The Hardball Times -- John Burnson

Nothing adds up

John Burnson — 2009-09-25T09:00:15+00:00

Last week, we described a new method for deriving fantasy values. First, some loose ends:

Readers will note that we spoke of “the last drafted player” and “the pool of draft-worthy players” without saying how we knew who these players were. The approach we favor is running thousands of Monte Carlo simulations of fantasy leagues—simply casting players onto rosters with no care for balance or value. Our base metric is something that we call Weight on Winners (WOW)—the frequency with which a player appears on the winning club. The higher the frequency, the greater the value. Note that, because our simulated leagues do not enforce a budget, we cannot turn these frequencies into dollar values; however, the frequencies should reveal the rankings of our players, so that we can pluck out the top 108 players or the 10th-best player or whomever.

Here were the steps for this study. We simulated a 12-team, standard-5x5, mixed-league contest. There are 108 total pitching slots. The average price of a slot (given a $260 budget and 23 slots on both sides of the roster) is $11.30.

1. Find the pool of potentially valuable pitchers.

For best results, the competition between our simulated teams should approximate the true level. We don’t want to consider every player who threw at least one pitch. On the other hand, we also do not want to unfairly exclude someone who, even in limited play, can have an impact.

We resolve this dilemma by tossing every pitcher into a simulation of a couple thousand leagues and finding the lowest IP total among the top 108 players. Every pitcher below this threshold is essentially given a grade of “Incomplete” and ignored in later steps. It is not fair—either to the player or to owners—to treat ultra-short seasons as if they are on the table. Nobody is weighing Chris Carpenter versus Andrew Carpenter.

At this point in the season, the threshold is 30 IP. Pitchers with slightly higher workloads who look to have a crack at the top 108 include Claudio Vargas (1.93 ERA in 37 IP), Randy Choate (3.62 ERA in 32 IP, 5 Saves), and Sergio Romo (3.94 ERA in 32 IP but 2 Saves and 5 Wins). A notable miss is Neftali Feliz, who has only 28.1 IP, but he is bound to top 30 IP by season’s end.

You can see from the above trio that our method appreciates value in a variety of configurations: low ERA; moderate ERA but Saves; unremarkable ERA but Saves plus Wins. These choices fall out of the simulation naturally; we didn’t have to “do” anything other than set up the parameters.

2. Find the top 108 pitchers.

We take all pitchers who survived the cut in Step 1 and simulate another couple thousand leagues to get the true top 108. Recall that our $11 slot is one that can freely float among any of these players.

Not surprisingly, Zach Greinke took the top spot; simulated teams with Greinke won 35% of their leagues. Tied for second place at 30% were Dan Haren and Tim Lincecum. Chris Carpenter, Felix Hernandez, and Javier Vazquez formed a 3rd tier at 27.5%, followed at 26% by the first closer on the list, Jonathan Broxton.

3. Identify the $1 pitchers.

Recall that we are going to be introducing $1 players onto our rosters. Now, we don’t want to put too much weight on the particular player in the 108th position—he might happen to be a beast in one area, which would bias our findings. Moreover, we may need to swap in multiple $1 players, and it would be better not to re-use one guy.

So we’ll draw our $1 players from a pool of 12—the last six draftable (#103-108), plus the first six non-draftable (#109-114). In alphabetical order, here are the $1 players for this study:

             IP   W  Sv   ERA  WHIP    K
Bergesen    123   7   0  3.43  1.28   65
Breslow      65   7   0  3.46  1.09   50
Condrey      39   6   1  3.20  1.17   23
Johnson Ji   67   4   8  4.05  1.32   49
Kawakami    152   7   1  3.92  1.33  102
Masset       70   5   0  2.56  1.04   65
Morales F    38   3   7  3.05  1.30   40
O’Day        55   2   2  1.80  1.00   53
Palmer      114  10   0  4.03  1.34   65
Peavy        87   7   0  4.05  1.18   97
Troncoso     79   4   5  2.75  1.39   52
Zambrano    154   8   0  3.91  1.43  138

Again, there’s a good mix of players there.

So we’ve defined our $11 slot (the pool of the top 108 pitchers) and our $1 slot (the pool of 12 end-rounders). All that’s left is to run the experiment that we outlined last week. We’ll start with a straight version of Roster #1 (Halladay plus eight free-floating slots) and then replace one, two, and three of the floating slots with $1 players. Roster #2 is fixed with nine free-floating slots.

