Monday, February 21, 2011

Value Investing: Player Contracts at the Dawn of a Hard Salary Cap

This week, we will identify the concept of value in a professional basketball player – in other words, what a player’s skills offer, taken in the context of what that player costs.  To make such an analysis more accessible, I will start with a glossary of statistical terms, which can be referred to by the reader:
SPR = [2PFGM + 1.5(3PFGM) + (FTM/2) + AST]/[FGA + (FTA/2) + AST + TOV]
TOT = TOV/[TOV + FGA + (FTA/2) + TRB + STL + AST]
SAR = [FGA + (FTA/2)]/AST

It is fun to imagine what we might do if given unlimited resources: buy that Gulfstream; vacation homes in Telluride and Tuscany; fix the New York Mets; et cetera, et cetera.  But the problem with a game like this is that it is too easy.  Provided an infinite cash flow, there isn’t anything we might not do, assuming such a thing does not live outside our moral code: If the money just keeps coming, and I do not find the objects within my sights reprehensible, then over time I would acquire just about anything.  There is no need for discretion when you have a bottomless wallet, at least not fiscally.

But if we live on a budget – and everybody, even the very wealthy, lives on a budget – we must purchase things based on the value they bring us:  The Gulfstream, for example, is not going to bring us joy if we cannot pay to fill it with gasoline, and the vacation home in Telluride is not worth much if its title leaves us with no money to buy a lift ticket or a mountain bike.

With the current collective bargaining agreement between the NBA and its players’ union about to expire, the concept of value in the context of player contracts has grown in importance.  The current rules governing team payrolls, which include a “soft” salary cap, place significant emphasis on contract value:  Since there is a limit, though flexible, to the amount of money a team can spend on payroll, any dollar given to Player A is one less dollar you might be able to offer to Player B, and so teams must be careful – if you pay too much for the Gulfstream, you might not have enough money left over to hire a pilot who can fly it (please refer to the New York Knicks from 2000 to 2010, who never even bought a Gulfstream, but overpaid for a used Suburban and a couple two-cylinder Yugos).

In the next collective bargaining agreement between the league and its union, it appears that the cap on team salaries may be lower, and it will almost certainly be a “hard” cap – in other words, there will be no flexibility that allows a team to exceed that cap limit, even by a temporary pittance.  If the NBA indeed implements such a system, some teams that have so shrewdly managed the current rules – for example, the Los Angeles Lakers of the last four years – will have a difficult time competing with their current model, since their discretionary spending depends so much on the flexibility of exceeding the cap.

And so teams will have an even greater internal mandate to seek out value – not talent at any cost, but relative talent at relative cost.  In the world of equity trading (i.e., stock trading), the concept of a stock’s value is often referred to in terms of its Price/Earnings Ratio (P/E) – how much does the stock cost in comparison to the profits that its company earns.  In this manner, Company X may be one-tenth as profitable as, let’s say, Apple – but if one share of stock in Company X costs only one-twentieth the price of a share in Apple, then Company X is the better value (it is, by this measure, twice as valuable).

With this investment paradigm in mind, I wanted to come up with a P/E rating for professional basketball players – a ratio of their salaries in comparison to their “earnings” on the court.  I figured that if you could monetize the relative value of professional basketball players, then you would be better positioned to spend more wisely for them when you are on a fixed budget – or, in this case, a hard salary cap.

As in a stock’s P/E ratio, the numerator of the formula was pretty easy to determine:  The player’s salary for the current year steps in and takes the place of the price of one share of a company’s stock.  But a player’s “earnings” was a little harder to determine:  What would be the analogue for the profits a single share of stock earns in a given year?

