The 2016 Election With the Threshold Proportional Vote

In 2012, I wrote a series of blog posts (starting here) studying what would happen if Electoral Votes were awarded proportionally according to the vote in a state, not winner-take-all as is the practice in all but two states today (the other two award two EV’s to the winner of the state and one to the winner of each Congressional District).  I concluded that:

  1. Because of arithmetic, a pure proportional vote wouldn’t fly — because each state has a mean of 10.5 electoral votes, and the median state has 9 electoral votes, a pure proportional system would, on average,  award one electoral vote per 10% or so of the state’s popular vote.  Since a swing of 10% is almost unheard of, this would render the election pretty much irrelevant in all but a few very large states.  A system with thresholds fixes that: 60% of the vote wins all of a state’s electoral votes, 40% none, between 40% and 60% a proportional fraction.  This, in the average state, awards one elector per 2% of the vote, which means most states will have some electors in play.
  2. A study demonstrated that all but the smallest states (partisan states with 3-4 electoral votes)  would have electors in play, so the electoral battleground would be something like 45 states, rather than the current 13-15.
  3. A threshold proportional vote tracked the national vote very closely.  In particular, Bush/Gore 2000 and Hayes/Tilden 1876 would both have gone the other way.

In sum, it kept the current system in place but made it more democratic and put many more states in play.

So an obvious question is, what would the 2016 election look like had such a system been in place?  The answer is that Hillary Clinton would have won a close election.  The specific version I studied awarded electoral votes only to the top two candidates in a state, and for purposes of awarding EVs only counted the votes given to the top two candidates, then used the 60/40 proportional rule among those two.  So in Wisconsin, for example, Clinton and Trump each got 5 EV’s.  Nationwide, Clinton wins 273-265.  I also looked at one variant, where states with an even number of EV’s award a bonus to the state winner, no matter how slight.  Under this scenario, Trump wins Wisconsin 6-4.  Overall, however, the election still goes to Clinton, 275-263 (Clinton gets the bonus EV in Maine, Minnesota, Nevada, New Hampshire; Trump in Michigan and Wisconsin).  The full calculation can be found here.


The Coming Clinton “Groundslide”

This tawdry campaign has little to recommend it; The Economist’s October 15th cover, The debasing of American politics, summed up just how far we’ve sunk.  As I write this, there are still ten wretched days in which the most disgraceful American political figure since Aaron Burr will continue to defecate upon our culture and democracy.  November 9 will be a day for a long, hot bath to wash off the stench of Trump.

However, even in the darkest, foulest cloud there is a silver lining.  We’re going to find out just how much a ground game is worth.  Traditional campaigns invest heavily in get-out-the-vote efforts, but Mr. Trump has spent very little on this effort.  The Clinton campaign and the Democratic National Committee employ three times as many staffers across the 15 battleground states (Florida, North Carolina, Pennsylvania, New Hampshire, Ohio, Michigan, Wisconsin, Iowa, Indiana, Colorado, Arizona, Nevada, Maine, Nebraska, and Georgia) as does the Trump campaign and the RNC, according to The Hill.  Further, Secretary Clinton has continued President Obama’s heavily analytics-driven micro-targeting operation.  In contrast, Trump has nothing.  All of this appears to be working: Secretary Clinton is ahead of where President Obama was in early voting, according to Bloomberg.

How much is this worth?  The answer is no one really knows.  President Obama led Governor Romney by 0.7%  in the final 2012 Real Clear Politics polling average.  His victory margin was 4%, indicating that a next-generation ground game was a 3% or so advantage over the standard, professional ground game.  Presumably it would have been even greater over the nonexistent get-out-the vote operation that Trump has.  In fact, the Trump campaign has been called a glorified concert tour.

Since no candidate has been as foolhardy as Trump in the past, we have no good data on how much a ground game really matters.  The National Review estimated it as worth between 2% and 4% nationwide; if that’s the case, the 5%-7% lead Secretary Clinton has in national polls is more like 7%-11% on Election Day.  True to his tawdry, pull-everything-down style, Trump’s strategy to combat this is voter suppression.