We submitted each two-team league (four versions) through 2,000 runs of our program and tracked the winning percentage of Halladay’s team at each stage.

Did we obtain Halladay’s value? No. Or, we don’t think so. Here’s the graph:

Nice curve, but you can see that it crosses the 50% mark well before we would expect it to. Based on this graph, Halladay’s roster would meet Roster #2 after replacing only 1-3/4 of Halladay’s $11 slots with $1 slots. This equality puts Halladay’s projected value at about $18. For a guy with 15 Wins, 193 K, and a 3.01 ERA in 221 IP.

We can get a slightly more customary valuation for Halladay if we extrapolate from only the first two points on the graph—that is, from a state with zero forced $1 slots to a state with one. Doing so raises Halladay’s estimated value by $3, to $21. Still probably $6-$10 below his real value, if standard valuation methods are to be believed.

What gives? We glean a clue from the line’s curved nature. By our hypothesis, each substitution of an $11 slot with a $1 slot should have led to the same $10 drop in Halladay’s value. But the slide here is not linear but exponential. Each added end-rounder degrades Halladay’s roster ever faster.

The notion of synergy among roster picks is not new. We know, for example, that once you get one super-speedster, additional super-speedsters have declining worth to you because you need only so many SB to seal the category. Ditto for anything that you’ve already bought enough of.

This study suggests that you can also have too much of nothing. Recall that the price of a player is $1 + the marginal price of his marginal worth. A pure $1 player, then, has no marginal worth. When you add a $1 player, you are giving up a chance to gain ground on the leader.

That wouldn’t be such a bad thing—if you had an infinite number of slots. But slots are precious. In fact, a case can be made that not all slots are created equal. For example, if you had a roster of Roy Halladay by himself, there would be a tremendous amount of value in simply adding a second slot. On the other hand, if you had a roster with 19 slots, the 20th would barely raise your interest.

Have we mislabeled our slots? For Halladay to merit a higher price, either the $11 slot needs to be re-priced upward or the $1 slot needs to be re-priced downward, so that the wage gap between the two slots is more than its current $10. Can we justify that? We'll keep you posted.

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Fantasy values by parallax

John Burnson — 2009-09-18T08:00:15+00:00

parallax n. : The apparent displacement of an object caused by a change in the position from which it is viewed.

Generating dollar values for fantasy players can be tedious. A common approach is to sum the stats above replacement level in a category and then divvy up those stats among a portion of the total budget and add up the contributions for each player. That’s doable, but there are challenges. For one thing, there are wrinkles to handling rate stats like BA and ERA and “clumpy” stats like saves and steals. Also, there is something unrealistic about treating categories as freely floating when there are obvious dependencies, such as between home runs and RBIs, or ERA and wins.

There is another approach. This one has its own challenges, including a longer time to derive the values, but it sidesteps the bumps with the usual method, and it’s easily tailored to many formats.

The key is to look at fantasy value from a different angle. Suppose that Roy Halladay is valued at $30 in your league. It’s true this says that Halladay’s stats are “worth” $30. But you could re-state this to say that paying $30 for Halladay neither helps nor hurts your odds of winning. If you get Halladay for less than $30, then your odds of winning go up, and if you pay more than $30, then they fall. But paying $30 neither raises nor reduces your odds; if it did, then $30 would be the wrong price.

So we have turned a statement of value (“Halladay is worth $X”) into a statement of probability (“Drafting Halladay at $X neither raises nor lowers your odds of winning your league”). Why is this good? Because now, to find the value of a player, we need only to find the price at which ownership of the player doesn’t alter your odds of winning. There are no other calculations—no defining of the spread of player stats, no breakdowns of categorical value.

Note that this method works in fantasy because we have a fixed budget. In the real world, things are looser—there is no price at which owning C.C. Sabathia “hurts” your odds of winning. However, real businesses are in the business of maximizing profits, and C.C.’s salary can surely hurt those.

