Do baseball salaries have "precious little" to do with ability?

Could MLB player salaries be almost completely unrelated to performance? 

That's the claim of social-science researcher Mike Cassidy, in a recent post at the online magazine "US News and World Report."

It argues an "economics lesson from America's favorite pastime." Specifically: How can it be true that high salaries are earned by merit in America, when it's not even the case in baseball -- one of the few fields in which we have an objective record of employee performance?

The problem is, though, that baseball players *are* paid according to ability. The author's own data shows that, despite his claims to the contrary. 

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Cassidy starts by charting the 20 highest-paid players in baseball last year, from Alex Rodriguez ($29 million) to Ryan Howard ($20 million). He notes that only two of the twenty ranked in the top 35 in Wins Above Replacement (WAR). The players in his list average only 2.2 WAR. That's not exceptional: it's "about what you need to be an everyday starter."  

It sounds indeed like those players were overpaid. But it's not quite so conclusive as it seems.

WAR is a measure of bulk contribution, not a rate stat. So it depends heavily on playing time. A player who misses most of the season will have a WAR near zero. 

In 2013, Mark Teixeira played only 15 games with a wrist injury before undergoing surgery and losing the rest of the season. He hit only .151 in those games, which would explain his negative (-0.2) WAR. However, it's only 53 AB -- even if Texeira had hit .351, his WAR would still have been close to zero. 

A-Rod missed most of the year with hip problems. Roy Halladay pitched only 62 innings as he struggled with shoulder and back problems, and retired at the end of the season.

If we take out those three, the remaining 17 players average out to around 2.6 WAR, at an average salary of $22 million. It works out to about $8.4 million per win. That's still expensive -- well above the presumed willingness-to-pay of $5 to $6 million per expected win.

If we *don't* take out those three, it's about $10 million per win. Even more expensive, but hardly suggestive of a wide disconnect between pay and performance. At best, it suggests that the one year's group of highest-paid players performed worse than anticipated, but still better than their lower-paid peers.

Furthermore: as the author acknowledges, many of these players have back-loaded contracts, where they are "underpaid" relative to their expected year's talent earlier in the contract, and "overpaid" relative to their expected year's talent later in the contract. 

Even a contract at a constant salary is back-loaded in terms of talent, since older players tend to decline in value as they age. I'm sure the Yankees didn't expect Alex Rodriguez to perform at age 37 nearly as well as he did at 33, even though his salary was comparable ($28MM to $33MM).

All things considered, the top-20 data is very good evidence of a strong link between pay and performance in baseball. Not as strong as I would have expected, but still pretty strong.

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As further evidence that pay is divorced from performance, the author notes that, even limiting the analysis to players who have free-agent status, "performance explains just 13 percent of salary."  It's not just a one-year fluke. For each of the past 30 years, the r-squared has consistently hovered in a narrow band between 10 and 20 percent.

That sounds damning, but, as is often the case, it's based on a misinterpretation of what the r-squared means. 

Taking the square root of .13 gives a correlation of .36. That's not too bad: it means that 36 percent of a player's salary (above or below average) is reflected in (above- or  below-average) performance.

Still, you do have to regress salary almost 64 percent to the mean to get performance. Doesn't that show that almost two-thirds of a player's salary is unrelated to merit?

No. It shows most of a player's salary is unrelated to *performance,* not that it's unrelated to *merit*. Performance is based on merit, but with lots of randomness piled on top that tends to dilute the relationship.

You might underestimate the amount of randomness relative to talent, especially if you're still thinking of those top-20 players. But most players in MLB are not far from the league minimum, both in salary and talent.

According to the article, the 358 lowest-paid players in baseball in 2013 made an average $534,000 each. 

With a league minimum of $500,000, those 358 players must be clustered very tightly together in pay. And the range of their talent is probably also fairly narrow. But the range of their performance will be wide, since they'll vary in how much playing time they get, and whether they have a lucky or unlucky year. 

For those 358 players alone, the correlation between pay and performance is going to be very close to zero, even if pay and talent correlate perfectly. (Actually, the author's numbers are based on only players with 6+ seasons in MLB, so it's a smaller sample size than 358 -- but the logic is the same.)

When you add in the rest of the players, and the correlation rises to 0.36 ... that's pretty good evidence that there's a strong link between pay and performance overall. And when you take into account that there's also significant randomness in the performances of the highly-paid players, it must be that the link between pay and *merit* is even higher.

