Bigger, Stronger, and Faster — but Not Quicker?

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HYPOTHESIS

There’s some controversial IQ research which suggests that reaction times have slowed and people are getting dumber, not smarter. Here’s Dr. James Thompson’s summary of the hypothesis:

We keep hearing that people are getting brighter, at least as measured by IQ tests. This improvement, called the Flynn Effect, suggests that each generation is brighter than the previous one. This might be due to improved living standards as reflected in better food, better health services, better schools and perhaps, according to some, because of the influence of the internet and computer games. In fact, these improvements in intelligence seem to have been going on for almost a century, and even extend to babies not in school. If this apparent improvement in intelligence is real we should all be much, much brighter than the Victorians.

Although IQ tests are good at picking out the brightest, they are not so good at providing a benchmark of performance. They can show you how you perform relative to people of your age, but because of cultural changes relating to the sorts of problems we have to solve, they are not designed to compare you across different decades with say, your grandparents.

Is there no way to measure changes in intelligence over time on some absolute scale using an instrument that does not change its properties? In the Special Issue on the Flynn Effect of the journal Intelligence Drs Michael Woodley (UK), Jan te Nijenhuis (the Netherlands) and Raegan Murphy (Ireland) have taken a novel approach in answering this question. It has long been known that simple reaction time is faster in brighter people. Reaction times are a reasonable predictor of general intelligence. These researchers have looked back at average reaction times since 1889 and their findings, based on a meta-analysis of 14 studies, are very sobering.

It seems that, far from speeding up, we are slowing down. We now take longer to solve this very simple reaction time “problem”.  This straightforward benchmark suggests that we are getting duller, not brighter. The loss is equivalent to about 14 IQ points since Victorian times.

So, we are duller than the Victorians on this unchanging measure of intelligence. Although our living standards have improved, our minds apparently have not. What has gone wrong? [“The Victorians Were Cleverer Than Us!” Psychological Comments, April 29, 2013]

Thompson discusses this and other relevant research in many posts, which you can find by searching his blog for Victorians and Woodley. I’m not going to venture my unqualified opinion of Woodley’s hypothesis, but I am going to offer some (perhaps) relevant analysis based on — you guessed it — baseball statistics.

APPROACH TO THE PROBLEM

It seems to me that if Woodley’s hypothesis has merit, it ought to be confirmed by the course of major-league batting averages over the decades. Other things being equal, quicker reaction times ought to produce higher batting averages. Of course, there’s a lot to hold equal, given the many changes in equipment, playing conditions, player conditioning, “style” of the game (e.g., greater emphasis on home runs), and other key variables over the course of more than a century.

Undaunted, I used the Play Index search tool at Baseball-Reference.com to obtain single-season batting statistics for “regular” American League (AL) players from 1901 through 2016. My definition of a regular player is one who had at least 3 plate appearances (PAs) per scheduled game in a season. That’s a minimum of 420 PAs in a season from 1901 through 1903, when the AL played a 140-game schedule; 462 PAs in the 154-game seasons from 1904 through 1960; and 486 PAs in the 162-game seasons from 1961 through 2016. I found 6,603 qualifying player-seasons, and a long string of batting statistics for each of them: the batter’s age, his batting average, his number of at-bats, his number of PAs, etc.

The raw record of batting averages looks like this, fitted with a 6th-order polynomial to trace the shifts over time:

FIGURE 1
batting-average-analysis-unadjusted-ba-1901-2016

That’s nice, you might say, but what accounts for the shifts? I considered 21 variables in an effort to account for the shifts, and ended up using 20 of the variables in a three-stage analysis.

In stage 1, I computed the residuals resulting from the application of the 6th-order polynomial. That is, I subtracted from the actual batting averages the estimates produced by the equation displayed in figure 1. For ease of reference, I call this first set of residuals the r1 residuals.

I began stage 2 by finding the correlations between each of the 21 candidate variables and the r1 residuals. I then estimated a regression equation with the r1 residuals as the dependent variable and the most highly correlated variable as the explanatory variable. I next found the correlations between the remaining 20 variables and the residuals of that regression equation. I introduced the most highly correlated variable into a new regression equation, as a second explanatory variable. I continued this process in the expectation that I would come across an explanatory variable that was statistically insignificant, at which point I would stop. But I ran through 16 explanatory variables without hitting a stopping point, and that exhausted the number of explanatory variables allowed by the regression function in Excel 2016.

The 16th regression on the r1 residuals left me with a set of residuals that I call the r2 residuals. In stage 3, I estimated a new equation with the r2 residuals as the dependent variable, following the same procedure that I used to obtain the 16-variable regression on the r1 residuals. In this case, I used 4 of the remaining explanatory variables; the 5th proved statistically insignificant.

I then combined the estimates obtained in the three stages to obtain the equation that’s discussed later, and at length. For now, I’ll focus on the apparent precision of the equation and its implications for the hypothesis that the general level of intelligence has declined with time.

SUMMARY AND DISCUSSION OF RESULTS

Here’s how well the equation fits the data:

FIGURE 2
batting-average-analysis-actual-and-estimated-ba-of-regular-players-1901-2016

The 6th-order polynomial regression lines (black for actual, purple for estimated) are almost identical.

Here’s how the final estimates (vertical axis) correlate with the actual batting averages (horizontal axis):

FIGURE 3
batting-average-analysis-estimated-vs-actual-ba_3-stage-analysis

I’ve never seen such a tight fit based on more than a few observations, and this one is based on 6,603 observations. I’m showing 6 decimal places in the trendline label so that you can see the 3 significant figures in the constant, which is practically zero.

Year (YR) enters as a significant variable in stage 3, with a coefficient of
-0.0000284 . (The 95-percent confidence interval is  -.0000214  to  -.0000355 ; the p-value is  3.40E-15 .) So, everything else being the same (a matter to which I’ll come), batting averages dropped by  .00327  between 1901 and 2016 ( -0.00327 =  -.0000284 x 115 ). (Note: It’s conventional to drop the 0 to the left of the decimal point in baseball statistics. And if you’re unfamiliar with baseball statistics, I can tell you that a difference of .00327 is taken seriously in baseball; many a batting championship race has been decided by a smaller margin.)