So we have the bare bones of an approach. Let’s create a two-team league. (In this exercise, we’ll stick with pitchers, so that we don’t have to worry about accommodating multiple positions.) On one roster, we’ll put our player of interest—in this case, Roy Halladay. Halladay always appears on this roster. The other eight slots on Roy’s roster, and all nine slots on the other one, are open:

Roster #1              Roster #2
============           =========
ROY HALLADAY           Pitcher
Pitcher                Pitcher
Pitcher                Pitcher
Pitcher                Pitcher
Pitcher                Pitcher
Pitcher                Pitcher
Pitcher                Pitcher
Pitcher                Pitcher
Pitcher                Pitcher

The open slots will be randomly filled with 17 distinct pitchers (no duplication within or across rosters.) After populating the rosters, we will determine the side that “won,” based on whatever categories we have in our league, and behaving as if these were the only two teams in our league. For example, in standard 5x5 roto league, there would be five categories—wins, saves, ERA, WHIP, and strikeouts. Finishing first in a category in our two-team league is worth two points, and finishing last is worth one. We’ll repeat this exercise 1,000 times for various roster configurations and track the winners.

(Why do we need to track only two rosters, even if our real league has more teams? Because each Halladay-less roster is identical. Suppose that there are 10 other rosters like Roster No. 2. Each is indistinguishable from Roster No. 2, because all rosters draw from the same pool. If we can balance Halladay’s roster with Roster No. 2, then we’ll also have balanced Halladay’s roster with the other rosters. A one-in-two chance of beating Roster No. 2 equates to a 1-in-12 chance of beating the league.)

Our ultimate aim is to make Halladay expensive enough that his team wins exactly half the time. “That’s swell, but you have no dollar figures. So you can’t turn your probabilities into prices.” And that’s true. We need points of reference.

How many points? Perhaps as few as two. If we have two points of reference, we might be able to adapt the method of parallax, which is used by astronomers to determine the distance to stars. But that’s getting ahead of ourselves, because we don’t have two points of reference.

But we do. For any fantasy league, there are two statements that we can say with certainty (both statements require us to identify the draft-worthy pool of pitchers—we’ll tackle that later):

1. The last drafted player is worth $1.

2. The worth of a slot that freely floats among all draft-worthy players is the average price spent on that slot. If owners in a 12-team league historically spend $99 on nine pitchers, then a pitching slot that freely floats among all 108 draft-worthy pitchers is worth $11.

Now, in a real auction, you can’t draft a “freely floating” slot. However, in our simulation, we can—in fact, in our diagram, each slot labeled “Pitcher” is exactly that. In a particular run of the simulation, the slot could be worth $1, or it could be worth $50. But the expected value of the slot is $11. (Actually, it is slightly less, since one pitcher—Halladay—is not available. But $11 works for our purposes.)

Armed with our two points of reference, we can employ parallax. Here’s the approach: Roster No. 2 will never change—it will always contain nine freely floating pitching slots. For our first 1,000 runs, Roster No. 1 will also be the same. Over time, though, we’ll swap free-floating slots (worth $11) for the last drafted player (worth $1). Each switch means a drop in value of $10 for Halladay’s team.

Eventually, we’ll reach a point at which Halladay’s roster wins only half the time. Since the odds are the same, the total value of each team must also be the same. We know the value of Roster No. 2 ($99), and of the non-Halladay slots on Roster No. 1 (either $1 or $11), so it’s easy enough to solve for Roy’s value.

If we replace all eight floating pitchers, we could end up with a graph like this (not real numbers):

Here, when Halladay is paired with eight freely floating pitchers, his team wins more than 75 percent of the time. However, when he’s stuck with eight $1 pitchers, he wins only about 15 percent of the time.

To find Halladay’s value, just read off the point at which the trend line crosses 50 percent. In this case, that’s around 3.5. So Roster No. 1 would be balanced with Roster No. 2 if 3-1/2 slots worth $11 were replaced with the same number of slots worth $1. Ergo, Halladay is worth $35.

That’s the idea, anyway. Will it work?

NEXT WEEK: Will it work?

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Measuring catcher defense

John Burnson — 2009-08-21T13:26:15+00:00

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Near-Sighted Marcels

John Burnson — 2009-08-21T06:30:15+00:00

In the sweep of human history, major-league baseball is, shall we say, a recent innovation. It’s not surprising, then, that we have a poor sense of the proper time scale for evaluating baseball talent. Only since a bunch of men met in La Rotisserie Française to draft mock baseball teams did what happened three years ago become more important to our survival than what happened yesterday.

