOU, just a little bit more than what he’s worth to the second-highest bidder.
by cwyers on Oct 13, 2009 1:36 AM EDT up reply actions 0 recs
The "problem" is the definition of a replacement player
Please correct me if I’m wrong, but a full replacement level roster gets you some 60 wins, yet on average a team manages 81 wins. So if we assume 21 average players on your rosters and 4 guys warming the bench, an average player averages 1 WAR.
Now, if we assume 1 WAR to equal 0 Wins Above League Average, or WALA, then Pujols = 7.4 WALA and Casey Blake = 3.3 WALA, so 1x Pujols > 2x Blake. This basically comes down to an earlier point, you have one more spot on your roster to fill with a league average player. If you have lot’s of 2 WAR players on your roster, then Pujols = 6,4 Wins Above Rest of Team, while Blake is only 2.3 WART (sorry, now it’s becoming a bit dodgy).
The problem with this line of thought would still be that if League Average = 1 WAR, you would need to pay 5 mln. above replacement for that.
So the question then becomes: how easy is it to get decent league average players at good prices ?
I don’t think the payment for WAR is linear, and it shouldn’t be. Paying 125 mln on 25 1 WAR players is madness. It gets you 85 wins…
Yet, if your team is already in the 85 win area, additional WAR coming from Pujols’ 8.4 WAR i.s.o. 1 WAR League Average is more valuable for you as a team then the first couple of WARs. Similar to the curve above. Also, 8.4 WAR players will sell more merchandise, but that’s a different topic.
Furthermore I have an issue with WAR being valued at around 5 mln. If you assume 60 wins to be replacement Value and you probably need 20 mln per annum to pay for salaries, the price for WAR should be: (Total league budget – 600 mln) / 610 Wins Above Replacement. That’s more like 3 mln. for 1 WAR
by OPS2000 on Oct 13, 2009 7:24 AM EDT reply actions 0 recs
I think you're just resetting baselines, from what I an gather
First off, a replacement level team is supposed to be around a .300 team, or somewhere between 47-50 wins, so the baseline you used is off a bit. An average position player for his position is basically 2 WAR at 600 PA (Tango says it’s like 2.25 WAR per 162 games). And this doesn’t factor pitchers in either.
Paying for WAR on the free agent level is (mostly) linear. Teams don’t pay a whole lot more or less for it, and as Dave Cameron mentions in the article Sky links, the best players usually only bargain for years, but they still get the same general rate.
At the going rate, an average team (81 wins) would cost something like $148.5M IF you purchased every player in the free agent market. Of course, no team, not even the Yankees, does that, though the Yankees’ payroll affords them that luxury. For pretty much any team, that’s a poor use of your funds, but it doesn’t mean that the rate is not believable. Teams get cheaper because of cost-controlled talent, not because the WAR rate is nuts.
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by SFiercex4 on Oct 13, 2009 10:47 AM EDT up reply actions 0 recs
Also, that is a very pretty graph
A classic Power distribution.
by vivaelpujols on Oct 13, 2009 10:38 PM EDT reply actions 0 recs
I would rather have one Zack Greinke than one Albert Pujols
SteakGrowsOnDmitri: /crams win into mouth
SteakGrowsOnDmitri: mmm, these s**ts taste like unfair an outmoded pitchin metrics
by natalys26 on Oct 14, 2009 7:18 PM EDT reply actions 0 recs
That's because Pujols plays 1B.
Greinke is a comparable talent with a better contract at a scarcer position.
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by hazel on Oct 15, 2009 5:32 AM EDT up reply actions 0 recs
Why is SP scarcer then 1B?
Simply because 95% of hitters can play 1B and there are more MLB-quality hitters than there are MLB-quality pitchers?
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by Sky Kalkman on Oct 15, 2009 8:11 AM EDT up reply actions 0 recs
I would actually prefer the position Player
Pitchers get injured at a higher rate than position players.
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by Jeff Zimmerman (TucsonRoyal) on Oct 15, 2009 9:50 AM EDT up reply actions 0 recs
I may be wrong...
But it makes sense that two Casey Blakes would be more valuable(in terms of actual wins) than an Albert Pujols.
If you think about it, all WAR does is quantify the contributions of a player to the team. It does not quantify the RESULTS of those contributions.
To understand this we just have to do a quick little thought experiment.
Imagine you have two fake team.
One has Albert and 8 guys who sstrike out every AB
the other has two Casey Blakes hitting back to back and 7 guys who strike out every AB.
The team with the two Caseys will score more runs than the one with just Albert.
This is because fundamentally all WAR is doing is telling you a players contribution to the team, not how the team itself does.
A great real life example is Zack Greinke this year, the Royals finished almost 6 games behind their predicted finish based on WAR. The primary reason is because much of that prediction was based on Zacks numbers, while the true results were based on his contributions PLUS those of his teammates.