I decided to combine three offensive measures that, taken together, estimate what a player earns on the court:  the Successful Possession Rate (SPR), the Turnover-Adjusted Points per Shot (TAPPS), and the Turnovers per Touch (TOT).  Since the TOT is the only statistic of the three in which a lower number correlates with excellence, for purpose of “earnings,” the TOT was subtracted from 1 (i.e., 1 – TOT).  And so the formula for earnings (E) was determined to be:

E = SPR + TAPPS + (1 – TOT)

And so a player’s P/E was determined to be:

P/E = Salary/[SPR + TAPPS + (1 – TOT)]

As I write this post, the NBA is celebrating its All-Star weekend – replete with the distractions of its upcoming negotiations with its union, and speculation on where All-Star Denver Nugget Carmelo Anthony might end up.  With this as a backdrop, I have decided to determine the value – the P/E ratios – of 11 of this weekend’s All-Stars: Dwyane Wade, Kevin Love, Kobe Bryant, Anthony, Rajon Rondo, Amare Stoudemire, Dwight Howard, Derrick Rose, Lebron James, Kevin Durant, and Chris Paul.  In addition, I have chosen to look at four players who participated in the weekend’s Rookies-Sophomores game – Landry Fields, John Wall, James Harden, and DeJuan Blair – plus one former All-Star who is still young, still mentioned in high-profile trade talks, and is probably the best player on one of the league’s lesser teams (Devin Harris).

We will start with a table of each player’s SPR, TAPPS, TOT and cumulative statistical earnings for the 2010-2011 season:

                        SPR      TAPPS     TOT    Earnings
Wade               .567     .987        .084    2.47
Love                 .570     1.036      .057    2.55
Bryant             .562     .961        .082    2.44
Anthony           .523     .956        .075    2.40
Rondo              .666     .761        .113    2.31
Stoudemire     .533     .973        .089    2.42
Howard           .527     1.004      .087    2.44
Rose                .590     .929        .087    2.43
Harris              .612     .878        .104    2.39
Fields               .602     1.040      .070    2.57
Wall                 .583     .780        .108    2.26
James              .596     .972        .087    2.48
Harden            .583     1.004      .073    2.51
Durant             .561     1.034      .080    2.52
Blair                .489     .865        .077    2.28
Paul                 .687     1.005      .075    2.62

As you can tell from the highlighted figures, there are five players among these 16 who have earnings values above 2.50:  Kevin Love, Landry Fields, James Harden, Kevin Durant, and Chris Paul (with an astronomical 2.62).  From this very small sample, one can also infer that All-Star quality is associated with an earnings value in the range of 2.40, and a solid performer earns a value of about 2.30 and above.

The immediate issue that comes to mind, however – particularly in light of Fields and Harden being included among the very best – is that the cumulative earnings statistic is derived from ratio values:  SPR, TAPPS and TOT are all averages of what a player does, and not absolute values of specific achievements.  In this manner, the earnings statistic does not give adequate weight to the time a player spends on the court:  Fields, who averages only 32.6 minutes played per game, has much higher earnings than his teammate, Stoudemire, who averages 36.8 minutes; and Harden, who plays only 25.7 minutes per game, is virtually deadlocked with his teammate, Durant, who plays a remarkable 39.6.  Two hamburger chains may sell the exact same number of burgers per minute, with the same relative overhead, but if one chain keeps its restaurants open 24 hours per day, and the other one is only open 12 . . . well, you can see the potential difference.

So it became clear that earnings, if expressed as a performance ratio, must be weighted by time spent in operation.  I figured that an adequate manner in which to weight performance would be playing time – a player’s average amount of minutes played per game (MPG), divided by 48 (the total number of minutes played in a game).  If this co-factor were multiplied by earnings, you would get a more accurate reflection of game-time performance – something I have referred to as the Weighted Cumulative Earnings (wCE):

wCE = (MPG/48) x [SPR + TAPPS + (1 – TOT)]

With this new, weighted measure, every player’s earnings changes in relation to one another:

                        MPG    Earn.    wCE
Wade               37.1     2.47     1.91
Love                 36.8     2.55     1.96
Bryant             33.9     2.44     1.72
Anthony           35.5     2.40     1.78
Rondo              37.7     2.31     1.81
Stoudemire     36.8     2.42     1.86
Howard           36.7     2.44     1.87
Rose                38.0     2.43     1.92
Harris              31.9     2.39     1.59
Fields               32.6     2.57     1.75
Wall                 36.9     2.26     1.74
James              38.3     2.48     1.98
Harden            25.7     2.51     1.34
Durant             39.6     2.52     2.08
Blair                22.2     2.28     1.06
Paul                 35.7     2.62     1.95

It is remarkable what weighting for playing time does to the interpretation of statistics:  Landry Fields, for instance, goes from being the second-best “earner” on this abbreviated list to the tenth.  LeBron James goes from number six all the way up to number two.  The six players who have a wCE of 1.90 or higher are:  Wade, Love, Rose, James, Durant, and Paul.  James Harden, who is a role player, is nowhere near the top of this list – in fact, he is near the bottom.  Rajon Rondo, whose un-weighted earnings were decent, ascends to near the top of the list – ahead of Kobe and Carmelo – on the basis of his significant playing time.

