Notes from the Diamond #8: Room For Doubt

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David A. Salem
Email: david.salem@epsilontheory.com
Twitter: @dsaleminvestor

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Trivia Question #8 of 108. By how many pounds does the American League (AL) MVP for 2014 and 2016 outweigh the same award’s winner in 2017? Hint: both players remain active — at the top of their games, in fact — with the larger man weighing 42% more than his more diminutive counterpart.  Answer below.

Narrowing Gyre.  Let’s be honest.  While the topics on which these Notes focus — baseball and investing — are endlessly interesting to some of us, they’re inconsequential relative to some topics on which Ben and Rusty comment frequently and incisively, including the “widening gyre” in American politics and culture.  Depressingly, that gyre has grown wider since the prior note in this series was published, with multiple mass shootings, the jailhouse death of a monstrous criminal, and heated controversies spawned by such events having unfolded in the meantime.  Happily, there’s at least one aspect of life in these increasingly Dis-United States in which an angst-inducing gyre has been narrowing of late: the baseball’s world unending debate over an all-purpose test of on-field excellence.  This note examines the whys and wherefores of that narrowing — and explores an old but by no means outdated standard for gauging investment excellence that independent-minded stewards of long-term portfolios might find useful in an era of generally inflated asset prices and correspondingly low yields.

The author’s daughter (right foreground) overseeing Mike Trout’s BP at Fenway Pahk 8/9/19. Trout is in red and gray, mid-cage, bat in hand. Daughter and father enjoyed the game; Trout surely did not, his Angels losing 16-4 with Trout going 1 for 3 in four plate appearances (double, walk, strikeout, groundout).

Myriad Duties.  As was true of the factors animating baseball analysts’ angrily divergent views of optimal performance metrics earlier this decade, the more recent convergence of such views is rooted in large measure in the impressively mounting achievements of a player also featured in my last note: 28 year-old Angels outfielder and “WAR machine” Mike Trout.  Despite his uncharacteristically pedestrian performance for my baseball-loving 10 year-old at Fenway earlier this month, Trout is on track to become this year’s AL if not MLB champ in at least two widely followed statistical categories: home runs and runs batted in (RBIs). 

Why does this matter, and how has Trout’s evolving performance de-escalated the war among baseball cognoscenti respecting WAR?  Both questions are answered with characteristic elan by baseball pundit par excellence Ben Lindbergh in a recent Ringer post available here.  As noted therein, Trout’s uniformly solid discharging of the myriad duties shouldered by a position player has kept him at or close to the top of most baseball experts’ subjective rankings of the sport’s most valuable players since his MLB debut in 2011.  Including 2019-to-date, Trout has also ranked #1 five times, #2 twice, and #6 in annual rankings of the American League’s roughly 400 players sorted by the least-worst objective metric for assessing on-field excellence: Wins Above Replacement or WAR, more on which follows. 

Importantly, one of Trout’s five #1 WAR seasons came in 2012, when he notched the 31st highest single season WAR in baseball history (of more than 40,000 observations) while finishing #2 to the Tigers’ Miguel “Miggy” Cabrera in the essentially subjective process by which the Baseball Writers’ Association of America (BBWAA) picks a Most Valuable Player for each of MLB’s two leagues (American and National) each year. 

How could an impartial judge of on-field output possibly have deemed Cabrera’s more valuable than Trout’s in 2012 when Trout produced 41% more WAR that season (10.5 vs. 7.1)?  Beats me — but, much as I wish things were otherwise, I don’t make a living following baseball, as do the beat writers comprising BBWAA’s MVP juries.  In 2012, 22 of 28 such writers comprising that year’s jury voted for Cabrera, causing the six dissenters (all of whom voted for Trout) plus a large and vocal phalanx of “statheads” to complain that the 22 ascribed undue weight to Cabrera’s #1 rank in the trio of “traditional” batting stats comprising baseball’s hallowed Triple Crown (see box).[1]


Impressive as the stats for Cabrera just cited were — absolute and relative to Trout’s — when combined with other objective measures of offensive output to produce a broader metric of same known as Offensive War (OW), Cabrera contributed 13% less value-added to his Tigers on offense (measured by estimated team wins) than Trout did to his Angels in 2012: 7.7 OW for Miggy vs. 8.7 OW for Mike.