If the compound equation resulting from stages 1, 2, and 3 accounts satisfactorily for all changes affecting BA, the estimate of  -.00327  might be attributed to the slowing of batters’ reaction times. However, despite the statistical robustness of the coefficient on YR, it’s necessary to ask whether there are factors not properly accounted for that might point to the conclusion that reaction times have remained about the same or improved. To get at that question, I’ll present and discuss in the next section a table that summarizes the complete equation and all 20 of its explanatory variables. As you read and interpret the table, keep these points in mind:

The 6th-order polynomial (stage 1) is a filter. It captures the fluctuations over time that must be accounted for by the 20 “real” variables that are listed in the table (including YR) and discussed below the table. The “year” terms in the 6th-order polynomial are therefore irrelevant to the question of whether reaction times have slowed.

Every p-value in the stage-2 and stage-3 regression equations is smaller than  0.0001 , and most of them are far, far below that threshold.

The significance of the explanatory variables notwithstanding, the standard errors of the stage-1 and stage-2 equations are both about  .0027 . Therefore, the 95-percent confidence interval surrounding estimates of BA derived from those equations is plus or minus  .0053 . As discussed above, that’s not a small error in the context of baseball statistics. In fact, it’s enough to swamp the effect of YR.

As discussed below, many of the explanatory variables have intuitively incorrect signs and are highly correlated with each other. This casts doubt on the validity of the derived coefficients, including the coefficient on YR.

I don’t mean to say that reaction times have stayed the same or become faster. I simply mean that this analysis is inconclusive about the trend (if any) of reaction times — possibly because there is no trend, in one direction or the other.

The equation, taken as a whole, does an admirable job of accounting for changes in BA over the span of 115 years. But I can’t take any of its parts seriously.

It’s been great fun but it was just one of those things.

DETAILS AND FURTHER DISCUSSION

Table 1 gives the coefficients and maxima, minima, means, standard errors, and 95-percent confidence intervals around the coefficients of the explanatory variables. Statistical parameters and estimated values are expressed to three significant figures. For ease of comparison, I use decimal notation rather than scientific notation for the explanatory variables.

TABLE 1
batting-average-analysis-regression-equation

Next is table 2, which gives the cross-correlations among the explanatory variables (including the 21st variable that’s not in the equation). Positive correlations above 0.5 are highlighted in green; negative correlations below 0.5 are highlighted in yellow; statistically insignificant correlations are denoted by gray shading.

TABLE 2 (right-click to open a larger image in a new tab)
batting-average-analysis-cross-correlations-of-explanatory-variables

Here’s my explanation and interpretation of the instrumental variables:

Intercept (c) (shown in table 1)

This is the sum of the intercepts derived from the 6th-order polynomial fit and the stage-2 and stage-3 regression analyses.

On-base-plus-slugging percentage minus batting average (OPS – BA)

BA is embedded in both components of on-base-plus-slugging percentage (OPS). By subtracting BA from OPS, I partly decouple that relationship and obtain rough measure of a batter’s propensity to get on base (mainly) by walking, plus his propensity for hitting doubles, triples, and home runs. But see OBP – BA and SLB – BA, below.

Strikeouts per plate appearance (SO/PA)

The positive coefficient on SO/PA is counterintuitive. In any particular at-bat, striving to hit a home run is thought to reduce a batter’s ability to make contact with the ball. The positive coefficient therefore reflects the positive relationship between HR/PA and BA (see below), and the tendency of home-run hitters to strike out more often than other hitters.

On-base percentage minus batting average (OBP – BA)

The negative coefficient on this variable probably means that it’s compensating for the residual component of BA that lingers in OPS – BA. This variable and OPS – BA should be thought of as a complementary variable — one that’s meaningless without the other.

Home runs per plate appearance (HR/PA)

The positive coefficient on this variable seems to capture the positive relationship between HR and BA. For example, most of the great home-run hitters also compiled high batting averages. (Peruse this list.)

Integration (BLK)

I use this variable to approximate the effect of the influx of black players (including non-white Hispanics) since 1947. BLK measures only the fraction of AL teams that had at least one black player for each full season. It begins at 0.25 in 1948 (the Indians and Browns signed Larry Doby and Hank Thompson during the 1947 season) and rises to 1 in 1960, following the signing of Pumpsie Green by the Red Sox during the 1959 season. The positive coefficient on this variable is consistent with the hypothesis that segregation had prevented the use of players superior to many of the whites who occupied roster slots because of their color.

Deadball era (DBALL)

The so-called deadball era lasted from the beginning of major-league baseball in 1871 through 1919 (roughly). It was called the deadball era because the ball stayed in play for a long time (often for an entire game), so that it lost much of its resilience and became hard to see because it accumulated dirt and scuffs. Those difficulties (for batters) were compounded by the spitball, the use of which was officially curtailed beginning with the 1920 season. (See this and this.) Batting averages and the frequency of long hits (especially home runs) rose markedly after 1919. Given the secular trend shown in figure 1, it’s surprising to find a positive coefficient on DB, which is a dummy variable (value =1) assigned to all seasons from 1901-1919. So DB is probably picking up the net effect of other factors. It should be considered a complementary variable.

Performance-enhancing drugs (DRUG)

Their rampant use seems to have begun in the early 1990s and trailed off in the late 2000s. I assigned a dummy variable of 1 to all seasons from 1994 through 2007 in an effort to capture the effect of PEDs on BA. The resulting coefficient suggests that the effect was (on balance) negative, though slight. Players who used PEDs generally strove for long hits, which may have had the immediate effect of reducing their batting averages.

Slugging percentage minus batting average (SLG – BA)

I consider this variable to be a complement to OPS – BA and OBP – PA.

Number of major-league teams (MLTM)

The standard view is that expansion hurt the quality of play by diluting talent. However, expansion didn’t keep pace with population growth over the long run. (see POP/TM, below). In any event, MLTM should be considered another complementary variable.