It appears that the wCE statistic rewards well-conditioned players who stay out of foul trouble and are valued by their coaches – all good things.  On the other side, an aging player with balky joints (Kobe), or one who fouls a lot (Howard), have a decreased wCE.  Players like James and, especially, Durant – who do things well, and do things all game long – are absolutely top-earners.  You can also see how a player whose unweighted earnings are so much better than another’s – Fields over Wall, for example – might have his advantage diminish when playing time is accounted.  Because playing time is a variable that can be manipulated by coaches for a variety of reasons, it is probably best, statistically, to evaluate both a player’s unweighted earnings (E) and wCE.

Likewise, a player’s P/E should probably be expressed in both an unweighted fashion, as well as a weighted fashion (wP/E):

                        Salary($mm)     P/E                 wP/E
Wade               14.0                   5.67               7.33
Love                 3.6                     1.41               1.84
Bryant             24.8                   10.16             14.42
Anthony           17.1                   7.13               9.61
Rondo              9.0                     3.90               4.97
Stoudemire     16.5                   6.82               8.87
Howard           16.5                   6.76               8.82
Rose                5.5                     2.26               2.86
Harris              9.0                     3.77               5.66
Fields               0.5                     0.19               0.29
Wall                 5.1                     2.26               2.93
James              14.5                   5.85               7.32
Harden             4.3                     1.71               3.21
Durant             6.1                      2.42              2.93
Blair                0.9                      0.39              0.85
Paul                 14.9                  5.69               7.64

A few things immediately come to mind: 1) If Kobe were a stock in your pension fund, he is an absolute “sell”; 2) rookie contracts, and contracts that were negotiated prior to a player becoming eligible for unrestricted free agency, have significant value, and thus should be considered to have commensurate trade value (are you listening, James Dolan?); 3) greatness in an unrestricted free agent seems to deserve a wP/E of around 7.50 (Wade, James, Paul, e.g.), while the limits of value seem to be pushed at about 9.00 (Stoudemire, Howard, Anthony at his current contract, e.g.).

Some other thoughts:

Kevin Love provides remarkable value at his current salary.  If he maintains his current statistics and is kept to a maximum wP/E of 7.0, his maximum contract value would come to $13.7mm per year.

If young players perform better as their salaries increase, this would bode quite well for John Wall.  Unfortunately, I don’t think you play better just because you get paid more.  That said, dollar for dollar, Wall gives you a value-adjusted performance that is remarkably similar to that of Derrick Rose, who has a couple years experience on him (and a much better team around him).

Carmelo Anthony, at his current salary, is already over-valued.  If his salary is increased to the $22mm that he wants, his wP/E increases to 12.34, which is an absolute cap-busting franchise-wrecker – and almost double what James, Wade and Paul currently earn in regards to their value.

What should we pay for valuable role players?  It looks like a very valuable team player with some limitations to his game (e.g., Rajon Rondo) is worth a wP/E of about 5.0.  At his current earnings, Rondo is appropriately paid.  So, too, is Devin Harris.  As future valuable role players, Landry Fields should probably have his salary capped at $8.75mm (but only after he is free to negotiate); James Harden at $6.7mm; and DeJuan Blair at $5.3mm.

Next post: Evaluating the contracts of young players with a P/E growth index.

Wednesday, February 9, 2011

Win One for the Jimmer?