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The author has demonstrated the "low r-squared" fallacy -- the idea that if the number looks low enough, the relationship must be weak enough to dismiss. As I have argued many times, that's not necessarily the case. Without context or argument, the "13 percent" figure could mean anything at all.

In fact, here's a situation where you have an r-squared much lower than .13, but a strong relationship between pay and performance.

Suppose that player salary were somehow exactly proportional to performance. That is, at the end of the season, the r-squared turned out to be 100 percent, instead of 13 percent. (Or some number close enough to 100 percent to satisfy the author.)

In baseball, as in life, people don't perform exactly the same every day. Some days, Mike Trout will be the highest-paid player in baseball, but he'll still wind up going 0-for-4 with three strikeouts.

So even if the correlation between season pay and season performance is 100% perfect, the correlation between *single game* pay and *single game* performance will be lower.

How much lower?  I ran a test with real data. I compiled batter stats for every game of the 2008 season, and ran a regression between the player's on-base percentage (OBP) for that single game, versus his OBP for the season. 

The correlation was .016. That's an r-squared of .000265.

The r-squared of .13 the article found between pay and performance is almost *five hundred times* as large as the one I found between pay and performance. 

Even though my r-squared is tiny, we can agree that Mike Trout is still paid on merit, right? It would be hard to argue that there was a fundamental inequity in MLB pay practices for April 11, just because Mike Trout didn't produce that day.

Well, I suppose, on a technicality, you could argue that pay isn't based on merit for a game, but *is* based on merit for a season. But if you make that argument for game vs. season, you can make the same argument for season vs. expectation, or season vs. career. 

The r-squared might be only 13 percent for a single season, but higher for groups of seasons. Furthermore, if you could play the same season a million times over, luck would even out, performance would converge on merit, and the r-squared would move much closer to 100%.

And the article provides evidence of that! When the author repeated his regression by using the average of three seasons instead of one, the r-squared doubled -- now explaining "just a quarter of pay." An r-squared of 0.25 is a correlation of 0.5 -- half of performance now reflected in salary.

Half is a lot, considering the amount of luck in batting records, and taking into account that luck is much more important than talent for the bunch of players clustered at the bottom of the salary scale. 

Again, the article's own evidence is enough to refute its argument.

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I think we can quantify the amount of luck in a batter's season WAR. 

A couple of years ago, I calculated the theoretical SD of a team's season Linear Weights batting line that's due to luck. It came out to 31.9 runs. 

Assuming a regular player gets one-ninth of a team's plate appearances, his own SD would be 1/3 the team's (the square root of 1/9). So, that's about 10.6 runs. Let's call it 10 runs, or 1.0 WAR. 

That one-win figure, though, counts only the kind of luck that results from over- or undershooting talent. It doesn't consider injuries, suspensions, or sudden unexpected changes in talent itself. 

Going back to the top 20 players in the chart ... we saw that three of those had injuries. Another three, it appears, had sudden drops in ability after they were signed (Vernon Wells, Tim Lincecum, and Barry Zito). 

Removing those six players from the list (which might be unfair selective sampling, but never mind for now), the remainder averaged 3.4 WAR. That's about $6.4 million per win -- very close to the consensus number. It would be even lower if we adjusted for back-loaded contracts.

At an SD of 1 WAR per player, the SD of the average of 14 players is 0.27 WAR. Actually, that's the minimum; it would be higher if any of the 14 were less than full-time. Also, the list includes starting pitchers -- I don't know if the luck SD of 1 win is reasonable for starters as well as batters, but I suspect it's close enough.

So, let's go with 0.27. We'll add and subtract 2 SD -- 0.54 --from the observed average of 3.4. That gives us a confidence interval of 2.9 to 3.9 WAR.

At 3.9 WAR, we get $5.6 million per win: almost exactly the amount sabermetricians (and probably front offices) have calculated based on the assumption that teams want to pay exactly what the talent is worth.

That is: it appears the results are not statistically significantly different from a pure "pay for performance" situation.

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When the US News article talks about luck, it's different from the kind of luck I'm calculating here. The author isn't actually complaining that the overpaid players got unlucky and underperformed their pay. Instead, he believes that the highly-paid players were overpaid for their true ability, because they were "lucky" enough to fool everyone by having a career year at exactly the right time:

"In America, we tend to think of income as a reward for skill and hard work. ...