Night baseball, that is, baseball played under lights (LITE)

It has long been thought that batting is more difficult under artificial lighting than in sunlight. This variable measures the fraction of AL teams equipped with lights, but it doesn’t measure the rise in night games as a fraction of all games. I know from observation that that fraction continued to rise even after all AL stadiums were equipped with lights. The positive coefficient on LITE suggests that it’s yet another complementary variable. It’s very highly correlated with BLK, for example.

Average age of AL pitchers (PAGE)

The r1 residuals rise with respect to PAGE rise until PAGE = 27.4 , then they begin to drop. This variable represents the difference between 27.4 and the average age of AL pitchers during a particular season. The coefficient is multiplied by 27.4 minus the average age of pitchers; that is, by a positive number for ages lower than 27.4, by zero for age 27.4, and by a negative number for ages above 27.4. The positive coefficient suggests that, other things being equal, pitchers younger than 27.4 give up hits at a lower rate than pitchers older than 27.4. I’m agnostic on the issue.

Complete games per AL team (CG/TM)

A higher rate of complete games should mean that starting pitchers stay in games longer, on average, and therefore give up more hits, on average. The positive coefficient seems to contradict that hypothesis. But there are other, related variables (P/TM and IP/P/G), so this one should be thought of as a complementary variable.

Number of pitchers per AL team (P/TM)

It, too, has a surprisingly positive coefficient. One would expect the use of more pitchers to cause BA to drop (see IP/P/G).

World War II (WW2)

A lot of the game’s best batters were in uniform in 1942-1945. That left regular positions open to older, weaker batters, some of whom wouldn’t otherwise have been regulars or even in the major leagues. The negative coefficient on this variable captures the war’s effect on hitting, which suffered despite the fact that a lot of the game’s best pitchers also served.

Bases on balls per plate appearance (BB/PA)

The negative coefficient on this variable suggests that walks are collected predominantly by above-average hitters, who are deprived of chances to hit safely. See, for example, the list of batters who collected the most career bases on balls. Anecdotally, during the many years when I regularly listened to and watched baseball games, announcers often spoke of the “intentional” unintentional walk and “pitching around” a batter. In both cases, a pitcher would aim for the outside edges of the plate, to avoid giving a batter a good pitch to hit. If that meant a walked batter and a chance to pitch to a weaker batter, so be it.

Innings pitched per AL pitcher per game (IP/P/G)

This variable reflects the long-term trend toward the use of more pitchers in a game, which means that batters more often face rested pitchers who come at them with a different delivery and repertoire of pitches than their predecessors. IP/P/G has dropped steadily over the decades, exerting a negative effect on BA. This is reflected in the positive coefficient on the variable, which means that BA rises with IP/P/G. But the effect is slight, and it’s prudent to treat this variable as a complement to CG/TM and P/TM.

AL fielding average (FA)

Fielding averages have risen generally since 1901, which was an especially bad year at .938. The climb from .949 in 1902 to .985 in 2016 was smooth and almost uninterrupted. How would that affect BA? Here’s an example: A line drive that in 1916 bounced off the edge of a fielder’s glove might have been counted as a hit or an error, and if it just missed the glove it would usually be counted as a hit. A century later the same line drive would almost always be caught in the much larger glove worn by a fielder in the same position. It therefore seems to me that the coefficient on this variable should be negative, that is, a higher FA should mean a lower BA. The positive coefficient points to a confounding factor (e.g., BLK).

Year (YR)

This is the crucial variable, and the value of its coefficient — given the inclusion of all the other variables — may say something about the IQ hypothesis. After taking into account the 19 other variables in this equation, the coefficient on YR is slightly negative, which suggests that batters have generally been getting a bit slower. But as discussed throughout this post, there’s much uncertainty about the validity of the equation and, therefore, about the validity of the coefficient on BA.

Maximum distance traveled by AL teams (TRV)

Does travel affect play? Probably, but the mode and speed of travel (airplane vs. train) probably also affects it. The slightly positive coefficient on this variable — which is highly correlated with YR, BLK, MLTM, and several others — is meaningless, except insofar as it combines with all the other variables to account for BA.

U.S. population in millions per major-league team (POP/TM)

POP/TM has been rising almost without pause, despite expansion, and is now at its peak value. The negative coefficient is therefore surprising, and probably reflects the strong correlation of POP/TM with BLK, and perhaps other variables.

Batter’s age (BAGE)

This is the 21st variable, which isn’t in the final equation. The r1 residuals don’t vary with BAGE until BAGE = 37 , whereupon the residuals begin to drop. Accordingly, this variable represents the difference between 37 and a player’s age during a particular season.

In sum, there’s no way of knowing whether the negative coefficient on YR is related to reaction time, the (probably) greater speed of today’s pitchers, the greater variety of pitches thrown by today’s pitchers,  or anything else that’s not adequately reflected by the 20 variables in the final equation. I rest my case and throw myself on the mercy of the court.

Corresponding with a Collaborator

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I correspond with a fellow whom I’ve known for more than forty years. He’s a pleasant person with a good sense of humor and an easy-going personality. He’s also a chameleon.

By which I mean that he takes on the ideological coloration of his surroundings. He agrees with his companions of the moment. It’s therefore unsurprising that he proudly calls himself a “centrist.” Though he wouldn’t put it this way, his centrism involves compromises between good and evil — the necessary result of which is more evil.

“Centrist,” in his case, is just another word for “collaborator.”

A recent exchange will tell you all that you need to know about him. It began with an e-mail from a third party, in which this was quoted:

IF YOU HAD A HUNCH THE NEWS SYSTEM WAS SOMEWHAT RIGGED AND YOU COULDN’T PUT YOUR FINGER ON IT, THIS MIGHT HELP YOU SOLVE THE PUZZLE.

ABC News executive producer Ian Cameron is married to Susan Rice, National Security Adviser.

CBS President David Rhodes is the brother of Ben Rhodes, Obama’s Deputy National Security Adviser for Strategic Communications.