Value Added.  If you’re following along as carefully as my daughter did when reading this note (approvingly) in draft form, you’ve already caught a curious twist in our tale of baseball’s decreasingly fierce war over WAR: Miggy’s overall WAR in 2012 (combining Offensive War or OW with its defensive analogue) was 8% lower than his OW alone — 7.1 vs. 7.7.  In contrast, in finance-speak terms, Trout “added value” on defense as well as offense, performing certain deeds as an outfielder (i.e., improbable catches and the like) while avoiding others (i.e., errors) and in the process boosting his overall WAR to the aforementioned 10.5 from his offense-only WAR (OW) of 8.7. 


These WAR differentials may seem trivial to some readers, and inconsequential to most given weightier money and other matters confronting them, but bear with me, please: I’m using WAR to frame a consequential and conspicuously current concern respecting capital deployment — one entailing far bigger stakes for some readers than the estimated $8 million that a single WAR is worth in MLB these days.  Don’t find that $8 million estimate credible? Check out the nifty blog post from which it plus the nearby graph was lifted.  FWIW, the ten retired players to whom Trout’s evolving output is compared in the graph include eight Hall of Famers; the graph was prepared in March 2019, and thus excludes the roughly 8 WAR Trout has racked up during the MLB season now underway.

Something Big.  Crucially for our purposes here, Trout’s play this year makes him the odds-on favorite to achieve the AL’s #1 rank in the only “traditional” baseball stat (as defined in footnote 1) in which he’s not already achieved a league-leading single season rank at least once: home runs.  In short, the large and loud cadre of baseball analysts who deemed Trout’s stellar all-around play in 2012 sufficient grounds for an AL MVP crown despite Trout’s sub-#1 rank in all traditional batting stats except Runs Scored (129 vs. Cabrera’s 109) were on to something.

Something big, it turned out, with 2012 and Trout’s near-but-not-top rank in a host of statistical categories that year presaging truly extraordinary performance in the 6+ seasons Trout has played since his official rookie year.  (Trout played in some big league games in 2011 but not enough to disqualify him for the AL Rookie of the Year award he ultimately notched in 2012.)  At this writing, Trout’s career WAR (per BP) of 72.3 puts him 87th on the all-time list of big leaguers ranked by that stat — a mounting tally exceeding that of roughly 70% of the 267 players enshrined in Cooperstown.

The Fog of WAR.  What exactly is WAR?  Truth be told, my youngest daughter’s baseball precocity notwithstanding, neither she nor her dad nor indeed the “God of WAR” himself could furnish more than a Trump-like simpleton’s answer to the foregoing query without consulting cheat sheets like those furnished herein.  In fact, when asked near the start of what’s become the largest accumulation of WAR by a 20-something in MLB history what he knew about WAR, the young deity just referenced (Trout) replied, “That’s a good question.  Not a lot.”

A Brief Primer on Wins Above Replacement (WAR)

•  WAR is a stat that seeks to capture in a single number a player’s total contributions to his team.  For reasons discussed in the main text, WAR is an imperfect metric that’s best viewed as an approximation of player value rather than a precise measure of it.

•    Despite or perhaps due to WAR’s growing importance to allocators of human and financial capital in baseball, multiple methods for computing WAR have been devised, spawning endless discussion over the pros and cons of each.  Among publicly available WAR tallies, the three most widely followed are arguably those of Baseball Prospectus (WARP), Baseball Reference (bWAR) and Fangraphs (fWAR). 

•    Over any given season, WARs for the 1,000 or so men snagging more than trivial playing time in MLB typically shape up very roughly as follows:

•    Over any given MLB career, a player’s WAR will reflect longevity as well as effectiveness, as suggested by these career bWAR tallies for selected superstars:

•  For position players, WAR typically comprises a weighted average of stats for batting, baserunning and fielding, with adjustments for a player’s position and playing venues (stadia) plus multiple other factors of lesser import.  For the benefit of readers combatting insomnia, here’s how Fangraphs computes a position player’s WAR:

Position Player WAR = (Batting Runs + Base Running Runs + Fielding Runs + Positional Adjustment + League Adjustments + Replacement Runs) / Runs Per Win