Take hitters. Tom Tango’s Marcel system says that a hitter’s expected performance in one year is a function of his (and his league’s) numbers in the prior three years. One element of the algorithm is a weighting of 3/12 for the hitter’s performance in the earliest of those three years. There is no way that fantasy leaguers credit 25% of a hitter’s expected performance in 2010 to his numbers in 2007. (In truth, the full weighting is less than 25% since Marcel also calls for 1,200 PA of league-average stats. However, 3/12 is the fraction of the hitter’s portion contributed by that early year.)

Likewise, Marcel asserts that the latest of the hitter’s last three seasons contributes 5/12 (out of all the hitter’s numbers) to the next year. Propose to your leaguemates that less than 50% of a hitter’s expected performance in 2010 hinges on his play in 2009 and you’ll be laughed out of the room.

But those are the ratios per Marcel (and I’m sticking with Marcel here, granting that it is simple, because “simple” can still mean “smarter than us”). The past is prologue, but the immediate past is not the whole story. The point is not that just-closed history is immaterial but that only slightly mustier history fades too fast. I don’t know about you, but six months ago feels like three years ago to me.

What we would be really useful, for fantasy games, is a way to identify players for whom we have exaggerated perceptions—those are the rich buying and selling opportunities. One route would be to examine ownership levels in online leagues or aggregate rankings in mock drafts. However, simpler would be a programmatic approach.

To that end, we’ve created Near-Sighted Marcels (NSM's). NSM’s are simply Marcels with a more, ahem, human-like ratio of memories. In Near-Sighted Marcels, the remote past still counts, but the recent past counts much, much more.

What ratio of the past three seasons should we use? After careful (in human terms!) deliberation, we went with 80/15/5—that is, our internal projections for players are composed roughly of 80% of this year’s numbers, 15% of last year’s, & a sprinkling of the year before’s. That seems a fair (if humbling) allotment. (In the Comments, feel free to discuss the ratio that you would choose.)

Here is a comparison of the coefficients for both standard and near-sighted Marcel (ratios adjusted to 100):

	'09	'08	'07
NSM	80	15	5
Marcel	42	33	25

By this light, humans judge the immediate past to be twice as relevant as does Marcel, but the prior year only 1/2 as much, and the outlying year only 1/5 so.

We generated both Marcels and NSM’s for 2010 for the current crop of hitters. We pro-rated the YTD numbers to a full season by multiplying by 4/3. We also expressed the ratio for NSM's as 9.6/1.8/0.6 so that the total magnitude (12) would be the same as with Marcels (5/4/3) and mesh with the injection of league-average PA.

Let’s stick to OPS. We’ll define “Sentiment” as a batter’s NSM OPS minus his Marcel OPS (so a Sentiment above 0 indicates a player who is regarded more favorably by humans than by Marcel).

The leader in Sentiment this year is Tampa Bay shortstop Jason Bartlett:

Jason Bartlett
Year	OPS
2007	699
2008	690
2009	932
2010	OPS
Marcel	775
NSM	855
Sentiment: +80

If you give this season a weighting of 80%, you anticipate an OPS for Bartlett of over 850. Now, Bartlett is having a stellar season, but Sentiment advises us not to get carried away by a guy who had a career 699 OPS in 1,700 PA entering this season, and who has hit as many home runs this season as he did for his entire career before 2009.

Among players with at least 300 PA, here are the leaders in Sentiment:

	Proj OPS
	Marcel	NSM	Sentiment
Bartlett	775	855	+80
Mauer	901	976	+75
Willingham	848	904	+56
Reynolds	855	906	+51
Zobrist	832	881	+49
Lind	806	853	+47
Young M	804	850	+46
Scutaro	757	799	+42
Overbay	784	826	+42
Upton J	831	872	+41

Say what you will about their maturation (and you will say it), these guys should be regarded with a dash of skepticism and off-loaded (for top dollar) with only seeming reluctance. Every thing that can go their way, has.

It’s harder to find laggards in Sentiment with more than 300 PA—depressed play usually means depressed playing time. Still, you could probably guess the big names: Giles, Ortiz, Cedeno, Ordonez, Renteria, Matsui, Upton (B.J.), Burrell, Atkins, Navarro. Guys who (as anyone is happy to tell you) are down to their last swings. If I had a rebuilding team, I would be scooping up these guys like souvenir cups (and at comparable prices).

It’s good to take stock of our limits. It’s even better if we can characterize those limits and play against them. As you plan your keepers for next season, remember those ancient eras when the year ended in an "8" or "7."