To quantify all of this, I downloaded FiveThirtyEight‘s complete polling data on October 20, and used their weights to compute polling averages for each state and nationally, and then normalized each state and the entire country so that the four leading candidates (Clinton, Trump, Johnson, and McMullin) received more than 98% of the vote in each jurisdiction, awarding undecideds pro rata.  The baseline result was a 49.4%-42.6%  popular vote victory for Secretary Clinton, and a 351-187 Electoral College victory.  The electoral vote, with any state won by < 5% of the vote considered a tossup, is Clinton 272, Trump 164, Tossups 102.

Click the map to create your own at

Now let’s add the ground game effect.  I gave Secretary Clinton a 3% bump in each state, taking from the other candidates in proportion to their share of the vote.  The result was a 52.4%-39.9% victory for Secretary Clinton, with Johnson at 5.7%.  In the Electoral College, Clinton now wins 387-151; Alaska (3) Georgia (16), Iowa (6), Maine CD-2 (1), and Missouri (10)  shift to Clinton.   With tossups included, the Electoral Vote is 357-80 Clinton, with 101 tossups. From a Trump perspective, the map is ugly; even Texas is a tossup!

Click the map to create your own at

3% is a pretty small ground game effect; suppose it’s 5%? At this point we’re talking a 1988-class landslide: Clinton wins 54.4%-38.2%, with Johnson still hanging in at 5.5% of the vote. The Electoral Vote is 458-80 with no tossups; Indiana (11), Kansas(!) (6), Nebraska CD-2 (1), South Carolina (9), Texas (38), and Utah (6) all shift to Clinton.

With tossups, it’s 374-47 Clinton, with 117 tossups. The map is here:

Click the map to create your own at

Of course, Secretary Clinton has intelligently focussed her get out the vote efforts on the 15 battleground states (counting Maine-2 and Nebraska-2 as battlegrounds). If we assume the ground effect is only seen there, the result is a comfortable 396-142 victory for Secretary Clinton. With tossups, the count is Clinton 374, Trump 133, and tossups 31 (Missouri, Nebraska-2, Utah, Alaska, Indiana). This is perhaps the most compelling map of all, because it indicates just how effective targeting is: Trump’s total gettable EV is 164.

Click the map to create your own at

In sum, on November 8 Secretary Clinton will win the largest electoral vote victory in a generation, the greatest since her husband’s 379-159 triumph over Bob Dole in 1996; she has an outside shot at matching George H. W. Bush’s 426-111 victory over Michael Dukakis in 1988. She will also very likely win a popular vote majority; this will mean the Democrats will have won the popular vote in three straight elections, for the first time since Franklin Roosevelt won the popular vote in four straight elections from 1932-1944.

A Twin Paradox Variant, With a Surprise

The “Twin Paradox” in Special Relativity is well known.  One of  the pair, conventionally Homer, remains on Earth while his twin, Ulysses, takes off in a high-speed rocket for another star, rounds the star and comes home.  When Ulysses emerges from his spacecraft he finds that Homer has aged far faster than he has.  A naive reading of SR holds that Ulysses could have considered himself stationary, while Homer moved at high speed, and therefore Ulysses should have aged faster, and that is the paradox.

The answer is that the roles of the twins are not symmetric: Homer remained in a single frame of reference, while Ulysses changed his frame of reference with at least three accelerations, and the age measurement is taken in Homer’s unchanged frame of reference.  Every detailed calculation shows that the “paradox” disappears when this is taken into account.

But a friend recently came up with a variant on this, where the roles of the twins were symmetric.  Suppose, he said, that Homer and Ulysses blasted off in opposite directions at the same speed, turned around after a set time, and then returned.  As they approach each other on the return, each sees the other’s clock as running more slowly than his own.  So when they pass each other, which is older?

The answer is that each sees the other’s clock as running more quickly than his own, but, amazingly, when they meet both find that they have aged the same amount!  The analysis follows here, and is encapsulated in this Spacetime Diagram


If you aren’t familiar with a spacetime diagram, the x axis is space, the t axis is time.   Lines are the motion of objects, their so-called “worldlines”.  The scale is such that the speed of light is 1; lines which are at 45o (slope = 1) are light rays. Lines with slope are the paths of objects moving at velocity .

In this diagram, the red lines are the path of Homer’s Rocket, and the green lines are the path of Ulysses’ rocket.   The black lines are light rays sent between the ships.