•  For pitchers, WAR typically reflects runs allowed, with material adjustments to actual runs allowed to pinpoint a pitcher’s effectiveness independent of his teammates’ performance on defense.  As a further aid to readers seeking to nod off — or to ponder formulas even more complex than those needed to compute internal rates of returns (IRR) in a finance context — here’s how Fangraphs computes a pitcher’s WAR:

Pitcher WAR = [[(League Fielding Independent Pitching (FIP) – Player’s FIP) / Pitcher Specific Runs Per Win] + Replacement Level Wins) * Innings Pitched/9)] * Leverage Multiplier for Relievers] + League Correction

•  Over any given interval, a player can mess up enough to produce negative WAR, as has Albert Pujols of late (#31 in all-time career WAR despite -1.1 cumulative WAR over the last three seasons).  Pete Rose backslid similarly toward the end of his 24-year career, producing -2.5 cumulative WAR in his last five seasons.

End of Brief Primer on WAR

Here’s another good question — one that’s central to this note’s exploration of optimal metrics for gauging excellence in baseball or investing: must such metrics be as simple and straightforward as the Triple Crown stats that enabled Cabrera to trump Trout in AL MVP balloting in 2012?  To be sure, the ease with which anyone who’s crossed the threshold of baseball consciousness can not merely grasp but compute a player’s Triple Crown stats suggests that my kids’ kids will cite such metrics in assessing batters’ prowess — assuming such progeny emerge and their DNA causes them to ape their granddad’s avocational interests.

But the simplicity of MLB’s hallowed Triple Crown stats, like the simplicity of total return as one’s chief metric for gauging investment success, is not an unqualified virtue. In fact, such simplicity in gauging professionals’ performance can be hazardous to a ballclub’s health, or an investor’s wealth, for reasons described memorably by two of my favorite thinkers in my favorite fields of human endeavor.

Not Obvious.  “It is dangerous to spring to obvious conclusions about baseball,” sportswriter Roger Kahn has observed, “or, for that matter, ball players.  Baseball is not an obvious game.”  Nor is investing, defined for purposes of these notes as the deployment of capital over long time horizons with the aim of preserving and ideally enhancing its inflation-adjusted value net of planned withdrawals.  As investment pro Jim Garland has argued in musings that merit much closer attention than they’ve received by institutional investors as a group, “[I]nvestment risk isn’t a function of betas or Sharpe ratios or Value at Risk.  Instead, the primary risk facing [long-term investors] is …  the risk of a decline in the earnings and dividends from the corporations in which they’re invested.” 

Borrowing a term from farming, Garland refers to the hazard just described as “fecundity risk” — the risk that a portfolio will produce insufficient cash for its owner “to buy something important”.

A Brief Primer on Fecundity

Fecundity [writes Garland] is a “portfolio’s long-term ability to generate spendable cash for its owner”.

• Since most portfolios’ owners are legally empowered to withdraw principal as well income, the near-universal practice is to set withdrawals at levels commensurate with long-term expected real returns, with the latter typically guesstimated as follows:

Long-Term Expected Real Return = Income Per Se (Dividends, Interest and Rent) + Anticipated Capital Gains – Investment-Related Expenses – Applicable Taxes on Net Nominal Total Returns – Projected Inflation.

• Most investors excluding Softbank devotees recognize the perils of extrapolating capital gains (especially unrealized ones) into the indefinite future. But too few investors heed a corollary principle: that market values and the total returns they underpin often constitute “false positives” respecting a portfolio’s evolving soundness.

• Quoting Garland, “Jane Austen … and her character Mr. Darcy knew that long-term wealth should be measured by sustainable cash flows rather than by ephemeral market values. But what Jane Austen knew has been lost in the thundering dissonance of modern finance.”

• Computing with even approximate accuracy a portfolio’s sustainable cash flows is difficult at best, requiring as do most mission-critical tasks in money management — or baseball — a combo of art, science and craftsmanship. 

End of Brief Primer on Fecundity

I gave Garland’s seminal work on investment metrics a shout-out by featuring him in a TIFF workshop conducted shortly after the 2004 publication of a note Jim guest-authored for Peter Bernstein’s strategy service.  By happy coincidence, 2004 was also the year my beloved Red Sox used seminal analytics devised by baseball sage Bill James to win their first World Series in 86 years — a feat they’d repeat thrice more (so far) this century, including 2013, the year Jim delivered one of the best talks on investing I’ve yet encountered.