(Here is a link to a spreadsheet with both regular and near-sighted Marcels for all hitters with at-bats in each of the last three years.)

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End of days

John Burnson — 2009-07-24T06:20:15+00:00

Betting on the emergence of prospects can be frustrating—apart from such matters as the caliber of the guy above the prospect on the organizational chart, and the will of the parent club to avoid contractual triggers, there’s the question of whether the prospect’s approach in the minors will even translate to the majors. However, once a player reaches the majors and gets an extended audition, predicting when he’ll leave should be more straightforward.

We decided to explore this question. We wanted to find the level of performance at which fielders post their final season of consequence.

We gathered all seasons from 1990-2008 that may have been fantasy-relevant. We chose 300 AB as the minimum load for a potentially valuable season; that’s probably low, but we wanted to err on the side of too many seasons. In each season, we assigned players to the position where they played the most games. (If a player played two positions equally often, we qualified him at both.)

We then asked: What is the OPS for these players in the year before they disappear—i.e., in their final 300-AB season? We could have used a more sophisticated metric than OPS, such as wOBA or Predicted OPS, but we went with OPS for its simplicity and familiarity. (In truth, the question is not by what measure players should be deemed done but by what measure players are deemed done by major-league GM’s. For all we know, GM’s steer by BA....)

We expect that the onset of obscurity varies by the offensive demands put upon the player, so we grouped the results by position. Note that the only position that mattered was the batter’s position in his final 300-AB season; we did not track whether players were shifted from more defensively stringent positions.

Because 2009 is not in the books, we did not treat 2008 as anyone’s final season (there may be a few players who last played in 2007 but whose careers are not over, but they should not soil the analysis). We did include players who had just one 300-AB season (by definition, their last one).

Here are the results:

End of the Road
Position	OBP	SLG	OPS
1B	.350	.440	.790
3B	.325	.397	.722

2B	.326	.370	.696
SS	.311	.358	.669

LF	.339	.416	.755
CF	.326	.380	.706
RF	.336	.428	.764

C	.322	.390	.712
DH	.338	.439	.777

Note that these are aggregate levels; some batters had better numbers when they checked out and some had worse. And obviously, there are team-level considerations that we are missing, notably who (if anyone) is ready to take over. Still, the trends are as we would expect: The bar for further paychecks is high for first base and the corner outfield positions and lower for 2B, SS, CF, and C.

This is a sound starting point—when a player slips to this level, he (and you) should be scouting other opportunities. However, even better would be to say “For an OPS of X, a player’s chance of losing his job is Y.”

So let’s try that. For players who qualified at first base, we arranged all the player-seasons from highest to lowest OPS. We would expect to find many more “final destinations” at the bottom of the list than at the top, and indeed there are: Only one of the 25 top-rated seasons (4%) was a cul-de-sac, whereas 9 of the 25 bottom-rated seasons (36%) were.

Here is the graph for first base. The blue line is OPS, for non-overlapping buckets of 25 batters. The purple columns are the observed fade rate for each group; the thick black line is a trend line. (We say “fade rate,” not “extinction rate,” because the players might still putter around baseball; however, never again do they log 300 AB in a season.)

The trend line lolls around 5% for a while (even the best players are vulnerable to a career-ending injury). And then, starting around .850 OPS, fade rate rockets up, eventually surpassing 30% for the dregs of MLB first basemen. (The miracle might be that that rate is not higher; it may speak to the slow pipeline of talent within an organization.)

Armed with this chart, and knowing the OPS of a first baseman, we can now guess his chance of not attaining 300 AB next season. Here are the projected fade rates for the first basemen who are on pace for 300 AB this season:

Bailout Neediness, 1B
Player	YTD OPS	Fade Rate
Pujols	1.161	3.3%
Fielder	1.047	4.1%
Votto	1.034	4.2%
Morneau	.996	4.4%
Youkilis	.979	4.6%
Cabrera Mi	.947	4.9%
Branyan	.941	5.0%
Helton	.934	5.1%
Berkman	.932	5.1%
Teixeira	.916	5.3%
Gonzalez Ad	.910	5.4%
Morales K	.896	5.7%
Howard	.878	6.2%
Prado	.871	6.5%
Pena C	.866	6.7%
Lee D	.864	6.9%
Konerko	.858	7.2%
Overbay	.849	7.9%
Johnson N	.835	9.1%
Garko	.807	13.4%
Butler	.804	14.0%
Cantu	.775	19.4%
LaRoche Ad	.770	20.2%
Loney	.758	22.1%
Kotchman	.747	24.0%
Huff A	.732	26.0%
Ishikawa	.727	26.7%
Giambi	.697	29.3%
Davis C	.671	30.5%
Murphy Dan	.662	30.9%

There’s roughly a 50% chance that at least two of the bottom five players won’t be entertaining fans in 2010.