The diagram is always drawn in some frame of reference.  In this case, I’ve chosen a frame of reference which moves along with Homer’s rocket on its outbound journey.

There are some text notations on the diagram.  Beside each colored line segment is a notation of the form , for some .  This gives the value of  the proper time  for a ship on that line  as a fraction of the time ; the proper time is just the time kept by a clock moving on the ship.

Beside the light rays are the values for the Doppler Shift of the light rays: the difference in frequency from the source to the observer.  When , the light rays have twice the frequency at the receiver that they had at the source; when , they have half the frequency.  It’s important to note that the Doppler shift affects every periodic phenomenon: in particular, it affects clock ticking.  When the Doppler Shift is 2, the observer will see clocks ticking twice as fast as the person at the source sees them.

For completeness, we should give the formulae for these things.  When two objects are approaching with velocity , .  When they are receding with velocity , .  The formula for is also simple: .

Now that that’s in place, we can describe the experiment.  Homer and Ulysses blast away from each other at 60% of light speed: .  After one year of proper time (, not ), they turn and blast towards each other at .  At all phases of their journey, they agree to flash lights every second, so each can keep track of the proper time on the other’s ship.  The total number of light flashes each sends is the total proper time on that ship.

Their journey is the red and green parallelogram in the diagram, which is the spacetime diagram as seen from an observer who moves in the direction of Homer’s ship as it moves away from Ulysses’ ship.  When Homer makes the turn, the observer doesn’t.

We start out at the bottom.  From , the ships blast away from each other.  Since the observer starts out moving with Homer, in the observer’s frame Homer is motionless but Ulysses is blasting away at , represented by a line with slope .  We can see that Homer’s proper time is just , but Ulysses’ proper time is — according to the observer, Ulysses’ clock is running slow.  Homer and Ulysses, meanwhile, are exchanging light signals (say one per second) but the Doppler Shift is 0.5 — they are receiving light signals at the rate of one every two seconds.  According to each, the other’s clock is running at half-speed.  At , Homer’s , so Homer makes the turn: Ulysses, however, keeps blasting away until , at which time Ulysses’ .  Once this happens, Ulysses is now co-moving with the observer (his velocity is the same as Homer’s original velocity), so from the perspective of the observer Ulysses is now motionless and Homer is blasting towards Ulysses at 60% of the speed of light, so now .

For the first part of this epoch, Homer is seeing light from Ulysses that left Ulysses’ ship while it was moving in the same direction that Homer’s ship is now.  As a result, there is no Doppler shift, and Homer and Ulysses both see the other’s clock as keeping perfect time.  This lasts until the light ray that left Ulysses’ ship at Ulysses’ turn reaches Homer’s ship, which is when , or .  Homer’s proper time at this point is .   The Doppler shift is now 2, so each of  Homer and Ulysses think the other’s clock is moving twice as fast as  his own.  This continues until they pass, at which time each sees the other’s clock is moving half as fast as his own.

However, if they stopped and compared clocks, they would each see that the same proper time had elapsed for both of them; if they counted flashes received vs sent, they would see that they had sent the same number of flashes.  In fact, if they exchanged one flash every tenth of a year (proper time), they would each report that during the first year of their journey, they sent 10 flashes and received 5; over the next six months, each sent 5 and received 5; and during the final six months, each sent 5 and received 10.  Each would report that the proper time of his journey was 2 years, and each sent and received 20 flashes.

Now (for the sake of completeness) let’s consider how an observer in the original frame of reference (the one Ulysses and Homer inhabited before they left) saw both journeys.  If Homer and Ulysses had relative velocity , each had velocity from the perspective of an observer in the original frame of reference, where .  A little algebra shows , and plugging in we get  So from his perspective, Homer and Ulysses each blasted away at 1/3 of the speed of light for years, turned, and returned at the same rate.  According to him, both were gone 2.12 years, while Homer and Ulysses each saw the journey take 2 years exactly.


Stopping Trump For Certain

There is a reasonable chance that Mr. Trump will get a majority of delegates on the first ballot at the Republican convention.  It is generally assumed that this guarantees him the nomination: majority election is interwoven into our political fabric so tightly we assume that it is a fact of nature.