This week, we will identify the college basketball player who, to this point in the season, could reasonably be considered the Player of the Year.  To make such an analysis more accessible, I will start with a glossary of statistical terms, which can be referred to by the reader.
SPR = [2PFGM + 1.5(3PFGM) + (FTM/2) + AST]/[FGA + (FTA/2) + AST + TOV]
TOT = TOV/[TOV + FGA + (FTA/2) + TRB + STL + AST]
SAR = [FGA + (FTA/2)]/AST

If the college basketball season were to end today, the John Wooden Award for national Player of the Year would almost certainly go to Brigham Young University’s Jimmer Fredette.  After all, he really is a great player, stringing together one terrific individual performance after another for a very good team that would, nevertheless, be quite ordinary without him, all the while leading the nation in scoring.

And then there’s the name.

Jimmer.  He sounds All-American, as if he walked directly off the screen of “Hoosiers” and right onto a Mountain West basketball court:  “Let’s run ‘em out there, Coach – Merle.  Ollie.  Strap.  And Jimmer.”

But with all due respect to the Jimmer – and I believe he is due his fair share – I wanted to compare him to other players whose names, as ordinary as they may be, enter fairly into the debate on college basketball’s best player.  Since recently ran a piece in which Fredette was considered for the award in a field that included Ohio State’s Jared Sullinger and Connecticut’s Kemba Walker, I have decided to narrow my mid-season finalists to those three players.  And though I don’t consider him to be a serious candidate for national Player of the Year, I have decided to include Duke’s Kyle Singler as a basis for comparison, since he played so admirably in leading his team to a national championship last season, and once again leads a juggernaut this year.

Let’s start by comparing the four players’ traditional statistics:

                        PPG      RPG     AST      FG%     FT%

Fredette          27.6     3.5       4.2       .474     .885
Walker            23.4     5.3       4.3       .427     .820
Sullinger          18.0     10.1     1.4       .582     .710
Singler             18.1     6.1       1.5       .449     .800

By these measures, I believe the Jimmer would earn the nod over Sullinger and the others, on the strength of his scoring, phenomenal free throw shooting, and very good field goal shooting (made even more impressive when considered that more than 40% of his field goal attempts are three-pointers).  Sullinger has a wide margin over the other players in terms of rebounds and his field goal shooting, but the Jimmer is equal or superior to his competitors in the other traditional categories.  Give Round One to the Jimmer.

Now, a reasonable knock on a player like the Jimmer, of course, is going to be the level of competition that he has faced.  A Mountain West Conference player, the argument might go, does not have to face teams like those found by players in the ACC, Big Ten, or Big East.

And in 2010-11, that statement is true – though not in the manner that most might expect.  With the exception of a player in the Big East, a Mountain West player has to face much stiffer competition than a player from the ACC or Big Ten.  The Big East is the toughest conference in the country this season, but the Mountain West – with BYU and San Diego State emerging as possible Final Four candidates; with UNLV as an established national program; and with New Mexico looming – is right up there.

Look at the numbers.  By the Rating Percentage Index (RPI), Jimmer’s BYU squad has faced the ninth most difficult schedule in the country this season, which is the toughest schedule faced of any of the four players examined here.  Compare that to Walker’s UConn, who has faced the thirteenth-toughest schedule; Sullinger’s Buckeyes, who have faced the thirty-sixth toughest schedule; or to Singler’s Duke, who, in a down year for the ACC, has faced the fifty-ninth toughest road!  On strength of schedule, give Round Two to the Jimmer.

A second possible detraction from the Jimmer’s candidacy might be the definition of what a “Player of the Year” or “Most Valuable Player” is.  Some might argue, as it is often done in professional baseball, that an MVP-type award should be given to the most valuable player on one of the most competitive teams.

By this definition, you could reasonably give the Player of the Year to any of the four mentioned here:  Each is the centerpiece of a highly competitive team.  But by RPI rankings, BYU is the best team in the country; Ohio State is the third-best; Duke is the eighth; and UConn is the ninth.  Once again, Round Three goes to the Jimmer.