ABC News correspondent Claire Shipman is married to former White House Press Secretary Jay Carney.

ABC News and Univision reporter Matthew Jaffe is married to Katie Hogan, Obama’s Deputy Press Secretary.

ABC President Ben Sherwood is the brother of Obama’s Special Adviser Elizabeth Sherwood.

CNN President Virginia Moseley is married to former Hillary Clinton’s Deputy Secretary Tom Nides.

Ya think there might be a little bias in the news?

The chameleon’s comment:

I share your concern about MSM bias, but am not as troubled by it. (I stopped watching the Big 3s’ evening news 50 years ago because I couldn’t get a straight view on the Vietnam War.)

My comment on his comment:

You may have stopped watching, and I did too, but millions haven’t. And too many of them are swallowing it whole, which is a big reason for the leftward drift of the country over the past 50 years. (JFK could pass for a conservative today.) So I’m very troubled by it.

His reply to me:

But at my absolute center is a belief in universal suffrage.
In a nation of 150m or so (potential) voters, tens of millions are going to be swayed by CBS or, egads, Fox. If it weren’t those sources, it would be something else like them.

I can’t fix that, and see trying as futile. That’s why I’m not troubled. (My lack of concern also stems from seeing the USA as fundamentally on the right track. The latest evidence for that is the rejection of Trump about to occur. And yes, we’ll get Hillary’s excesses in consequence — but Congress will put on the brakes. We survived the Carter presidency when I’d have preferred Ford.)

Let’s parse that.

But at my absolute center is a belief in universal suffrage. What’s sacred about universal suffrage? If suffrage should encompass everyone who’s looking for a free ride at the expense of others — which it does these days — it should certainly include children and barnyard animals. Why should suffrage of any kind be the vehicle for violating constitutional limits on the power of the central government? That’s what it has come to, inasmuch as voters since the days of TR (at least) have been enticed to elect presidents and members of Congress who have blatantly seized unconstitutional powers, with the aid of their appointed lackeys and the connivance of a supine Supreme Court.

In a nation of 150m or so (potential) voters, tens of millions are going to be swayed by CBS or, egads, Fox. If it weren’t those sources, it would be something else like them. True, and all the more reason to keep the power of the central government within constitutional limits.

I can’t fix that, and see trying as futile. That’s why I’m not troubled. You, and I, and every adult can strive to “fix it” in ways big and small. Voting is one way, though probably the least effective (as an individual act). Speaking and writing on the issues is another way. I blog in the hope that some of what I say will trickle into the public discourse.

My lack of concern also stems from seeing the USA as fundamentally on the right track. It’s on the right track only if you think that the decades-long, leftward movement toward a powerful, big-spending, paternalistic government is the right track. That may very well suit a lot of people, but it also doesn’t suit a lot of people. Even FDR never won more than 61 percent of the popular vote, and his numbers dwindled as time went on. But perhaps you’re a utilitarian who believes that the pleasure A obtains from poking B in the eye somehow offsets B’s pain. You may not believe that you believe it, but that’s the import of your worship of universal suffrage, which is nothing more than blind allegiance to the primitive kind of utilitarianism known as majority rule.

The latest evidence for that is the rejection of Trump about to occur. Trump hasn’t yet lost, and even if he does, that won’t be evidence of anything other than desperation on the part of the operatives of the regulatory-welfare state and their various constituencies. Rejection, in any case, would be far from unanimous, so rejection is the wrong word — unless you believe, as you seem to do, that there’s a master “social conscience” which encompasses all Americans.

And yes, we’ll get Hillary’s excesses in consequence — but Congress will put on the brakes. Not if the Dems gain control of the Senate (a tie will do it if HRC is elected), and the ensuing Supreme Court appointees continue to ratify unconstitutional governance.

We survived the Carter presidency when I’d have preferred Ford. There have been more disastrous presidencies than Carter’s, why not mention them? In any event “survival” only means that the nation hasn’t yet crashed and burned. It doesn’t mean that there hasn’t been irreparable damage. Mere survival is a low hurdle (witness the Soviet Union, which survived for 74 years). Nor is mere survival an appropriate standard for a nation with as much potential as this one — potential that has been suppressed by the growth of the central government. So much loss of liberty, so much waste. That’s why I’m troubled, even if I can do little or nothing about it.

In closing, your political philosophy is an amalgam of “all is for the best … in the best of all possible worlds,” “What, me worry?,” “I’m all right, Jack,” and “Befehl ist Befehl.”

I won’t send the reply because I’m too nice a guy. And because it would pointless to challenge anyone who’s so morally obtuse — but likeable.

Pennant Droughts, Post-Season Play, and Seven-Game World Series

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PENNANT DROUGHTS

Everyone in the universe knows that the Chicago Cubs beat the Cleveland Indians to win the 2016 World Series. The Cubs got into the Series by ending what had been the longest pennant drought of the 16 old-line franchises in the National and American Leagues. The mini-bears had gone 71 years since winning the NL championship in 1945. And before last night, the Cubs last won a Series in 1908, a “mere” 108 years ago.

Here are the most recent league championships and World Series wins by the other old-line National League teams: Atlanta (formerly Boston and Milwaukee) Braves — 1999, 1995; Cincinnati Reds — 1990, 1990; Los Angeles (formerly Brooklyn) Dodgers — 1988, 1988; Philadelphia Phillies — 2009, 2008; Pittsburgh Pirates — 1979, 1979; San Francisco (formerly New York) Giants — 2014, 2014; and St. Louis Cardinals — 2013, 2011.

The American League lineup looks like this: Baltimore Orioles (formerly Milwaukee Brewers and St. Louis Browns) — 1983, 1983; Boston Red Sox — 2013, 2013; Chicago White Sox — 2005, 2005; Cleveland Indians — 2016 (previously 1997), 1948; Detroit Tigers — 2012, 1984; Minnesota Twins (formerly Washington Senators) — 1991, 1991; New York Yankees — 2009, 2009; and Oakland (formerly Philadelphia and Kansas City) Athletics — 1990, 1989.