Well, it isn’t.  It’s a rule of each party: in the case of the Republican Party, it’s Rule 40(d) of the Republican Party Rules.  And these rules can be, and are, modified at each convention.  There’s been lots of speculation that the RNC would modify Rule 40(b) to permit individuals that hadn’t won eight states to be placed in nomination.  If they can do that, they can raise the threshold for nomination.

So how much should they raise it?  One reasonable target is 2/3 of the delegates, or, this year, 1650 delegates.  This was actually the standard for the Democratic Party from 1832-1936, when it was abolished at the time of the unanimous renomination of FDR.  Interestingly, the rule had been suspended in 1836 and 1840, only to be reinstituted to prevent the renomination of President Martin van Buren.   It’s worth noting that every Republican nominee since 1976 easily passed the 2/3 threshold, and in the postwar years only Eisenhower (1952), Richard Nixon (1968), and Gerald Ford (1976) won on the first ballot with less than 2/3 of the vote.

It is still mathematically possible for Mr. Trump to win 2/3 of the delegates; only 734 delegates to date are committed against him, and it would take 825 to keep him from a 2/3 majority.  If he runs the table on the remaining primaries, he could do it.

Now, should the GOP stop him this way?  Of course they should: Mr. Trump is not an acceptable candidate for President of the United States, or the leadership of any major Democracy.  He has disqualified himself through his unceasing threats of lawlessness and violence.  This has nothing to do with his policies or ideology, or, frankly, lack of same: it has everything to do with his behavior.  His behavior and rhetoric would have had him censured or expelled from any legislative body; recused from any bench, and likely impeached; fired for cause as an executive with any public corporation.  Should a political party have lower standards than that?  Of course not; the simplest and most direct solution would be to just refuse to permit him to have his name placed before the convention.  Failing that, at least require him to get a supermajority.

Justin’s Amazing Poem

It’s hard to overemphasize Justin Trudeau‘s overwhelming victory on Monday night. While neither the percentage of the vote (39.47%) nor his percentage of seats won (54.44%) were very remarkable, it represents a turnaround without equal in the history of Canadian politics — and, as nearly as I can tell, the history of advanced democracies.

When Justin Trudeau took over the Liberal Party in 2012, it appeared to be in terminal decline. It had lost seats and votes in four consecutive and five of six elections stretching back a decade. From a once-reliable base of the 35%-40% of the national vote, it had sunk to under 20% of the vote and third-party status, with just over 10% of the seats in Parliament. Its leader in the 2011 election, Michael Ignatieff, had lost his own seat. Far worse, its fall had corresponded to the rise of the social-democratic party NDP. Under the charismatic Jack Layton, the NDP had increased both its share of the vote and seats in Parliament in the same elections, so by 2011 the NDP had won over 30% of the vote and had about 1/3 of the seats in the House of Commons. The Liberals and the rise of the NDP in the period 2001-2011 was remarkably similar to the decline of the British Liberal Party and the rise of Labour during the 1920’s. It seemed certain that Canada was on the way to becoming a fairly conventional Parliamentary Democracy, with a center-right coalition (“Conservative” or “Christian Democrat”, or (in Australia, Japan, and British Columbia), “Liberal”) facing a center-left labor-allied coalition (typically, “Labour” or “Social Democrat”). In fact, at the start of this campaign, seven weeks ago, it appeared likely that Canada was about to get its first Social Democratic government.

And then Trudeau, dismissed as handsome and pleasant but lightweight, pulled off one of the most remarkable campaigns in the history of advanced democracies. Consider the numbers:

  • Trudeau increased his party’s vote from 18.91% of the vote in 2011 to 39.47%, an increase of 20.56% of the vote. This easily the largest increase for an existing party in Canada’s history; only the Mulroney landslide of 1984 (17.58%), the Diefenbaker landslide of 1958 (15.17%) and the 2011 rise of the NDP (12.45%) were in double digits.
  • This is only the second time in Canadian history that a third-place party became the largest party in the next election, and the only time that a third-place party has formed a majority.
  • This is only the third time in the last eighty years that a majority government of one party has been replaced by a majority government of another party, and only the fifth time over that span that a majority government has lost at all.
  • Trudeau increased his share of House seats from 11.04% of the seats to 54.44%, an increase of 43.4%. Once again, this is a record for Canadian elections. Only Mulroney in 1984 (38.30%) and MacKenzie King in 1935 (34.29%) even come within 10% of Trudeau’s triumph.
  • Trudeau’s freshman class — MP’s who first won election in 2015 — is so large that it would easily be the largest party in the House. In fact, it’s bigger than three minority governments (1962, 1972, 2006) and very close to two more (1957, 2004).