That talk — Memo to the Darcy Family: To Thine Own Self Be True — does a better job than I ever could propounding fecundity as the soundest metricfor gauging the evolving performance of so-called permanent portfolios: pots of money created and managed to enable their ultimate owners, taxable or tax-exempt, to buy important things — including but not limited to necessities — on an essentially indefinite basis.

Self-Awareness.  Given fecundity’s intuitive appeal as a metric for gauging permanent portfolios’ evolving health, one wonders when if ever during the century now unfolding a critical mass of such portfolios’ ultimate owners will become true to their own selves in the manner Garland commends.  How might such enhanced self-awareness cause principal-agent relations to change in the money management biz, and what events might catalyze such change?


Mr. Fitzwilliam Darcy (played by Colin Firth) and Miss Elizabeth Bennet (played by Jennifer Ehle).  This scene from a BBC adaptation of Jane Austen’s 1813 novel Pride and Prejudice ranked #1 in a 1995 UK-wide poll of the most memorable scenes in British TV drama.  Famously, Austen’s omniscient narrator describes Darcy’s prodigious wealth in income rather than net worth or market value terms, citing a “report which was in general circulation within five minutes [of Darcy’s entrance into the initial gathering of the novel’s protagonists] of his having ten thousand [pounds] a year”.

Answering the second question first (if not also stating the obvious), sustainable cash flow yields as distinct from recent returns and the market values underpinning them will reassume Darcy-like importance in wealth management when but perhaps ONLY when investors in WeWorks paying scant heed to such yields start losing far more than they win. 

As a true believer in Ben’s gospel that no one can foretell accurately when global capital markets will morph from the political utilities they’ve become back into “Two-Body Markets” (to quote Rusty) susceptible of effective analysis by thoughtful allocators, I won’t hazard a guess respecting when the losses just prophesied will materialize.   What I can foretell with confidence is that the forward-looking and hence unavoidably pliable character of Garland’s preferred method of gauging long-term portfolios’ evolving health will remain offputting to many fiduciaries, even after the tide turns and market values that such folks currently deem sound become fishy at best. 

I’m confident making this prediction because I’ve encountered such obstinacy multiple times in my career, most memorably when trustee groups for whom TIFF was managing money nixed portfolio moves animated by my team’s carefully considered judgment that technology stocks as a group couldn’t possibly generate sustainable cash flows commensurate with their fin de siècle valuations. 

Of course, I’ve also witnessed such obstinacy in an avocational as distinct from vocational setting, as noted in the above account of supposed experts making the silly but unsurprising choice to pick Miggy Cabrera over Mike Trout as AL MVP for 2012 despite Trout’s superior overall play as measured by WAR.  To be sure, Cabrera’s votaries rejected WAR-based arguments in Trout’s favor not because WAR is unduly speculative or forward-looking in a way that Cabrera’s Triple Crown-winning stats self-evidently were not; rather, Cabrera got the nod because three backward-looking stats he compiled more robustly than anyone else in his league including Trout (BA, HRs and RBIs) were more hallowed by MVP balloteers than the broader and better but equally retrospective valuation metric that Trout conquered in 2012 (plus five of the seven full or partial seasons since then!): WAR. 

Ardor for Ambiguity.  Its enhanced clout in player appraisals since Trout entered The Show notwithstanding, WAR continues to challenge even the brainiest baseball aficionados.  As anyone who’s consumed his analyses for ESPN or Fangraphs can attest, Sam Miller is among the brainiest (and wittiest) of such folks.  In an essay I enjoyed lots upon its initial publication in 2013 and re-read when assembling this note on the pursuit of excellence when gauging excellence in baseball or investing, Miller writes:

WAR is a crisscrossed mess of routes leading toward something that, basically, I have to take on faith.  And faith is irrational and anti-intellectual, right?  Faith is for rain dances and sun gods, for spirituality but not science.  Actually, no.  Faith is how we organize a complicated modern world … The complicated nature of WAR … isn’t an argument against it.  That’s just what human advancement looks like in the 21st century … I trust the recipes of FanGraphs, Baseball-Reference and Baseball Prospectus [BP] because these sites incorporate decades of research, the scope of which I could never match on my own.  These recipes will get even better because they get smarter with more data.  [BP] will soon incorporate into its WAR catchers’ ability to frame pitches.  The numbers next to each player’s name on that site will change.  Does that mean the numbers we have now are wrong?  Of course they’re wrong.  Everybody is wrong about everything all the time, and WAR leaves room for this doubt.  Doubt has driven us toward better answers for millenia, from Socrates’ “I only know that I know nothing” to the guys who made billions betting against a seemingly invicible housing market.  Don’t accept any number that doesn’t leave you room for doubt.” [Emphasis added]