"But baseball shows us this view of the world is demonstrably flawed. Pay has preciously little to do with performance. Instead, being a top earner means having a good season immediately preceding free agency in a year where desperate, rich teams are willing to award outsized long-term contracts. ... 

"In other words, while ability and effort matter, it’s also about good luck."

Paraphrased, I think he's saying something like: "I've shown that pay is barely related to performance. Why, then, are some players paid huge sums of money, while others make the minimum?  It can't be merit. It must be that some players have a lucky year at a lucky time, and GMs don't realize the player doesn't deserve the money."

In other words: baseball executives are not capable of evaluating players well enough to realize that they're throwing away millions of dollars unnecessarily.   

The article gives no evidence to support that; and, furthermore, it appears that the author himself doesn't try, himself, to evaluate players and factor out luck. Otherwise, he wouldn't say this:

"But among average players, salaries vary enormously. For every Francisco Cervelli (Yankees catcher, $523,000 salary, 0.8 WAR), there is a CC Sabathia (Yankees pitcher, $24.7 million salary, 0.3 WAR). Both contribute about the same to the Yankees’ success (or lack thereof), but Sabathia earns roughly 50 times more."

Does he really believe that Sabathia and Cervelli should have been paid as equal talents?  Isn't it obvious that their 2013 records are similar only because of luck and circumstance?

Francisco Cervelli earned his +0.8 WAR in 61 plate appearances. That's about one-and-a-half SDs above +0.3, his then-career average per 61 PA.

Sabathia's salary took a jump after the 2009 season, at a time where he was averaging around 4 WAR per season. From 2010 to 2012, he actually improved that trend, creating +15.6 WAR total in those three years. It wasn't until 2013 that he suddenly lost effectiveness, dropping to 0.3 as reported. 

So it's not that Sabathia was just lucky to be in the right place at the right time. It's that he was an excellent player before and after signing his contract, but he suffered some kind of unexpected setback as he aged. (Too, his contract was structured to defer some of his peak years' value to his declining years.)

And it's not that Cervelli was unlucky to be in the wrong place at the wrong time, unable to find a "desperate" team otherwise willing to pay him $20 million. He's just a player recognized as not that much better than replacement, who had a good season in 2013 -- a "season" of 61 plate appearances where he was somewhat lucky.

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In his bio, the author is described as "a policy associate at The Century Foundation working on issues of income inequality." That's really what the article is getting at: income inequality. The argument that MLB pay is divorced from performance is there to support the broader argument that inequality of income is caused by highly-paid employees who don't deserve it.

Here's his argument summarized in his own words:

"The first thing to appreciate is just how unequal baseball is. During the 2013 season, the eight players in baseball's 'top 1 percent' took home $197 million, or $6 million more than the 358 lowest-paid players combined. The typical, or 'median,' major league player would need to play 20 seasons to earn as much as a top player makes in one. ...

"But ... pay has preciously little to do with performance. ...

"In other words, while ability and effort matter, it’s also about good luck. And if that’s true of a domain where every aspect of performance is meticulously measured, scrutinized and endlessly debated, how much more true is it of our society in general?

"We end up with CEOs that make 300 times the average worker and 45 million poor people in a country with $17 trillion in GDP. And we accept it as fair."

Paraphrasing again, the argument seems to be: "Salary inequality in baseball is bad because it's caused by teams rewarding ability that isn't really there. If baseball players were paid according to performance instead of circumstance, those disturbing levels of inequality would drop substantially, and the top 1% would no longer dominate."

It sounds reasonable, but it's totally backwards. If the correlation between pay and performance were higher, players' pay would become MORE unequal.

Suppose salaries were based directly on WAR. At the end of the season, the teams pay every free agent $6 million dollars for every win above zero, plus the $500,000 minimum. (That's roughly what they're paying now, on expectation. Since expected wins equal actual wins, that would keep the overall MLB free-agent payroll roughly the same.)

Well, if they did that the top salary would take a huge, huge jump.

Among the top 20 in the chart, the top two WAR figures are 7.5 (Miguel Cabrera) and 7.3 (Cliff Lee. 