Those data speak to the historic magnitude of Trudeau’s victory.  No party leader in Canada has ever increased his party’s share of the vote or seats by anything like as much as Trudeau did.  Comparisons are often made to his father‘s 1968 victory — the “Trudeaumania” election.  But that was in fact quite modest — Pierre  Trudeau added a modest 5.19% of the vote and 8.9% of the seats to the 1968 Liberals’ pre-election totals,  compared to his son’s 20.56% of the vote and 43.4% of the seats.  But more impressive was the efficacy of his campaign.  Historical data to compare to other leaders are not available here, but it’s hard to imagine a campaign that had a more significant effect.

According to the authoritative, the Liberals started the campaign in third place with 25.9% of the vote, compared to the NDP’s lead with 33.2% and the Conservatives’ 30.6%.  The Liberals managed to increase their vote total marginally, to about 29.6% of the vote, by Sept. 20, while the NDP declined slightly to 29.8%.  But then there was a decisive break — over the last month of the campaign the Liberals added about 10% support while the NDP dropped 11%.  Effectively, Trudeau persuaded about one-third of NDP supporters to vote for him instead.

Now that’s impressive.  Part of the credit surely belongs to Prime Minister Harper, who inspired a depth of antipathy that led to at least some strategic voting.  Though there have been many news reports of the “Anyone-but-Harper” movement, I haven’t seen any quantitative analysis of its effect.  Part of Mr. Trudeau’s massive victory was surely momentum; some percentage of those who switched from the NDP to the Liberals in October were motivated by the fact that Mr. Trudeau had the best chance to unseat Mr. Harper.  Some of his gains  from the NDP in Quebec, too, were surely due to the niqab affair;  even Quebec NDP candidates opposed NDP leader Thomas Mulcair’s principled stand that Muslim women should be permitted to wear the traditional face covering when taking the oath of Canadian citizenship.  However, Mr. Trudeau used the issue as the centerpiece of a thoughtful speech on individual liberty and collective responsibility, which I recommend reading.

Still more impressive is Mr. Trudeau’s popularity.  It’s a common experience in politicians that the day they are nominated (or, in the case of a Canadian political leader, elected to the leadership) is the peak of their popularity.  Indeed, that was the case for Mr. Trudeau, up until yesterday.  Liberal popularity peaked at 38% just after his election as leader, and then declined, more or less steadily, until the start of the campaign.  Then, as noted above, it leveled and then began a continuous rise until election day, where he peaked at 39.47%.

An analysis of his success would be worthwhile, and will come later.  And governing is not campaigning — as New York Governor Mario Cuomo observed, you campaign in poetry and govern in prose.  Of course one doesn’t know Mr. Trudeau’s skills as an essayist.  Today, however, we can observe he has written a marvelous poem.

And Then There Were Four…Andre Iguodala Joins The World’s Most Exclusive Club

Three years ago, Alvin AuYoung and I pointed out that  Shaquille O’Neal held all three major championships in basketball: the NBA Championship, (2000, 2001, 2002, 2006), the Olympic Gold Medal (1996), and the FIBA World Cup (1994).   We incorrectly said that he was, at the time, the only member of Basketball’s Triple Gold Club: David Robinson had the 1986 World Cup, the 1992 and 1996 Gold Medals, and the 1999 and 2003 NBA Championships.  Less than a month after we wrote the piece, Tyson Chandler added the 2012 Olympic Gold Medal to his  2010 FIBA World Cup Championship and 2011 NBA Championship.  Now there’s a fourth: with the Golden State Warriors victory over the Cleveland Cavaliers last month, Warriors’ Sixth Man Andre Iguodala added the 2015 NBA Championship to his 2010 FIBA World Cup Championship and his 2012 Olympic Gold Medal.