But now let’s look at the same players again, using the less traditional, Basketball I.Q. statistics:

                        SAR      SSI        TAPPS    SPR    TOT

Fredette          5.41     .356     1.08       .605   .089
Walker            5.10     .391     0.98       .568   .058
Sullinger          10.2     .673     1.12       .598   .050
Singler             10.7     .272     1.02       .548   .063

By these numbers, Ohio State’s Sullinger appears to have the edge.  His shot selection (SSI) is fantastic, and by far the best amongst the four.  Players of his Shot-to-Assist Ratio (SAR) quintile (fifth quintile, or Finisher), however, generally have higher SSIs because they shoot so close to the basket; Fredette and Walker, who are third quintile Balanced Scorers, have SSIs that, though nowhere near as good as Sullinger’s, are pretty good for players with a strong perimeter game.  Singler has a below-average SSI – almost certainly because 43.9% of his shot attempts are three-pointers, and in this way Singler is the collegiate version of Charlie Villanueva.

Sullinger also has the highest Turnover-Adjusted Points per Shot (TAPPS) of all four players – in part because of his excellent shot selection and field goal shooting, and in part because he takes extremely good care of the ball:  his Turnovers per Touch (TOT) is a very low .050, the best among the group (although low-post players should have lower TOTs than players who handle and pass the ball more, like Walker and Fredette).  That said, Fredette probably turns the ball over a little too much for a player who shoots as readily as he does, and Walker’s TOT of .058 is downright impressive in light of how much he passes, and the competition he faces.

Sullinger’s Successful Possession Rate (SPR) of .598 is extremely high for a Finisher (whose numbers do not benefit from the skew provided by assist totals), and perhaps more impressive than Fredette’s SPR of .605, which is aided significantly by his assists.  In the context of player quintile, Sullinger’s SPR is the most impressive of the lot.

And so, by the non-traditional statistics, Round Four goes to Sullinger.

So, with the traditional basketball numbers favoring the Jimmer, and the non-traditional statistics tipping toward Sullinger, I’ll have to go with team achievement as the tie-breaker.  Fredette’s BYU team is, currently, the best in the country (by RPI), and Fredette has led his team against a much more difficult schedule than Sullinger has (also by RPI).  As such, I’ll give the mid-season Player of the Year award to the Jimmer.

But I’d like to examine one more question before concluding:  Of the four players, who would I predict to make the better NBA player?

A few statistics stick out in my mind here, not the least of which is the players’ varying three-point basket rates.  If you look at the players’ 3-Point Rates (3PR, or 3PFGA/FGA) – I was tempted to name this stat the “D’Antoni Index” – Fredette and Singler take 41.7% and 43.9%, respectively, of their shots from behind the arc.  And if you look at what I refer to as their 3-Point Skew (3PS, or 3PFGM/FGM), 36.8% of Fredette’s buckets, and 36.4% of Singler’s, are of the three-point variety.  This does not bode well for either player in the NBA, where the arc will be pushed back another three feet behind the key, and another 15 inches at the corners.  Since so much of each of these players’ production is generated from three-point shots – particularly their TAPPS and SPR – I would expect a serious decline at the professional level.

Compare this to Walker, whose 3PR is only .325, and whose 3PS is only .250; or to Sullinger, whose 3PR is a negligible .040, and whose 3PS is only .014 (clearly, Sullinger only heaves the three as the shot clock winds down, or the half concludes).  The increased difficulty of scoring a three will have less of an impact on Walker at the professional level, and no impact at all on Sullinger.

The other statistic to consider is the SSI:  Expect each player’s shot selection to get worse at the professional level.  This bodes extremely poorly for Singler, and the decreased trips to the foul line will de-emphasize free throw shooting for Singler, Walker and Fredette – all of whom currently feature excellent free throw shooting as one of the most valuable parts of their game.  I would expect Sullinger to also take fewer trips to the line – but if his free-throw shooting is only 71%, and his field goal shooting is above 50%, this hurts him less.

Third, I lend a tremendous amount of weight to turnovers, particularly when you consider the extraordinary level of athletic defense these players would face in the NBA.  Sullinger and Walker both have impressive TOTs – and Walker has done this as a ballhandler in a very difficult and aggressive conference.  I would predict that both of these players will figure out how to care for the ball at the next level (though expect their turnovers to nevertheless increase).

And lastly, players’ respective ages suggest who as more room to grow – and Sullinger is the youngest among the four, with Walker right behind him.

And so, as a prediction of who will step it up as a pro, I might stand by the Jimmer as the college player to envy – but my professional money is on Sullinger first, and Walker second.

Next post: Monetizing players with a Price-to-Earnings Ratio