What about the expansion franchises, of which there are 14? I’ll lump them because two of them (Milwaukee and Houston) have switched leagues since their inception. Here they are, in this format: Team (year of creation) — year of last league championship, year of last WS victory:

Arizona Diamondbacks (1998) — 2001, 2001

Colorado Rockies (1993) — 2007, never

Houston Astros (1962) — 2005, never

Kansas City Royals (1969) — 2015, 2015

Los Angeles Angels (1961) –2002, 2002

Miami Marlins (1993) — 2003, 2003

Milwaukee Brewers (1969, as Seattle Pilots) –1982, never

New York Mets (1962) — 2015, 1986

San Diego Padres (1969) — 1998, never

Seattle Mariners (1977) — never, never

Tampa Bay Rays (1998) — 2008, never

Texas Rangers (1961, as expansion Washington Senators) — 2011, never

Toronto Blue Jays (1977) — 1993, 1993

Washington Nationals (1969, as Montreal Expos) — never, never

POST-SEASON PLAY — OR, MAY THE BEST TEAM LOSE

The first 65 World Series (1903 and 1905-1968) were contests between the best teams in the National and American Leagues. The winner of a season-ending Series was therefore widely regarded as the best team in baseball for that season (except by the fans of the losing team and other soreheads). The advent of divisional play in 1969 meant that the Series could include a team that wasn’t the best in its league. From 1969 through 1993, when participation in the Series was decided by a single postseason playoff between division winners (1981 excepted), the leagues’ best teams met in only 10 of 24 series. The advent of three-tiered postseason play in 1995 and four-tiered postseason play in 2012, has only made matters worse.

By the numbers:

  • Postseason play originally consisted of a World Series (period) involving 1/8 of major-league teams — the best in each league. Postseason play now involves 1/3 of major-league teams and 7 postseason series (3 in each league plus the inter-league World Series).
  • Only 3 of the 22 Series from 1995 through 2016 have featured the best teams of both leagues, as measured by W-L record.
  • Of the 22 Series from 1995 through 2015, only 7 were won by the best team in a league.
  • Of the same 22 Series, 11 (50 percent) were won by the better of the two teams, as measured by W-L record. Of the 65 Series played before 1969, 35 were won by the team with the better W-L record and 2 involved teams with the same W-L record. So before 1969 the team with the better W-L record won 35/63 of the time for an overall average of 56 percent. That’s not significantly different from the result for the 22 Series played in 1995-2016, but the teams in the earlier era were each league’s best, which is no longer true. . .
  • From 1995 through 2016, a league’s best team (based on W-L record) appeared in a Series only 15 of 44 possible times — 6 times for the NL (pure luck), 9 times for the AL (little better than pure luck). (A random draw among teams qualifying for post-season play would have resulted in the selection of each league’s best team about 6 times out of 22.)
  • Division winners have opposed each other in only 11 of the 22 Series from 1995 through 2016.
  • Wild-card teams have appeared in 10 of those Series, with all-wild-card Series in 2002 and 2014.
  • Wild-card teams have occupied more than one-fourth of the slots in the 1995-2016 Series — 12 slots out of 44.

The winner of the World Series used to be its league’s best team over the course of the entire season, and the winner had to beat the best team in the other league. Now, the winner of the World Series usually can claim nothing more than having won the most postseason games — 11 or 12 out of as many as 19 or 20. Why not eliminate the 162-game regular season, select the postseason contestants at random, and go straight to postseason play?

Here are the World Series pairings for 1994-2016 (National League teams listed first; + indicates winner of World Series):

1995 –
Atlanta Braves (division winner; .625 W-L, best record in NL)+
Cleveland Indians (division winner; .694 W-L, best record in AL)

1996 –
Atlanta Braves (division winner; .593, best in NL)
New York Yankees (division winner; .568, second-best in AL)+

1997 –
Florida Marlins (wild-card team; .568, second-best in NL)+
Cleveland Indians (division winner; .534, fourth-best in AL)

1998 –
San Diego Padres (division winner; .605 third-best in NL)
New York Yankees (division winner, .704, best in AL)+

1999 –
Atlanta Braves (division winner; .636, best in NL)
New York Yankees (division winner; .605, best in AL)+

2000 –
New York Mets (wild-card team; .580, fourth-best in NL)
New York Yankees (division winner; .540, fifth-best in AL)+

2001 –
Arizona Diamondbacks (division winner; .568, fourth-best in NL)+
New York Yankees (division winner; .594, third-best in AL)

2002 –
San Francisco Giants (wild-card team; .590, fourth-best in NL)
Anaheim Angels (wild-card team; .611, third-best in AL)+

2003 –
Florida Marlines (wild-card team; .562, third-best in NL)+
New York Yankees (division winner; .623, best in AL)

2004 –
St. Louis Cardinals (division winner; .648, best in NL)
Boston Red Sox (wild-card team; .605, second-best in AL)+

2005 –
Houston Astros (wild-card team; .549, third-best in NL)
Chicago White Sox (division winner; .611, best in AL)*

2006 –
St. Louis Cardinals (division winner; .516, fifth-best in NL)+
Detroit Tigers (wild-card team; .586, third-best in AL)

2007 –
Colorado Rockies (wild-card team; .552, second-best in NL)
Boston Red Sox (division winner; .593, tied for best in AL)+

2008 –
Philadelphia Phillies (division winner; .568, second-best in NL)+
Tampa Bay Rays (division winner; .599, second-best in AL)

2009 –
Philadelphia Phillies (division winner; .574, second-best in NL)
New York Yankees (division winner; .636, best in AL)+

2010 —
San Francisco Giants (division winner; .568, second-best in NL)+
Texas Rangers (division winner; .556, fourth-best in AL)

2011 —
St. Louis Cardinals (wild-card team; .556, fourth-best in NL)+
Texas Rangers (division winner; .593, second-best in AL)

2012 —
San Francisco Giants (division winner; .580, third-best in AL)+
Detroit Tigers (division winner; .543, seventh-best in AL)

2013 —
St. Louis Cardinals (division winner; .599, best in NL)
Boston Red Sox (division winner; .599, best in AL)+

