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]
TAPPS = PTS/[FGA + (FTA/2) + TOV]
TOT = TOV/[TOV + FGA + (FTA/2) + TRB + STL + AST]
SSI = FTA/FGA
SAR = [FGA + (FTA/2)]/AST
3PR = 3PFGA/FGA
3PS = 3PFGM/FGM
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.