Faced with the choice of nominal gains or no gains at all, investors have opted for the former, in the hope that they’ll come out ahead once the economies have finished resetting. In the euphoria of the last few months it can be argued many investors have actually been unable to distinguish between real and nominal gains — blame the short attention span a pile of cash earning 0% causes — and have bought into the rally with commitment, ignoring the naysayers’ warnings of a repeat of the whipsawing markets of the Great Depression. The central banks, of course, are just relieved the naysayers are being ignored, regardless of what’s going on: they’ve run out of tools so the perception of confidence and control are all they can offer. Anyway, who’s to say the rally is unsustainable or that this is a fool’s rally — aren’t markets the only authority on themselves?

I claim no expertise at interpreting the wider economic implications of what’s going on, but it’s becoming apparent that what’s happened is that inflation, the beastie we were all fearing has been replaced by devaluation, it’s more subtle twin. The FT had a good article examining how cross-currency investors were possibly the best positioned for last year’s meltdown (though clearly the right combination of currency and asset was crucial). The traditional safe havens, US treasuries and gold, have become less attractive, both because inflation has been under control and because of their own problems (US treasuries are dollar-denominated and don’t offer a yield, and gold has reached a psychological ceiling).

So, my view? Nothing you haven’t heard already, I’m afraid: Inflation in the mid-to-long term, and whipsawing markets in the short term. Great time to be trading currency :)

The Constitution only guarantees the American people the right to pursue happiness. You have to catch it yourself.

- Benjamin Franklin

I don’t claim to know what Mr. Franklin was thinking, but I find it telling that the quote works equally well if you leave out the second sentence. That, my friends, is what American exceptionalism is actually about.

With that in mind, it’s interesting to read J.A. Adande’s recap of Game 4 with a scorecard on hand. What we see is that Kobe Bryant, who scored 38 points on 66% shooting in 39 minutes, ended the game with a +4 rating, the same as Luke Walton, who chipped in 9 points on 50% shooting in 19 minutes. Sasha Vujacic had a +9 for his contributions of 9 points on 33% shooting in 17 minutes. The guys who fare the best are Lamar Odom (10-15-6 line on 40% shooting in 41 minutes, for +20) and Pau Gasol (13-10-1 in 41 minutes, for +15). Clearly, those numbers are all over the place, but what’s weird is how Kobe ended up with just a +4, given how much everyone insists he dominated the game. The following excerpt from Adande’s article helps to explain this:

Bryant came out firing. … He scored the Lakers’ first 11 points and 13 of their first 15, hitting 6-of-8 shots in the first quarter. … But the rest of the Lakers went 2 for 10 and Utah led, 25-20. The turning point actually came when he was on the bench at the start of the second quarter and the Lakers fielded a lineup of Shannon Brown, Sasha Vujacic, Luke Walton and starters Lamar Odom and Pau Gasol. It was the reserve players who hit three consecutive 3-pointers to take the Lakers from a seven-point deficit to a two-point lead.

A-ha! Kobe, may have scored a full one-third of the team’s points over the course of the game, but he was sitting out during a key stretch. Worse, while he was lighting it up in the first quarter, everybody else’s ineptitude was costing him in the +/- stakes.

This situation captures almost perfectly the beauty and the shortcomings of +/-: on the one hand, it zooms in on what matters most — winning — without ascribing arbitrary weightings to individual statistics like points, rebounds and assists while still incorporating the value of intangible contributions. On the other hand, the value of the individual is so tightly tied to who is on the court with him that +/- as a comparative tool becomes worthless, since it reflects more the overall quality of the team and the ability of the coach to construct effective rotations. It’s sort of the classic curse of single-number metrics.

One is tempted to abandon +/- as the ‘holy grail’ statistic at this point, but it’s really a very good idea in as far as cutting out the pseudo-science of sports statistics and focussing on what actually leads to wins. One wonders if the problem is ’snapshotting’ +/- ratings at the end of the game, which necessarily throws out all the information that a real-time +/- score would have. Behold:

Utah-L.A. Game 4, Playoffs 2009 - Selected Plus-Minus Ratings

What you’re seeing is a graph of realtime +/- ratings for the teams (ie, overall) as well as for various players over the course of the entire game. The overall team rating is just the point differential between L.A. and Utah (I’m a Lakers fan); for the individual players, you can see how their +/- rating was related to that of the team through time. The flat regions (eg, Luke Walton from the beginning of the game until about 7:30 in) are periods when the player’s +/- didn’t change — ie, he was either off the court, or he was on, but neither team scored. You’ll also see some periods when everyone’s rating moves together — eg, the plotted players’ +/- ratings all fell between 10:30 and 14:30 — which implies that they were all on the court (in the 10:30 – 14:30 period, the falling ratings mean Utah made a run).

The plot makes it immediately apparent how, for example, Luke Walton ended up with the same +/- rating as Kobe: he simply sat out the last 10 minutes of the game, when Utah was cutting L.A.’s lead. This, of course, raises some interesting questions, such as how starting and ending games ends players’ +/- ratings; from this example, it looks like garbage time can hurt the winning team’s ratings (though conversely, Utah’s players’ ratings benefited from garbage time), while starting can be good or bad for one’s score depending on who starts the game stronger (ie, there’s no bias there, whereas there is for garbage time).