2014 —
San Francisco Giants (wild-card team; .543, 4th-best in NL)+
Kansas City Royals (wild-card team; .549, 4th-best in AL)

2015 —
New York Mets (division winner; .556, 5th best in NL)
Kansas City Royals (division winner; .586, best in AL)+

2016 —
Chicago Cubs (division winner; .640, best in NL)+
Cleveland Indians (division winner; .584, 2nd best in AL)

THE SEVEN-GAME WORLD SERIES

The seven-game World Series holds the promise of high drama. That promise is fulfilled if the Series stretches to a seventh game and that game goes down to the wire. Courtesy of Baseball-Reference.com, here’s what’s happened in the deciding games of the seven-game Series that have been played to date:

1909 – Pittsburgh (NL) 8 – Detroit (AL) 0

1912 – Boston (AL) 3 – New York (NL) 2 (10 innings)

1925 – Pittsburgh (NL) 9 – Washington (AL) 7

1926 – St. Louis (NL) 3 – New York (AL) 2

1931 – St. Louis (NL) 4 – Philadelphia (AL) 2

1934 – St. Louis (NL) 11 – Detroit (AL) 0

1940 – Cincinnati (NL) 2 – Detroit (AL) 1

1945 – Detroit (AL) 9 – Chicago (NL) 3

1947 – New York (AL) 5 – Brooklyn (NL) 2

1955 – Brooklyn (NL) 2 – New York (AL) 0

1956 – New York (AL) 9 – Brooklyn (NL) 0

1957 – Milwaukee (NL) 5 – New York (AL) 0

1958 – New York (AL) 6 – Milwaukee (NL) 2

1960 – Pittsburgh (NL) 10 New York (AL) 9 (decided by Bill Mazeroski’s home run in the bottom of the 9th)

1965 – Los Angeles (NL) 2 – Minnesota (AL) 0

1967 – St. Louis (NL) 7 – Boston (AL) 2

1968 – Detroit (AL) 4 – St. Louis (NL) 1

1971 – Pittsburgh (NL) 2 – Baltimore (AL) 1

1972 – Oakland (AL) 3 – Cincinnati (NL) 2

1973 – Oakland (AL) 5 – New York (NL) 2

1975 – Cincinnati (AL) 4 – Boston (AL) 3

1979 – Pittsburgh (NL) 4 – Baltimore (AL) 1

1982 – St. Louis (NL) 6 – Milwaukee (AL) 3

1985 – Kansas City (AL) 11 – St. Louis (NL) 0

1986 – New York (NL) 8 – Boston (AL) 5

1987 – Minnesota (AL) 4 – St. Louis (NL) 2

1991 – Minnesota (AL) 1 – Atlanta (NL) 0 (10 innings)

1997 – Florida (NL) 3 – Cleveland (AL) 2 (11 innings)

2001 – Arizona (NL) 3 – New York (AL) 2 (decided in the bottom of the 9th)

2002 – Anaheim (AL) 4 – San Francisco (NL) 1

2011 – St. Louis Cardinals (NL) 6 – Texas Rangers (AL) 2

2014 – San Francisco Giants (NL) 3 – Kansas City Royals (AL) 2 (no scoring after the 4th inning)

2016 – Chicago Cubs (NL) 8 – Cleveland Indians (AL) 7 (decided in the 10th inning)

Summary statistics:

33 seven-game Series (29 percent of 112 series played, including 4 in a best-of-nine format, none of which lasted 9 games)

17 Series decided by 1 or 2 runs

12 of those 15 Series decided by 1 run (6 times in extra innings or the winning team’s last at-bat)

4 consecutive seven-game Series 1955-58, all involving the New York Yankees (10 percent of the Yankees’ Series — 8 of 41 — went to seven games)

Does the World Series deliver high drama? Seldom. In fact, only about 10 percent of the time (12 of 112 decided by 1 run in game 7). The other 90 percent of the time it’s merely an excuse to fill seats and sell advertising, inasmuch as it’s seldom a contest between both leagues’ best teams.

Election 2016

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REVISED AND UPDATED 11/03/16

If you’re new to my fearless forecast of the coming election, here’s what I do: I begin with the popular vote, then use statistical relationships that I’ve derived from past elections to translate the popular vote split into electoral votes and changes in the composition of the House and Senate.*

11/03/16 — I caught Reuters cheating (as discussed below), so I no longer use that poll in computing my baseline forecast. The baseline forecast still portends a victory by Clinton, though her lead is shrinking:

  • Clinton takes 51 percent of the two-party popular vote, as against 49 percent for Trump.
  • Clinton wins 276-312 electoral votes, leaving Trump with 226-262.
  • Given the Trump-Clinton split (which isn’t yet a given), the GOP will lose no more than 4 House seats, retaining a solid majority of at least 243-192, though a loss of as many as 16 seats (for a 231-204 split) isn’t out of the question.
    • And given the same Trump-Clinton split, the GOP might not lose a Senate seat, leaving that chamber with 54 Republicans and 47 Democrats (counting the so-called independents as Democrats). However, a 2-seat loss is strong possibility. That would leave the GOP with 52 seats to retain a nominal majority. But the defection of 2 RINOs would leave the Senate tied at 50-50. And if Killer Kaine becomes vice president, his tie-breaking vote would hand control of the Senate to Democrats.

Now, the big picture. The scale for polling results is on the left axis. Additional indicators are measured on the right axis.**

FIGURE 1
election-indicators

The key events represented by vertical black lines are the first Trump-Clinton debate on September 26, the release of the infamous “Trump tape” on October 7, the second debate on October 9, the third debate on October 19, and James Comey’s announcement on October 28 that the FBI had re-opened the investigation into Clinton’s e-mails.

Just how far south (for Clinton) will things turn? To get a handle on that question, I’ve plotted some polling results since the third debate:

FIGURE 2
clinton-vs-trump-in-5-polls-since-oct-9_2

The points plotted at November 8 represent the linear trend in each poll since its most recent peak. The trend lines fit the actual and projected plot points.