Under the new salary scale, both players would get sharp increases. Cabrera would jump to $45 million, and Lee to $44 million. The highest salary in MLB would go to Carlos Gomez, whose 2013 season was worth 8.9 WAR (4.6 of that from defense). Under the new system, Gomez would earn some $53 million. 

Under pay-for-performance, it would take only around 4.8 WAR to earn more than the current real-life highest salary, A-Rod's $29.4 million. In 2013, that would have been accomplished by 32 players. 

Carlos Gomez's salary would exceed the real-life A-Rod by 82 percent. Meanwhile, replacement players would still be making the minimum $500K. And Barry Zito, with his negative 2.6 wins, would *owe* the Giants $15 million. 

Clearly, inequality would increase, not decrease, if the connection between pay and performance became stronger. 

Mathematically, that *has* to happen. When luck is involved, and applies equally to everyone, the set of outcomes always have a wider range than the set of talents. As usual,

var(outcomes) = var(talent) + var(luck)

Since var(luck) is always positive, outcomes always have a wider range than expectations based on talent. 

In fairness to the author, he doesn't think teams are paid by talent. As we saw, he believes teams pay by misinterpreting random circumstances, a "right place right time" or "team likes me" kind of good luck. 

If that's really happening, and you eliminate it by basing pay directly on measurable performance, then, yes, it's indeed possible for inequality to go down. If Francisco Cervelli were being paid $100 million per season, because he was Brian Cashman's favorite, then instituting straight pay-by-performance would lower the top salary from $100 million to $53 million, and inequality would decrease.

But, as we saw, that's not the case: the real-life top salaries are much lower than the "pay-by-performance" top salaries. That means that teams aren't systematically overpaying. Or, at least, that they're not overpaying by anything near as much as 82 percent.

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Imagine an alternate universe in which players have always been paid under the "new" system, $6 million per WAR. In that universe, as we have seen, the ratio between the top and median salaries is much higher than it is now, maybe 50 times instead of 20.

Then, someone comes along and presents a case for more equality:

"MLB salaries aren't as fair as they could be. They're based on outcomes, where they should be based on talent. Francisco Cervelli gets credit for 0.8 wins in 61 PA, even though we know he's not that good, and he just happened to guess right on a couple of pitches. 

"Players should be paid based on their established and expected performance, by selling their services to the highest bidder, before the season starts. That eliminates luck from the picture, and salaries will be based more on merit. The salary ratio will drop from 50 to 20, the range will compress, and the top players will earn only what they merit, not what they produce by luck."

Isn't THAT the situation that you'd expect someone to advocate if they were concerned about (a) rewarding on merit, (b) not rewarding on luck, and (c) reducing inequality of salaries?

Why, then, is this author advocating a move in the exact opposite direction?




(Hat tip: T.M.)

Corsi, shot quality, and the Toronto Maple Leafs, part VI

A year ago, I wrote about how I wasn't completely sold on Corsi and Fenwick as unbiased indicators of future NHL success. In a series of five posts (one two three four five), I argued that it did appear that "shot quality" issues could be a big factor -- if not for all teams, then maybe at least for some of them, like, perhaps, the Toronto Maple Leafs.

I haven't kept up with hockey sabermetrics as much as I should have, but, as far as I know, the issue of how much shot quality impacts Corsi remains unresolved.

In that light, and in hopes that I haven't rediscovered the wheel, here's some more evidence I came across that seems to suggest shot quality might be a bigger issue than even I had suspected.

It's from a post at Hockey-Graphs, where Garret Hohl looked at some shot quality statistics for every NHL team, for approximately the first 30 road games of last season (2013-14). 

His data came from Greg Sinclair's "Super Shot Search," which plots every shot on goal by plotting it on the ice surface. Sinclair's site allows you restrict your search to what he calls "scoring chances," which are shots taken from closer in. Specifically, a "scoring chance" is defined as a shot on goal taken from within the pentagon formed by the midpoint of the goal line, the faceoff dots, and the tops of the two circles. 

Hohl calculated, for every team, what percentage of opposing shots were close-in shots. (He limited the count to 5-on-5 situations in road games, in order to reduce power-play and home-scorer biases.)  Data in hand, he then ran a regression to see how well a team's "regular" Fenwick corresponded to its "scoring chances only" Fenwick. His chart shows what appears to be a strong relationship, with a correlation of 0.83. 