There is a lot of room to extend this study. The natural next variable would be age—it is possible that MLB owners are pokier with the pink slip for younger players than for older ones. We could also focus on base skills, such as contact rate and walk rate, rather than on surface stats. Still, this approach is fresh ground for figuring long-term worth, for fantasy and major-league GM’s alike.

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Worst Monday: Balloting open

John Burnson — 2009-07-21T11:59:15+00:00

A broad slate of games yesterday, including five teams that scored 10 runs or more. Will the hitting outweigh the pitching? How low will this week's winning score be? Will it even be negative? Let's find out.

Entering's a snap:

1. Send an email to .

2. Put Worst Monday in the subject line along with your Monday point total.

3. Attach a screen shot of your roster and their points scored for Monday. (You can paste the screen shot in a Word document and attach that.) We need the screen shot—don't spell out the tallies in the email.

4. Add brief biographical material.

We'll sift through the entries & give the lowest score on Wednesday. Each weekly winner gets a year of Heater Magazine. The winner with the lowest score for the season gets a free copy of the 2010 Graphical Player, coming out in December.

Also, we wanted to recognize the winners from Week 5, John Kral and Ricardo Elorza. Only one of the two owned Johnny Cueto, but both were undone by starting pitching.

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Worst Monday: Balloting open

John Burnson — 2009-07-07T14:20:15+00:00

Do you have a Big Red Machine pounding in your head this morning? Or maybe you went to the Millwood once too often, or ordered "Pettitte" when you meant "petite"?

Let us know. Entering's a snap:

1. Send an email to .

2. Put Worst Monday in the subject line along with your Monday point total.

3. Attach a screen shot of your roster and their points scored for Monday. (You can paste the screen shot in a Word document and attach that.) We need the screen shot—don't spell out the tallies in the email.

4. Add brief biographical material.

We'll sift through the entries & give the lowest score on Wednesday. Each weekly winner gets a year of Heater Magazine. The winner with the lowest score for the season gets a free copy of the 2010 Graphical Player, coming out in December.

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Mark DeRosa needs a raise

John Burnson — 2009-07-06T05:01:15+00:00

Recently, 34-year-old Mark DeRosa was traded from the Indians to the Cardinals. The occasion brought to light an aspect of DeRosa’s value that is overlooked (or, at least, under-enumerated).

That aspect is DeRosa’s versatility. Thus far in 2009, DeRosa has played 44 games at third base, 17 games in left field, 9 in right field, and 8 at first. Last year, his main spot was 2B (95 games), but he also played at least 20 games at 3B, LF, and RF, along with one game each at 1B and SS.

Such flexibility is not trivial. Why did St. Louis want DeRosa? As Rotowire.com put it, DeRosa “can play all over the infield, which makes him a perfect fit for the Cardinals.” Assuming this is true (and it’s almost inarguable), then there is an element of DeRosa that we need to account for. Sure, we can go through and total DeRosa’s Wins Above Replacement at each position. But that exercise dodges the value of the ability itself to play multiple positions.

There are two major ways in which DeRosa provides greater value than does a player of the same total WAR but single-position eligibility:

1. Higher resale value

Because DeRosa can play multiple positions, he can fill holes on a larger number of teams; hence, the demand for his services is stronger and so the winning bid should be higher. (This is true even if each team intends for DeRosa to play only one spot; it’s the volume of bids that matters here.)

Cleveland almost certainly fielded more offers for DeRosa—and hence got a better deal for him—than if he played only one spot. Likewise, in the expert fantasy league LABR, the winning FAAB bid for DeRosa was so high ($80!) in good part because most teams could justify submitting bids. (There may even be an add-on effect, whereby teams pay a premium because they know that DeRosa will be easy to off-load later.)

If you want a bargaining chip, you can’t do better than one that appeals to every buyer.