Compare the Reuters values with those that I plotted yesterday. Caught cheating for Clinton, and thereby ejected.***

So the valid trends all point to a win for Trump, albeit a narrow one in the case of the RCP 2-way poll. My gut feeling (as of now) is that Trump’s margin of victory in the two-party popular vote is unlikely to exceed 4 percentage points. And he could still lose. Projections (like regression analysis) are accurate only in their representation of the past.

Where will it end? Stay tuned.
_________
* I start by averaging the current split between Trump and Clinton in these polls and aggregations of polls:

  • the Reuters poll, which is heavily skewed toward Clinton, but which I’ve adjusted to the  account for the likely direction of respondents who now say that they’ll vote for Johnson, Stein, or “other,” or who respond “wouldn’t vote” or “don’t know”
  • the two-way (Clinton vs. Trump “poll of polls” at RealClearPolitics (RCP), which I adjust as discussed in this post
  • RCP’s 4-way poll (Clinton, Trump, Johnson, Stein), similarly adjusted to account for likely defections from voters who say that they prefer Johnson, Stein, or “other”
  • and, for balance, the IBD/TIPP poll, which has a good track record, a high rating from FiveThirtyEight, and is somewhat of an outlier in that it’s less favorable to Clinton than the preceding polls. (I’ve also adjusted this poll to account for the likely direction of respondents who say that they’ll vote for Johnson, Stein, or “other,” or who respond “not sure.”)

** In addition to the Reuters, RCP, and IBD/TIPP polls (see preceding footnote), the graph includes the USC/LA Times poll, which is another Trump-leaning one. All of these polling results are plotted on the left axis.

These are the additional indicators, plotted on the right axis:

  • the Iowa Electronic Markets (IEM) Winner-Take-All (WTA) market, where the IEM WTA line represents the percentage-point spread between the percentage of money bet on Clinton and Trump
  • Rasmussen’s approval index for Obama (percentage of respondents strongly approving of his performance minus the percentage strongly disapproving), which I report because perceptions of Obama’s performance are likely to rub off on Clinton.

I plot all of the values against the dates on which polling was conducted or bets were made, not the dates on which results were released. And in the case of multi-day polling, I use the central date of the polling period. Therefore, almost all of the indicators are slightly out-of-date, a fact that one should consider when interpreting the indicators — especially if the race continues to tighten.

*** I said this yesterday:

I must draw your attention to the downward trajectory of the Reuters poll. Of the polls that I track, it has been and continues to be the most favorable to Clinton.

The following graph, from yesterday’s version of this post, is the one that inspired my statement:

clinton-vs-trump-in-5-polls-since-oct-9

I derived the values for the Reuters poll from results that appeared briefly online and then were withdrawn. New values, much more favorable to Clinton appeared this morning and are included in figure 2 (above).

Is a Theory of Everything Necessary?

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I begin with Wikipedia:

A theory of everything (ToE), final theory, ultimate theory, or master theory is a hypothetical single, all-encompassing, coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe. Finding a ToE is one of the major unsolved problems in physics. Over the past few centuries, two theoretical frameworks have been developed that, as a whole, most closely resemble a ToE. These two theories upon which all modern physics rests are general relativity (GR) and quantum field theory (QFT).

Michael Brooks, in “Has This Physicist Found the Key to Reality?” (The New Statesman, October 21, 2016), puts it this way:

In relativity, time is a mischievous sprite: there is no such thing as a universe-wide “now”. . .

He continues

. . . and movement through space makes once-reliable measures such as length and time intervals stretch and squeeze like putty in Einstein’s hands. Space and time are no longer the plain stage on which our lives play out: they are curved, with a geometry that depends on the mass and energy in any particular region. Worse, this curvature determines our movements. Falling because of gravity is in fact falling because of curves in space and time. Gravity is not so much a force as a geometric state of the universe.

Moreover:

The other troublesome theory is quantum mechanics [the core of QFT], which describes the subatomic world. It, too, is a century old, and it has proved just as disorienting as relativity. As [Carlo] Rovelli puts it, quantum mechanics “reveals to us that, the more we look at the detail of the world, the less constant it is. The world is not made up of tiny pebbles, it is a world of vibrations, a continuous fluctuation, a microscopic swarming of fleeting micro-events.”

But . . .

. . . here is the most disturbing point. Both of these theories are right, in the sense that their predictions have been borne out in countless experiments. And both must be wrong, too. We know that because they contradict one another, and because each fails to take the other into account when trying to explain how the universe works.

All of this is well-known and has been for a long time. I repeat it only to set the stage for my amateur view of the problem.

As is my wont, I turn to baseball for a metaphor. A pitcher who throws a fastball relies in part on gravity to make the pitch hard to hit. Whatever else the ball does because of the release velocity, angle of release, and spin imparted to the ball at the point of release, it also drops a bit from its apparent trajectory because of gravity.

What’s going on inside the ball as it makes it way to home plate? Nothing obvious. The rubber-and-cork core (the “pill”) and the various yarns that aare wound around it remain stationary relative to each other, thanks to the tightness of the cover, the tightness of the winding, and the adhesives that are used on the pill and the top layer of wound yarn. (See this video for a complete explanation of how a baseball is manufactured.)

But that’s only part of the story. The cover and the things inside it are composed of molecules, atoms, and various subatomic particles. The subatomic particles, if not the atoms and molecules, are in constant motion throughout the flight of the ball. Yet that motion is so weak that it has no effect on the motion of the ball as it moves toward the plate. (If there’s a physicist in the house, he will correct me if I’m wrong.)

In sum: The trajectory of the baseball (due in part to gravity) is independent of the quantum mechanical effects simultaneously at work inside the baseball. Perhaps the the universe is like that. Perhaps there’s no need for a theory of everything. In fact, such a theory may be a will-o-the-wisp — the unicorn of physics.

My Platform

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A voting guide published in my local newspaper asks seven questions of the presidential candidates. I list them below, with the answers that I would give were I a candidate for the presidency of the United States.

Question 1: What is your personal statement?