However: the biggest outlier was ... Toronto. 

Just as in the previous two seasons, the Leafs continued to outperform their Fenwick in 2013-14. What Hohl has done is to produce some data that shows that the effect resulted, at least in part, by their opposition taking lower quality shots. 

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Anyway, the Leafs are really just a side point. What struck me as much more important are some of the other implications of the data Hohl unearthed. Specifically, how teams varied so much in those opponent scoring chances. The differences were much, much larger than I expected.

I'll steal Hohl's chart:

The Minnesota Wild defense was the best at limiting their opponents to weaker shots: only 32.3 percent of their shots allowed were from in close (206 of 637). The New York Islanders were the worst, at 61.4 percent (475 of 773). 

Shot for shot, the Islanders gave up twice as many close-in chances as the Wild. 

Could this be luck?  No way. The average number of shots in Hohl's table is around 750. If the average scoring-chance ratio is 44 percent, the SD from binomial luck should be around 1.8 percentage points. That would put the Islanders around 9 SD from the mean, and the Wild 7 SD from the mean. 

The observed SD in the chart is 5.6 percentage points. That means the breakdown is:

1.8 SD of theoretical luck
5.3 SD of real differences
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5.6 SD as observed

Now, the "real" differences might be score effects: shooting percentages rise when a team is ahead, presumably because they take more chances and give up more odd-man rushes, and such. Those effects are large enough that they screw up a lot of analyses, and I wish more of those little studies you find on the web would limit themselves to 5-on-5 tied to avoid those biases.

But, in this case, the differences are too big to just be caused by score effects.

In 5-on-5 situations from 2007-2013, the league shooting percentage was 7.52 percent when teams were tied, but 9.19 percent for teams ahead by 2 goals or more. As big an difference as that is, it can't be that the Islanders were behind 2+ goals that much that it could make such a huge difference in scoring chances.

From my calculations, the difference between the Islanders and Wild is something that would happen naturally only if the Islanders were *always* down 2+ goals, and the Wild were *always* up 2+ goals.** But that obviously isn't the case. In fact, the Islanders were down 2+ goals only about 10 percent more often than the Wild last year, and up 2+ goals only 21 percent less often. The total of the two differences is about eight periods total out of a full 5-on-5 road season.

(** How did I figure that?  Suppose the shooting percentage on close shots is 13%, and 4% on far shots. At 45 percent close and 55 percent far, you get a shooting percentage of 8.1% percent. At 65 percent close, and 35 percent far, shooting percentage rises to 9.8%. That's a little bigger than the difference between up 2+ and tied.

So, it seems like, when you're up 2+ goals, 60 to 65 percent of your shots are scoring chances, compared to 35 to 40 percent when you're down 2+ goals.)

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As for the Leafs: they were fourth-best in the league in percentage of shots that were scoring chances, at 38.2%. That's despite -- or because of? -- allowing the most shots, by far, of any team in the sample, at 926. (The second highest was Washington, at 843.)

It seems to me like this is significant evidence that teams vary in the quality of shots they allow -- in a huge way. The score effects can't be THAT large.

The only possibility that I can think of is biased scorers. But Hohl confirms that each team had an assortment of opposition home team scorers and rinks, so that shouldn't be happening.

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Here's some additional evidence that the scoring chance data is meaningful. 

I ran a correlation between team scoring chance percentage and goalie save percentage. If scoring chance percentage didn't matter, the correlation would be low. If it did matter, it would be high. (For save percentage, I used 5-on-5, tie score, both home and road.)

The correlation turned out to be ... -0.44. That's pretty high. (Especially considering that the scoring chance percentage was based on only 30 road games per team.)  

The SD of save percentage was 0.96 percentage points. The SD of scoring chance percentage (after 3/4 of the season) was 5.6 points. 

That means for every excess percentage point of scoring chance percentage, you have to adjust save percentage by 0.075 percentage points. 

The Los Angeles Kings gave up a bit more than 3 percentage points weaker shots than normal. That had the effect of inflating their goalies' save percentage by about 0.25 points. So, we can estimate that their "true talent" was closer to 93.45 than 93.7. 

If you like, think of it as two or three points of PDO: the Kings move from 1000 to 997.5 on this adjustment. 

For Toronto, it's five points: they drop from 1019 to 1014. 