“WAR Is the Answer” by Sam Miller (2013)

Dunno ‘bout you, but if I chaired an investment committee (IC) and were tasked with finding a new member for it, Miller might plausibly get my nod.  He’d get it because the tolerance and indeed ardor for ambiguity he displays is a vitally important  condition for investment success. 

Cognitive Errors.  More to the point, having a kindred soul like Miller at hand could boost the odds of getting the IC as a whole to practice what Garland preaches so persuasively in his Memo to the Darcy Family — teachings evocative of those Jane Austen illumines so artfully in her majestic novel about the Darcys’ evolving fortunes, Pride and Prejudice.  That novel’s central teaching  — that one should weigh all relevant info before acting or choosing consciously not to act — has obvious relevance to investing, even if its practical utility to conscientious investment pros is diminished episodically by tidal waves of cheap money that temporarily lift all boats, including those with skippers named Musk spiffy topsides but irreparably leaky hulls. 

The Austenian precept just flagged is germane to baseball too, of course, though typically tougher for ballplayers than investors to follow due to the high speeds at which baseballs and baseballers often move.  That said, clear eyes and a concomitant commitment to weighing all relevant facts before acting are undeniably vital for people who make their livings in baseball, including especially those who get paid not to play the game but to evaluate those who do. 

As we’ve seen, some of these folks messed up big time in 2012, weighing Miggy Cabrera’s dominance of three hallowed but batting-specific metrics against Mike Trout’s overall body of work and somehow judging Cabrera’s play in 2012 to have been more valuable than Trout’s.  It’d be unfair to Cabrera, and overstating my chief argument here, to label Miggy’s Triple Crown-winning stats in 2012 the baseball equivalent of Garland’s “ephemeral market values” — “noise” meriting scant attention as opposed to “signals” meriting the converse.  But, c’mon: given Trout’s extraordinary overall play since and including 2012, both absolute and relative to Cabrera’s, how can any competent judge of such matters deem Cabrera’s MVP award for Trout’s first full season as a big leaguer in 2012 to have been anything other than a cognitive error by those who conferred or applauded it?

Open Questions.  Which big money allocators (if any) are committing comparable cognitive errors at present?  As argued repeatedly in these notes, fielding such a blatantly censorious question presupposes a clear articulation of the metrics used to gauge investment success and the time horizon over which such metrics are optimally applied.  By my lights, the longer one extends the horizon over which investment success is judged, the more relevant Garland’s preferred metric of fecundity becomes — less as a precise gauge of the evolving utility of a portfolio than as a test of what the persons managing a portfolio truly know and think about each of its parts.

I know what you’re thinking as you ponder the words just written:

• Wouldn’t the ongoing fulfillment of these Garlandian expectations require the hired guns involved to know MUCH more about each holding they’ve selected than they typically do at present — to know each holding well enough to fashion the credible bottom-up assessment of its fecundity needed to compile top-down or fund-level estimates of what funds’ owners can withdraw and spend on a sustainable basis? 

• Wouldn’t principal- or owner-imposed requirements that money managers furnish such assessments trigger big changes in managers’ methods (i.e., asset selection, sizing, timing and reporting)?         

• Wouldn’t the widespread adoption of Garlandian metrics for assessing long-term funds’ evolving performance catalyze changes in institutional funds management as material as those MLB has undergone through the widespread adoption of advanced statistics like WAR and the complex array of task-specific stats that the WAR formula requires?

• Wouldn’t changes like those just conjectured enhance some investment pros’ value-added and in turn incomes, reduce others’ incomes, and likely force some if not many raccoons players out of the game of managing OPM for a living?       

You know how I’d answer the bulleted questions above — with enthusiastic yesses to all of them, mindful that the sabermetric revolution in baseball from which big money asset owners might usefully borrow certain tricks has spawned harmful as well as healthy changes in how MLB gets played, who gets to play it, and how much they get paid to do so. 