2. Easier replacement of teammates

Because DeRosa can play multiple positions, he indirectly expands the list of tenable substitutes at positions that he can play but that he’s not currently playing. Your left fielder goes down? Well, you can keep DeRosa at 2B and look for a LF—or you can put DeRosa in LF and look for a 2B. Whichever's better.

The thing to note about this factor is that it’s REUSABLE—each time that DeRosa’s team loses a player at a spot that DeRosa can play, DeRosa’s owner can cast a wider net for fill-ins. And a larger pool of candidates should mean a higher-caliber substitute. (Note that we are not saying that DeRosa has the same value at each position, only that he expands options.)

Moreover, DeRosa’s owner can discriminate not only among overall value but among the nature of that value—maybe the team wants speed, maybe they want a left-handed bat, maybe they want a closer. Whichever the case, more applicants means a better fit.

Imagine two teams. Every player has the same relative value for his position, but on one of the teams, players can play only one spot, whereas on the other team, players can play every spot.

Which team will finish with the better record? The first team—IF two things are true:

1. Players are inconsistent. If players never got hurt or had bad genuinely match-ups, or they never went on stretches that (rightly or wrongly) left them open to demotion, then positional flexibility wouldn’t matter because players would never need to be replaced.

2. Replacement talent is not evenly distributed. If every replacement player who was available to a team had the same relative value for his position, AND talent was evenly distributed among replacement players such that players were identically skilled from both sides of the plate, on the basepaths, and with the glove, then positional flexibility wouldn’t matter because no player would address a need better than would any other.

Fortunately, both things are true: Players are inconsistent, and replacement talent is not evenly distributed. And if the first team does beat out the second team, then our notion of “value” must be incomplete.

In fact, it seems to me that NO extant valuation method properly accounts for DeRosa’s versatility. Valuation systems generally treat a season as a set of numbers—add up the player’s contributions at the plate and in the field and you have his value. However, a season can also be seen as a string of events (some within a team’s control, some out of it). In that light, finding a player’s value entails not a comparison of that player’s success to the success of other players at his position, but a comparison of his team’s success to the success of teams (real or conceived) that lack the player.

Current valuation models are static. They miss that flux; they miss the ebb and flow of a season.

Mark DeRosa “makes his team better,” not because of pats on the back but in a true economic sense: He expands the options for the team when one of his teammates goes down, or when the team is looking to deal him for a needed quantity.

Whatever Mark DeRosa’s making, it’s not enough.

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Worst Monday: Week 4 results

John Burnson — 2009-07-01T14:50:15+00:00

Reader Jim Ulbrich on Monday sent forth nine batters—well, he hired nine batters to go forth. Most of them took the money and ran:

                 Monday's result
J.D. Drew           3-for-5
Bobby Abreu         2-for-4
7 other batters     0-for-28

Making things worse is that Jim plays in a linear-runs league in which all outs are negative. As a result, Jim's team put up -5 points. For his efforts, Jim receives a year's subcription to Heater Magazine. The race for the overall prize, a free copy of the 2010 Graphical Player, is still led by two past winners who recorded -5.7 points.

Of the other entrants, we are also going to recognize Brian Mills. Brian actually finished Monday with 1 point, which would have been a stroll on the beach for Jim Ulbrich; Brian's problem is that his opponent scored 65.5 points, for a Monday deficit of 64.5 points. That'll happen when your opponent runs out Tim Lincecum, and you run out Rick Porcello. For Brian's efforts, we will also be setting him up with a subscription to Heater.

Thanks to everyone who entered!

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Worst Monday: Balloting open

John Burnson — 2009-06-30T14:19:15+00:00

Finally, a Monday with some meat! Twelve games—plenty of opportunities for heroes or (in our case) goats.

Are you gazing this morning at a double-digit deficit in the standings for the week? March out the offenders!

Entering's a snap:

1. Send an email to .

2. Put Worst Monday in the subject line along with your Monday point total.

3. Attach a screen shot of your roster and their points scored for Monday. (You can paste the screen shot in a Word document and attach that.) We need the screen shot—don't spell out the tallies in the email.

4. Add brief biographical material.

We'll sift through the entries & give the lowest score on Wednesday. Each weekly winner gets a year of Heater Magazine. The winner with the lowest score for the season gets a free copy of the 2010 Graphical Player, coming out in December.

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