The Rangers, for one more example, went the other way -- they gave their opponents 8 percentage points more close-in shots than average. Adjusting for that would boost their adjusted save percentage from 91.6 to 92.2, and their PDO from 974 to 980.

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OK, one more bit of evidence, this time subjective.

Recently, a survey from nhl.com ranked the best goalies in the league, from 1 to 14, with 15-18 mentioned in the footnotes. (I'm leaving out John Gibson, who only played one regular-season game, and I'm considering goalies not mentioned to have a ranking of 19.)

I checked the correlation between team goalie ranking and save percentage. It was -0.45. Again, that's pretty strong, considering how subjective the rankings are. 

Of course, some goalies were probably ranked high *because* of their the save percentage. So cause and effect are partly mixed up here (but I think that will actually strengthen this argument).

For the next step, I adjusted each goalie's save percentages to give credit for the quality of the shots their team faced. That is, I raised or lowered their SV% for the shot quality percentages listed in Hohl's post, at the rate of 0.075 points we discovered earlier. 

What happened?  The correlation between ranking and SV% got *stronger* -- moving from -0.45 to -0.50. 

It looks like the voters "saw through" the illusion in save percentage caused by differing shot quality. Well, that might be giving them too much credit: they might have ignored save percentage entirely, and just concentrated on what they saw with their eyes. Actually, I'm probably giving them too *little* credit: they're no doubt basing their evaluations on a full career, not just one season, and maybe team shot quality evens out somewhat in the long run.

Either way, when the voters differed from SV%, it was in the direction of the goalies who faced tougher tasks.  I think that's reasonable evidence that differences in shot quality are real. 

Oh, and one more thing: the highest correlation seems to occur almost exactly at the theoretical adjustment the regression picked out, 0.075. When I drop the adjustment in half (to 0.0375), the correlation drops a bit (-0.48, I think). When I double the adjustment to 0.15, the correlation drops to -0.44. 

Now, that *has* to be coincidence; the voters can't be that well calibrated, can they? And ranking numbers of 1 to 19 are kind of arbitrary.

Still, it does work out nicely, that the voters do seem to agree with the regression.

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I think all this casts serious doubt on the idea that PDO (the sum of team shooting percentage and save percentage) is essentially random. The Islanders had a league-worst PDO of 982, but that's probably because their opponents took 61.4% of their shots from close-in, compared to the Islanders' own 42.8%. In other words, if you calculate a "shot quality PDO", the Islanders come in at 814. (That's calculated as 428 + (1000-614).)

The Leafs had the league's fourth best PDO, at 1019. But their shots were much higher quality than their opponents', 47.2% to 38.2%. So their "shot quality PDO" was 1090. 

For all 30 teams, the correlation between PDO and "shot quality PDO" was 0.43 -- signficantly high. The coefficient works out to approximately a 1:10 ratio. The Islanders' -186 point "shot quality PDO" difference translates to around -19 points of PDO. The Leafs' +90 works out to about +9.

I'll show data and work out more details in a future post (probably next week, I'm out of town for a few days starting tomorrow). 

(One thing that's interesting, that I want to look into, is that the SD of team quality shot percentage *for* is only about half of the SD of quality shot percentage *against* (2.7 versus 5.6). Does that mean that defenses vary more than offenses? Hmmm...)

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So I think all of this comprises strong evidence that teams differ non-randomly in the quality of shots they allow. That doesn't invalidate the hypothesis that Corsi is still a better predictor of future success than goals scored. But it *does* suggest that you can likely improve Corsi by adjusting it for shot quality. And it *does* suggest that PDO isn't random after all.

In other words: Corsi might be misleading for teams with extreme shot quality differences.

A baseball analogy: using Corsi to evaluate NHL teams is like using on-base percentage average to evaluate MLB teams. Some baseball teams will do much better or worse than their "OBP Corsi", for non-random reasons -- specifically, if they have high "hit quality" by hitting lots of home runs, or low "hit quality" by building their "OBP Corsi" on "lower quality" walks.

In 2014, the Orioles were fifth-worst in the American League with an OBP of only .311. But they were above average in runs scored. Why?  Mostly because they hit more home runs than any other team, by a wide margin.

Might the Toronto Maple Leafs be the Baltimore Orioles of the NHL?

(There are seven parts. Part V was previous. This is Part VI.  Part VII is next.)