Certainly the enhanced stature and incomes of multi-talented stars like Trout or Jose Altuve — a player whose stellar advanced stats negate timeworn arguments that big leaguers must be big to be great — are welcome by-products of the cardinal importance ascribed to sabermetrics in modern baseball.  Certainly, too, the silver linings just flagged adorn menacingly large clouds: changes in MLB games’ length and character that have made them less fun for many fans and prevented countless others from becoming baseball fans in the first place. 

Two of MLB’s biggest stars: 6’2”, 235 pound Mike Trout (AL MVP in 2014 and 2016) and 5’6”, 165 pound Jose Altuve (AL MVP in 2017

On Deck.  I owe it to my youngest daughter if not also others with budding addictions to baseball to weigh in on MLB’s sagging “production values” (TV-speak for fan appeal) and will do so in a future NftD, though not the next one. That Note (#9) will focus on the inevitable and laudable extension of rigorous analytics to a hitherto unquantified and perhaps unquantifiable aspect of big league baseball (and big money investing): the impact of players’ character and temperaments on their and their teammates’ performance.  Consistent with the age-old principle that “you get what you measure”, MLB front offices are paying both closer attention to and more money for players’ invisible as distinct from visible gifts, with the former dowry defined broadly to include mindsets conducive to continuous improvement (“player development” in MLB-speak) plus interpersonal skills conducive to healthy team karmas and the winning records often spawned by same. 

Tellingly but perhaps unsurprisingly, the best player in MLB now and perhaps ever proved recently that he possesses interpersonal skills worthy of pro sports’ largest pay package ($432 million over 12 years), displaying acute empathy and grace in response to the sudden death of his Angels teammate Tyler Skaggs. 

Would exhaustive analysis of Mike Trout’s potential as a pro baseballer just before he became one as an 18-year old have foretold with actionable certainty the bounties he’d produce as a pro — analysis as thorough as the fecundity-focused probes that Garland commends to folks putting long-term capital to work?  Given the unavoidable uncertainties surrounding the future paths of young baseballers — or companies of any age or size — I doubt it.  But just because there’s room for doubt with any such analysis doesn’t mean it shouldn’t be undertaken.  It should — especially by allocators seeking to gain an edge under market conditions inimical to the profitable use of methods that served disciplined investors well in the past but have produced as many whiffs as homers since capital markets became political utilities Mike Trout signed his first pro contract in 2009. 

End

Mike Trout consoling Tyler Skaggs’s mother Debbie before the team’s first home game following Tyler’s death.  A longtime softball coach, Mrs. Skaggs delivered what the AP labeled a “heartbreakingly perfect strike” on the game’s ceremonial first pitch. Trout drove in six runs in the Angels’ 13-0 win, including a towering 454-foot two run homer off the first pitch he saw from Seattle starter Mike Leake.
Summer “school” for the author’s youngest daughter (2019). 
Nail colors are no accident.

Up next: the importance of character and temperament in “weak link” endeavors like pro baseball and institutional investing


PDF Download (Paid Subscription Required): Notes from the Diamond #8 – Room For Doubt


[1] I’ve put traditional in quotes because there’s no universally accepted rule for distinguishing baseball’s so-called advanced stats from all others, excepting perhaps a calendar-based rule rooted in the 1985 publication of stathead Bill James’s Historical Baseball Abstract, i.e., stats devised before 1985 can’t be “advanced” so they’re “traditional” by defaultThat transparently suspect point having been made, we’ll note that with the possible exceptions of On Base Percentage (OBP, which became an official MLB stat in 1984) and OPS (OBP plus Slugging Average), most statheads would agree that “traditional” batting stats comprise the two just mentioned (OBP and OPS) plus Batting Average, Hits, Homes Runs, Runs Batted In, Runs Scored and Slugging.  As my 10-year old daughter would be pleased to tell you if asked, Slugging = Total Bases/At Bats.  

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Peter
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Peter

David-great analogy, baseball to investing. Both look like team sports, but are really individual sports.

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Roy Blanchard
Member

Mr. Darcy’s 10,000 a year is a lot more meaningful than the value of his estates. I’m an 80-year-old egg farmer type who has chickens enough for us to live comfortably on the eggs for the rest of our lives. This story all by itself makes the pittance I pay epsilon for access a mere trifle. Thanks, all.

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