I am sick and tired of the nanny state, which is centered in Washington DC and extends into almost every city, town, and village in America.

Question 2: What are your top three goals?

Economic and social liberty for all Americans; protection of the lives, liberty, and property of innocent Americans; defense of Americans’ legitimate overseas interests.

Question 3: What will you do to support a vibrant economy across the U.S.?

I will send legislative proposals to Congress that will deregulate the economy; eliminate the death tax and corporate income taxes; reduce the central government to its essential and legitimate functions (mainly national defense), and cut taxes accordingly; and phase out all unconstitutional federal programs (which is most of them), beginning with Social Security, Medicare, and Medicaid. I will revoke all executive-branch policies that are contrary to the program spelled out in the preceding sentence.

Question 4: What, if any, actions will you support to create a pathway to citizenship?

I will ask Congress to deter illegal immigration by eliminating welfare programs that attract it; to provide the manpower and technical means to prevent, detect, and prosecute illegal immigration; and to establish more stringent citizenship requirements, including demonstrated proficiency in English. I will revoke all executive-branch policies that are contrary to the program spelled out in the preceding sentence.

Question 5: What should government do to provide an equitable, quality public education for all children pre-K through grade 12?

The central government should have no role in the funding of education or in the making of policies related to it. I will make one exception, for liberty’s sake, which is to propose an amendment to the Constitution that would require every State (and therefore the subordinate jurisdictions in every State) to allow parents to choose the schools to which they send their children, and to give vouchers to parents who choose private schools. The value of each State’s voucher would be the average cost of educating a child in grades K-12 in that State. (It would be up to each State to decide how to recover the shares owed by local jurisdictions.)

Question 6: What actions would you support the U.S. undertake to protect its interests abroad?

In view of the rising Russian and Chinese threats to Americans’ overseas interests — and the persistent threat posed by terrorist organizations — I will ask Congress to rebuild the nation’s armed forces, at least to the levels attained as a result of President Reagan’s buildup; to provide for the acquisition of superior, all-source intelligence capabilities; to support a robust research and development program for defense and intelligence systems; and to provide the funding needed to fully man our armed forces with well-trained personnel, and to keep the forces in a high state of readiness for sustained combat operations.

Regarding the use of armed forces, I will act immediately and vigorously to defend Americans’ legitimate overseas interests, which include international commerce around the globe, and to protect resources that directly affect international commerce (e.g., oil-rich regions on land and at sea). As necessary, I will seek the authorization of Congress to conduct sustained combat operations for those purposes.

I will not otherwise use or seek the approval of Congress to use the armed forces of the United States, which are maintained at great cost to Americans for the benefit of Americans. Those forces are not maintained for the purpose of defending countries that refuse to spend enough money to defend themselves, nor to “build nations” or engage in humanitarian operations that have no direct bearing on the safety of Americans or their interests. By the same token, America’s armed forces should be used to help defend nations that attempt to defend themselves and whose defeat would destabilize regions of strategic value to Americans’ interests.

Finally, I will not enter into treaties or agreements of any kind with the leaders of nations whose aim is clearly to undermine Americans’ legitimate economic interests. To that end, I will renounce Barack Obama’s agreement with Iran, his endorsement of the Paris agreement regarding so-called anthropogenic global warming, and all other agreements detrimental to the interests of Americans.

I will further ask to Congress to direct by law that the United States withdraw from the United Nations, which serves mainly as a showplace for regimes hostile to Americans’ constitutional ideals and interests. The U.N. will be given two years in which to remove all of its offices and personnel from the United States. I expect the U.N. to become overtly hostile to the United States when this country has withdrawn from it, but those member states who provoke and finance hostile acts on the part of the U.N. will be held to account, and will not be able to hide behind the false front of the United Nations.

Question 7: What kinds of policies will you pursue to promote social and racial justice for all Americans?

I will nominate judges and executive-branch officials who are demonstrably faithful to the Constitution of the United States, as its various portions were understood when they were ratified or modified through Article V amendments. This will mean the reversal of many judicial and executive actions that are contrary to the moral traditions that underlie the greatness of America, and which have been contravened arbitrarily to serve narrow interests and misguided ideologies. I am especially eager to defend life against those who seek to destroy and defile it, and to see that there is truly “equal protection of the law” by restoring freedom of speech and association where they have been suppressed in the name of equal protection.

Social and moral issues such as same-sex marriage should be decided by the States, and preferably by the people themselves, through the peaceful and voluntary evolution and operation of social norms. Such issues are outside the constitutional purview of the central government.

A Lesson in Election-Rigging

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A leading story on yesterday’s NBC evening news broadcast trumpeted an ABC News poll showing Hillary with a 12-point lead over The Donald. It could have been a story about polls in which NBC News participates: The latest NBC News/SM poll gives Clinton an 8-point edge, and the most recent NBC News/Wall Street Journal poll has Clinton up by 10 points. Or it could have been about the latest CBS News poll, which has Clinton leading by 11 points.

Why single out a poll that’s not representative of the world of polling? Why not trumpet the the overall average computed by FiveThirtyEight, a reputable outfit spawned by The New York Times? The answer is that FiveThiryEight‘s consensus forecast gives Clinton only a 6-point edge. (As do I.)

Why do you suppose FiveThirtyEight reports “only” a 6-point edge for Clinton? Because it adjusts for the bias inherent in polls like those conducted by ABC, CBS, and NBC.

And why do you suppose that the three networks conduct and report polls biased in Clinton’s direction, just as they routinely conduct and report polls biased toward Democrats? To ask the question is to answer it.

What better way to rally Clinton voters (and Democrats generally) while discouraging Trump voters (and Republicans generally) than to make a Clinton victory (or any Democrat victory) seem inevitable?

If presidential elections in America are in any sense “rigged,” they’re rigged by the pro-Democrat bias of the mainstream media, which comes through loud and clear on ABC, CBS, and NBC (and others). The bias shows up not only in what stories those networks choose to run and how they report those stories; it also shows up in the polls that they conduct and their reporting on those polls.