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by RoyalPug on Oct 19, 2009 7:58 PM EDT reply actions 0 recs
You would never have...
…the 7-8 guys striking out every time. They would be WAY below replacement level and you would certainly cut them for replcaement level players.
I think once you figure in a real minimum performance level for the rest of the team, that issue largely disappears.
by erosen on Oct 27, 2009 2:12 PM EDT up reply actions 0 recs
Using the baseballmusings lineup analyzer...
…seems to break when using 0 OBA and 0 SLG players.
Putting in one .443/.658 player and eight .000/.000 players yeilds -3.3 runs per game when it would more likely be around 0.3 [depending on how HR heavy the good player was]. Similarly, I got a negative number using two .363/.468 players and 7 .000/.000 players.
If we assume that average replacement level hitters might have .300 OBA and .350 SLG [2009 NL average was .331/.409], then the two Blakes plus replacement level (-ish) teammates have a range of 3.85 to 4.05 RPG for worst to best line-up combinations. The Pujols line-up comes up as 3.88 to 4.17 RPG.
Using NL average for the rest of the line-up, I get 4.92-5.14 RPG for Pujols vs 4.78-4.87 for the Blakes.
So, atleast this simulation says that the lousiest team worth putting together around these scenerios is about a wash either way. On a better team, the single player is a bit more valuable.
Granted a flaw in this is that I was using their actual OBA and SLG which won’t match up with WAR for a number of reasons [park, baserunning, positional adjustment, etc]
Only 31.7% of Blakes total RAR came from the batting component [which presumably contains some baserunning/GIDP value]. the same for Pujols was 86%, so what I just did might be better comparing two full-time players from the same team where one had 2x the batting portion of WAR as the other….
by erosen on Oct 27, 2009 2:42 PM EDT up reply actions 0 recs
Using 1998 Astros, Alou and Bell instead
Same team, nearly identical PAs. Alou .399/.582, Bell .364/.490
Alou plus eight .300/.350 players gave a range of 3.77-3.97
2xBell plus seven .300/.350 players gave 3.89-4.10 runs
Using the balance of the team with all average players [still using .331/.409]:
Alou 4.79-4.95
2xBell 4.81-4.93
Same for a uniformula well above average team [using .362/.468]:
Alou 5.83-5.93
2xBell 5.73-5.76
so, looks like a small postive on a uniformly great team to have the concentrated better player; about a wash on an average team and favoring splitting up the great player on a lousy team.
by erosen on Oct 27, 2009 3:50 PM EDT up reply actions 0 recs
Going to the another poster's idea...
… What about four 2 WAR players instead of the one 8 WAR player. Doing the same as my last post, I found twoplayers with similar PAs from the same team where one had a quarter of the batting value of the other. The 2006 Miguel Cabrera .430/.568 vs Dan Uggla .339/.480
Cabrera plus eight .300/.350 players gave a range of 3.79-4.05
4xUggla plus five .300/.350 players gave 4.20-4.45 runs
Using the balance of the team with all average players [still using .331/.409]:
Cabrera 4.83-5.02
4xUggla 4.88-5.00
Same for a uniformly well above average team [using .362/.468]:
Cabrera 5.86-5.99
4xUggla 5.62-5.51
Same results, but even more spread out. the 4:1 is even better for a bad team than the 2:1 and even worse for the uniformly great team.
by erosen on Oct 27, 2009 4:04 PM EDT up reply actions 0 recs
All about context
I’m sure all of these arguments have been laid out, but
1) You shed risk by diversification (see 2009 Mets)
2) Depends on the player that would take Blake Casey’s roster spot if you only had Pujols
3) You mention salary, but what about contract length?
In general, the 8-win player is the better upside play and the 2 4-win players is the better “safe” play. It also depends on how far away you are from a playoff spot, etc.. There’s inherent risk in each player you place on your roster. If you have 2 roster spots and 4 more wins gets you into the playoffs, you take the 2 4-win players. It’s very unlikely that you’ll get less than 4 WAR from the 2 4-win players due to simultaneous injuries or ineffectiveness. If you need more like 7-8 wins, you take the 8-win player and hope you’re capable of finding an above replacement-level player to occupy the 25th roster spot.
1 8-win player is, in essence, more valuable than 2 4-win players. That’s if they’re guaranteed to produce, though. Due to risk factors incurred by acquiring top-shelf talent (i.e. losing one of them has a disproportionate effect), teams don’t pay players based on an exponential curve. It’s linear. Much research has been done and the risk factors of placing that many resources into 1 player cancel out the benefit of getting that much production out of 1 roster spot. Therefore the relationship between wins and dollars is linear.
All things equal. It doesn’t matter. In a vacuum, 1 Albert Pujols is the exact same as 1 Casey Blake and 1 Blake Casey.
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by PWHjort on Oct 24, 2009 4:30 AM EDT reply actions 0 recs
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