Iguodala’s march to the triple gold was similar to Shaq’s.  Shaq won the 1994 World Cup while a member of the Orlando Magic, the 1996 Gold Medal after his last season with the Magic, and the 2000 NBA title with the Lakers.   Iguodala won the 2010 World Cup while a member of the Denver Nuggets and the 2012 Gold Medal after his last season with the Nuggets.  Both were Finals MVPs in their first NBA championship.  Shaq was younger (28 at his triple gold while Iguodala was 31).

Though there are now only four members, they had better make room for more.  Both of the Splash Brothers,  Klay Thompson and Stephen Curry, have both the  2015 NBA Championship and the 2014 World Cup Championship, and are locks for the US team in the 2016 Summer Olympics.  In fact, Curry has two World Cups, from 2014 and 2010.  Curry would have joined  the club with Iguodala,  except that he was prevented from playing in the 2012 Olympics because of a knee injury.

While Thompson and Curry seem to be locks, others are knocking on the door.  Kevin Love has both a Gold Medal and a World Cup Championship, and the Cavaliers are likely to be strong contenders next year.  Kevin Durant, Russell Westbrook,  Anthony Davis, and James Harden also are only missing the NBA Championship.  Kyrie Irving needs both an NBA Championship and a Gold Medal, but given his near-certain selection to the US team next year and the Cavaliers’ strength, he could win both the Gold Medal and the Larry O’Brien trophy in a single year.  LeBron James heads a list of great players (Kobe Bryant, Dwyane Wade, Chris Bosh, Tayshaun Prince) with both a Gold Medal and an NBA Championship, but he won’t have an opportunity to complete the Triple until 2019.  At that point he’ll be 35, and may not want to play international basketball.

Similarly, Manu Ginobili has a 2004 Gold Medal to go with his four NBA Championships (2003, 2005, 2007, 2014), but in 2019 he’ll be 42, and, realistically, Argentina is a longshot.  So this looks to be an exclusively American club for a number of years.

Obama’s Community College Idea Should Get GOP Support

I haven’t annoyed my Republican friends for some time, and I’ve been kicking my Democratic friends in the shins, so it’s time to restore a little balance.  President Obama’s Community College idea is a good one, and it should be supported.  And even Prof. Milton Friedman (might) say it’s a good idea.  Here’s why.

Here’s why.  Friedman proposed a college financing proposal in which a student sold equity in himself to the government.  It’s summarized here, but the net is really simple: the student gets a grant to attend school, and in return promises to pay a proportion of his income to the government.  In effect, he’s sold stock in himself to the government.

Great idea.  But we already have such a program.  It’s called the income tax.

Now, I am not a huge fan of the income tax.  It’s basically a tax on work, saving, and investment, and if you tax anything you get less of it.  That’s why we have sin taxes on booze and cigarettes; we’re trying to discourage their consumption.  I don’t like the income tax because I don’t want to discourage work, saving, and investment.  But that said, we have it, and it’s not going away anytime soon.  If you net it out, community college graduates earn about 1/3 more than high school graduates.  About 20% of that accrues to government through taxes.  That pays for the cost of college, many times over, and is thus an exceedingly good fiscal bet.  In effect, the income tax acts as Prof. Friedman’s equity collector — with zero transactions costs.



#DeflateGate culprit? Physics

PV = nRT.  It’s one of those laws you learned in high-school physics.  For any gas, pressure x volume = number of molecules x temperature.  The New England Patriots’ balls were tested in the Referee’s Room before the game.  We don’t know the temperature, but 70°F = 20°C = 293.5°K is a good guess.  The temperature dropped into the low 40’s (275°K or so) during the game.  That’s a drop of about 6% from testing conditions, and so — you guessed — pressure would also drop by 6%.  The Patriots say that they inflate the balls to 12.5 psi, the minimum allowable under the rules.  That’s above ambient pressure of 15 psi, for a total of 15 + 12.5 = 27.5 psi.    6% of 27.5 is about  1.65 psi, so a drop in temperature alone explains a reading of  11.1 psi.   ESPN reports the actual number as 11 psi, so that’s it.    Physics did it.