Of course, since one now has a nice time-series describing the players’ contributions (as encapsulated by +/-), one can try computing a single-number metric of performance (though, obviously, YMMV*) by simply computing the correlation between the team’s overall +/- and the players’ individual ratings. Note that this number really only makes sense in the context of the team’s performance — ie, a player with a perfect score on the Kings is clearly worse than a player with a perfect score on the Lakers, since correlation doesn’t differentiate between covariance that leads to team success or failure. That said, let’s take a look at what this ‘+/- correlation’ metric looks like for Game 4:

Utah-L.A. Game 4, Playoffs 2009 - +/- correlations

I’ve shown both team’s players on this one chart, so what you’re seeing is who contributed to what ultimately proved to be a Lakers’ win as a normalised score based on players’ full real-time contributions. So if you were to say a dude is absolutely indispensable to a team’s success (ie, the MVP), you would expect him to have, over the course of the season, a +/- correlation of almost +1. We see that, for example, for Pau Gasol, implying he was on the court for almost every significant period of the game (even if he didn’t contribute as much as Kobe in raw numbers). The implications for Andrew Bynum are also interesting, since a correlation that low means he basically didn’t matter much as far as the team’s ultimate success is concerned. I’m really itching to see what it says about Shane Battier ;)

Unfortunately, it’s not the end-all, be-all of metrics because by construction the amount of playing time a player receives will bias it, and because it’s basis in the overall winning ability of the five players on the court means it doesn’t break down how much of that success is attributable to any individual player. However, it does roughly put players where we expect them in the pecking order, and gives a rudimentary sense of how much responsibility a team’s results individual players should be ascribed. And there are ways to improve this metric, a topic which really deserves another post (although here’s an obvious extension: define the overall team +/- to always be in favour of the team that wins).

In summary, what complaints we have against +/- ratings might be resolvable by analysing players’ +/- ratings as they evolve through time. In abstract terms, +/- seems a much more objective metric than the weighted-average metrics in more common use (eg, PER, Wages-of-Wins), which make assumptions that borne out only by a couple of decades’ history.

I’m attaching the spreadsheet containing my data as well in case anyone’s interested in taking a look at it. If I get time — and if there’s interest — I might compile this sort of data for all the games next year and put it on the web. Let me know what you think.

Utah-L.A. Game 4, Playoffs 2009 – Data

Utah-L.A. Game 4, Playoffs 2009 – Scorecard

• I have trouble using this phrase in polite conversation now, but hopefully we’re all on the same page as to why I’m using it!

Kamen … said every entrepreneurial innovator he’s ever seen shares a few characteristics.

“It’s not that they’re brilliant or well-educated,” Kamen said. “They work all the time. They don’t let failure demoralize or destroy them. They pick themselves up and keep going and eventually, every once in a while, one of your ideas actually breaks through and works, and it makes all that stuff seem worthwhile.”

In other words, Mr. Kamen agrees with Ammi :)

The reason for that is probably the extreme complexity of the issue under examination — simply taking a handful of countries and establishing some relationship between their respective levels of corruption and growth doesn’t make sense because there are too many other factors at play. Economists always try to take a ‘partial derivative’, linearised view of the world (ie, all else equal, find a single driving variable), since that’s the most obvious way to decompose a complex issue into aspects that can be studied individually, but there are inevitable limitations to how effective this approach can be at the macro level, where there are dozens of significant variables, with unknown cross-effects that are likely deserving of separate study.

It’s clear that corruption impedes growth and development, indirectly through economically suboptimal allocation of resources and directly through the increased costs it imposes. Beyond that, it’s pretty hard to make any substantial, justifiable statement. Perhaps rather than drilling until some tenuous relationship is established, the focus should be to establish how corruption becomes systemic and what measures can be taken to prevent this from happening. In places like Pakistan where corruption is an everyday occurrence, people simply assume it will continue unimpeded and price it in as a cost of business. We know there it is exacerbated by extreme social inequality, exceptionally poor pay for officials, and a bizarre mindset (particularly in communities like the Memons) that considers bribes a mark of respect and an essential element in building necessary relationships with officials. In short, there’s a significant cultural component to corruption that must not be obscured by the economic aspect.

Of course, once corruption becomes so commonplace that society’s perception of it vacillates between necessary evil and competitive advantage, obvious steps like making examples of a few chosen offenders become useless, and even attempts to tackle the root issues — such as the double-salary schemes offered by the Federal Board of Revenue under reforms agreed with the World Bank — are only marginally effective. Certainly, gimmicky (the National Accountability Bureau is a massive sham) and/or highly focussed measures (the double-salary scheme was only offered to key officials) are a waste of time and not deserving of discussion. Bold steps, applied with commitment and consistency and monitored actively, are needed in order to remove the root causes and steadily (if slowly) rub out corruption. And of course, these steps would need to address each facet of the problem.

One bold step might be to draw the problem out into daylight by legitimising and regularising the bribes officials are already taking in the form of some minimal extra fee; this would be additional remuneration for providing a service. This immediately circumvents the problem of burdening the government with higher payroll and actually encourages efficiency in directing the remuneration to those who have earned it. In an indirect way, it might also go some way in addressing the cultural issues (continuing to pick on Memons — assuming they don’t pay doctors more than their quoted fee, I don’t see why they would feel obliged to push further bribes on officials). Doing this would likely create issues of nepotism in the allocation of official duties and potentially harmful competition between colleagues, but these are straightforward problems with more obvious solutions. The government would simultaneously have to empower citizens to report negligence or incompetence or — more tricky — officials charging in excess of the permitted fee. With sufficient political will and clout to aggressively prosecute citizens and officials who continue to flout the law, maybe we would have a workable system.

(Holy never-ending-sentence-alert, Batman! My brain isn’t working these days…)