All in, The Unbalanced Schedule Wasn’t That Unfair


The 2013 Major League season is (almost) over, with only a tiebreaker playoff between the Tampa Bay Rays and the Texas Rangers remaining.  But the complaints have been flying fast and furious that the Major League schedule for 2013 was unfair to teams in the American League East.  Specifically, contending teams from the West and Central divisions were able to fatten up on relatively weak opponents (Houston, Seattle, the White Sox, Minnesota) while the AL East was strong top-to-bottom.  Since the wild card is a competition among teams from all divisions, the claim is that in a balanced schedule the AL East teams would have been far more competitive for the two wild-card spots.  See, for example, for a representative complaint.

Interesting thesis: but is it true?  To find out, we calculated the Balanced Schedule Equivalent Record for major league teams.  The BSER calculates what team’s records would have been had the Major Leagues played a balanced schedule in 2013.

The logic behind the BSER is simple: each team played a total of 142 games against the 14 other teams in its own league, plus 20 interleague games.  This works out to an average of just a little over 10 games against each team in a balanced schedule, as opposed to 19 games against teams in its own division and an average of 6.6 games against teams in the other two divisions.  If we scale each head-to-head record by the appropriate factor (142/(19*14) for teams in one’s own division; 142/(6.6*14) for teams in the other divisions) we arrive at what the in-league record would have been for each team, had they played a balanced schedule.  Add in the interleague games, and, voila; we have the final BSER.

The results for the National League are shown in Table 1

Team BSER Wins Actual Wins
LA Dodgers 97.83413078 92
St. Louis 97.56504899 97
Atlanta 94.48849396 96
Cincinnati 92.28844839 90
Pittsburgh 91.04198916 94
Washington 83.27080108 86
Arizona 82.23747789 81
San Diego 77.39849624 76
Milwaukee 76.40145819 74
NY Mets 73.71747551 74
Colorado 73.56945359 74
Philadelphia 71.31897927 73
San Francisco 69.66860626 76
Chi Cubs 69.4157176 66
Miami 61.11854544 62

Though there are some differences here (LA finishes with the National League’s best record, instead of having the third seed, and Pittsburgh goes to Cincinnati for the wild card instead of the other way round), the playoff teams are unchanged.  In the American League this is (almost) true as well.

Team BSER Wins Actual Wins
Boston 97.52548651 97
Oakland 96.24581214 96
Cleveland 91.35019367 92
Tampa Bay 90.27956254 91
Detroit 89.38933271 93
NY Yankees 88.68694463 85
Baltimore 88.61631351 85
Kansas City 83.01655794 86
LA Angels 82.45823198 78
Texas 81.26986123 91
Toronto 77.72932331 74
Seattle 68.79630142 71
Minnesota 68.04830257 66
Chi White Sox 66.44679882 63
Houston 49.00820232 51

Boston keeps the league’s best record, and Oakland remains the #2 seed, a game behind. Interestingly, Cleveland actually wins the Central by two games over Detroit, and Tampa Bay is the other wildcard.  The complaints do have some validity: Texas did benefit enormously from the unbalanced schedule, winning 10 games more than they would have done in a balanced schedule.  However, the AL East teams wouldn’t have done a great deal better under a balanced schedule (Tampa Bay would actually have lost a game, and the Yankees and Baltimore would only have picked up three each).

The calculation here is quite simple; if Major League baseball is genuinely perturbed by this season’s outcome, it could shift to the BSER to calculate wild-card teams and home-field seedings for the playoffs, thus permitting MLB to retain the unbalanced schedule and the excitement of the division races while maintaing fairness in inter-division competitions.

Or not.  The flaws in that plan are easy to see from the above tables: the whole point of unbalanced schedules is to emphasize division games.  Suppose a team finished second in its division in the unbalanced schedule, but third in the wild-card race behind the third-place team in its own division (as you can see from the above, the BSER can invert standings in a division).  Who goes to the wildcard?  And should Cincinnati or Pittsburgh have the home-field this year?  Pittsburgh finished ahead in the division, but Cincy in the BSER race…

The World’s Most Exclusive Club

The Triple Gold Club[This is written jointly with Alvin AuYoung]

What’s the NBA’s Most Exclusive Club?  Well, let’s first consider this question in the context of other sports. The Club should honor specific, noteworthy achievements, and have very few members.  The Club of Golf Grand Slam Champions might qualify: a purist would argue that the only member is Bobby Jones, but with four straight Grand Slam Championships across two years, Tiger Woods might also be considered a member.

But we do know of one high-achievement club with only one member, and it’s very likely that it will contain only one until June of 2013: the Basketball Triple Gold Club.   Who’s the member?  Well, that’s the trivia question…but, first, we should describe the Basketball Triple Gold Club.

The Basketball Triple Gold Club consists of people who have won all three of basketball’s most prestigious tournaments: the NBA Championship, the Olympic Gold Medal, and the FIBA Basketball World Cup.  It’s modeled on the Hockey Triple Gold Club,  which features the winners of the Stanley Cup, the Olympic Gold Medal, and the IIHF World Championship.  There are 25 members of the Hockey Triple Gold Club: nine Canadians, eight Russians, six Swedes, and two Czechs, and  the hockey world does take it very seriously.

But the Hockey Triple Gold Club has a large, and unavoidable, element of bogusness to it: the IIHF World Championship resembles college basketball’s NIT more than anything else.  It’s held annually, and it is held at the same time as the Stanley Cup playoffs.  As a result, it features mostly players who couldn’t make the NHL, or whose teams missed the playoffs, and occasionally a few stars whose teams got knocked out in the first round.    Players whose teams perennially go deep in the NHL playoffs are unlikely to ever participate in the IIHF World Championship, so there’s a large element of luck involved in even playing in the tournament.

Triple Gold and Mystery Man

Who’s the Mystery Member?

The Basketball Triple Gold Club is not nearly as inherently suspect: the FIBA World Cup is held quadrennially, and doesn’t conflict with the NBA season.  The world’s best could, if they wanted to, show up every fourth year to play for their country.  And, typically, unless the players are Americans, they do.  However, in 1998 NBA players were barred from playing in the FIBA World Cup due to that season’s NBA lockout, and in 2002 a number of NBA stars skipped the FIBA World Championships.    The shocking sixth-place finish of the US in 2002 and its bronze medal in the 2004 games reinvigorated America’s commitment to international basketball, and it’s possible that the FIBA World Cup will attain the stature in basketball that the World Cup does in soccer.    Barring injury, no top soccer player would miss the FIFA World Cup, and no top European player would miss the UEFA European Championship.

OK, enough suspense: who’s the guy?  The sole member of  the Basketball Triple Gold Club is Shaquille O’Neal, and, yes, that noise you hear in the background is Kobe Bryant‘s teeth gnashing.  O’Neal won the 1994 FIBA World Championship, four NBA Championships, and an Olympic Gold Medal in 1996.  Kobe has five NBA championships and an Olympic Gold from 2008, but has never been on a FIBA World Cup champion.


The Sole Member of the Triple Gold Club

So who’s likely to join Shaq?  The only possibility at the Olympic Games this year is Pau Gasol.  Gasol has a FIBA World Championship (2006), and two NBA titles (2009, 2010, Lakers).  The only other NBA/FIBA champions are  Peja Stojakovic of Serbia (FIBA champions, 2002) and, recently, the Dallas Mavs (NBA champions, 2011), Lamar Odom  (World Cup, 2010; NBA Champion, 2009, 2010), and Chauncey Billups (World Cup, 2010; NBA Champion, 2004). But Peja has retired and Serbia didn’t qualify for the Olympics this year, Billups is unable to play until December with a torn Achilles and  Odom wasn’t named to the Olympic team.

Shaq might get company before too long, though.  The US are heavy favorites in London, and if they do bring home the  gold five members of the team will have both FIBA World Championships (from 2010) and Olympic Gold Medals — Kevin Love, Kevin Durant, Tyson Chandler, Russell Westbrook and Andre Iguodala; and the smart money is that an NBA title is in the future for at least some of these young and rising stars.  So Shaq might have company as early as June of 2013.

The next opportunity will be at the FIBA World Cup of 2014, and a number of the game’s greatest could have a shot then, if they want it: Kobe Bryant, LeBron James, Dwyane Wade, and Chris Bosh, (for the latter three, Gold Medal 2008, NBA Championship 2012), to name four.  Manu Ginobli has a Gold Medal (2004) and three NBA Championships (2003, 2005, 2007)  to his credit, and so long as he plays Argentina has a live chance.  He turn  37 in 2014, however, and has been a professional since 1995.