12-05-26 Once in many lifetimes?

How do you calculate odds for something that only one instance is known to have occurred?

A few days ago, a fan at a baseball game caught two home run balls hit by consecutive batters, as has been widely reported.

Calib Lloyd’s amazing day at the Cincinnati Reds’ game earlier this week had me wondering what the odds were, but there were no mentions that I could find of anyone else having this happen.

That does not mean we cannot give an estimate of the likelihood of the event, it just suggests that the estimate will be lousy.  Anyway here’s my take:

There are 2430 regular season games per season, and maybe ≈5,000 seats or so in the outfield, and each team averages roughly ≈1 home run/game.  Last year it was .94 HR/team/game, whereas in 2000, the steroids era, it was 1.17 (STATS LLC).  Then, using Poisson to inform us the likelihood of various numbers of home runs by a team in a game is simple.

There are about 40 plate appearances per team per game (baseballgurus.com). A little bit of math tell us the number of consecutive home runs in a game per team would be about 0.013.

We guess the odds of a ball being caught by someone is ≈0.8, since some leave the stadium and some land in the bullpens or in the area in center field where there are no seats.

Thus, in a given game, the odds that this might happen to someone is about

So, in a hundred years of baseball (yes, there were formerly fewer games per year, but this will only affect the calculations by a factor of two at most probably) this would happen roughly once.  That it would happen to you at a game would be about 1.5 billion to 1.

Of course I am not the only one to ask this question, so we can compare it to others’ calculations:

http://www.morethanafan.net/2012/05/24/off-base-percentage-what-are-the-odds/

Here, using an slightly higher average number of home runs per game and a different methodology gave about twice the likelihood of its occurance.  That is not atypical for this type of calculation, and either calculation does suggest that there is a good chance that Caleb Lloyd is the only person to ever catch home runs hit by consecutive batters.

12-05-13 Is a Pythagorean Triple

That is all.  Cheers.

12-05-13 Atypical City

After an exciting season in the Premier League (English Football/Soccer), Manchester City F.C. stood atop the standings and was looking today for a first league championship since 1968.  Some background information is necessary to set the stage.

After the Chicago Cubs, Manchester City might be the world’s next most famous cursed team.  The label fans and the media have attached to the continuous heartbreak this team has offered its fans for 132 years is “Typical City”. 

Lists of their failures are available elsewhere, but the important thing is that they have suffered the same confluence of a rabid fan base, historically bad leadership and painfully bad luck that the Cubs have endured.  To make matters worse, Manchester United is their crosstown rival, and is of course one of the world’s most successful teams.  Thus, a good parallel might be if Cubs fans had to watch the White Sox in the World Series almost every year.

The team has been known for its quirkiness.  Its anthem is the not-terribly-inspiring “Blue Moon”, its mascot is a pair of space aliens from the moon, and fans bring large inflatables of animals or fruits (particularly bananas).  They wear the colors of AC Milan as their away uniform simply because a random assistant manager (Malcolm Allison) in the midcentury decided they should wear the uniforms of a good team.  They also have a famously good-natured fan-base, and have won two UEFA Fair-Play first-place recognitions (a feat matched by only Viking FK of Norway).

Today, Manchester City and their rivals Manchester United were tied for the league lead with the final game to be played today.  City held the tiebreak over United so they required only a win in their game today.  Manchester City was playing today against Queen’s Park Rangers (QPR).  City was playing at home, where in the first 18 games of the season they had won 17, drawn 1 and lost none.  QPR in 18 away games had won 3, drawn 2 and lost 13.

After a perfunctory first half, Manchester City led 1-0, having totally dominated possession as QPR played for a draw until City scored shortly before halftime.  With the title all but clinched, the stage was now set…for Typical City.

City’s important playmaker Yaya Toure left the game with a hamstring injury shortly after helping cause the first-half goal.  Within three minutes of the second half, QPR scored to tie the game.  It is important to note that with a draw, QPR could clinch a place in next year’s league (which keeps the top 17 teams of 20 and the other three are replaced by the best teams in the league one level down). 

It was thus bizarre that Joey Barton (QPR captain, has a hot temper and has been ejected several times this season) got himself deservedly ejected for a violent elbowing of a City player during a stoppage of play.  Even more bizarrely, after receiving the ejection he attacked another City player, and continued his one-man brawl until he was literally removed from the pitch by stadium security.  One cannot make up this stuff.

So City now had an extra player, and in typical City fashion gave up a silly goal to a QPR team with no remaining forwards, as the stunned crowd could only gasp in horror.  Then, City, despite continual attacks, could not score as the QPR keeper made repeated amazing saves, and needed two goals.

Now it is important to note that the Premier League plays the final games of the season simultaneously for all teams, so that no team knows more about what result it needs (particularly if a draw is sufficient) compared to the other teams.  It is also important to note that due to Barton’s antics, the City-QPR game was running behind the other games.  Particularly important was the Manchester United-Sunderland game (which United won comfortably) and the Bolton-Stoke game, in which Bolton needed a win plus a QPR loss to overtake QPR and steal their place for next season.  Bolton actually held the lead in their game until Stoke managed a draw in the last 15 minutes of the game, but with five minutes left in the City game, the Bolton game and the United games were approaching their conclusions, and City fans were resigned to perhaps the worst Typical City in 50 years.

Then, City scored on its 18th (!) corner of the game, and City had life, and 3.5 minutes to score another.  A minute later the QPR fans and bench saw the official result of the Bolton draw, and burst into wild cheers as they were now safe in the top 17.  Also, several of the QPR players who had been defending so resolutely and learned this and, between their exhaustion and satisfaction, lost concentration (one can clearly see several QPR players standing around in the replay!) and MCFC’s Sergio Aguero received a great pass from Mario Balotelli and scored.

So, City won the game and stole the championship from their arch-rivals even as United’s players and fans stood on the pitch at Sunderland waiting for the trophy ceremony.  I have been a Manchester City fan for a long time, admittedly, but I think regardless of their team such an incredible story is worth telling.  For once, City fans experience euphoria, while the United fans got to experience Typical City instead.

12-05-12 Technology Marches On (or Something)

This is a few days old, but you cannot beat this for an example of business logic and cost-cutting taken to the extreme:

One might imagine the bad press a bank would receive if someone walked into a bank and was told that making a deposit was impossible.  Apparently, it is happening, at least in Norway.

The web address tells it all:

http://www.thelocal.no/page/view/bank-tells-customer-we-dont-take-cash-anymore

The 98-branch Nordea currently handles cash at only nine of its branches.  However, one can still make withdrawals using ATMs, just not deposits.  That said, I doubt many people will would want to deposit money in such a bank.

12-05-09 You must be present to win: The Republican Primary continues its absurdity

Earlier I described how the primary/caucus process was broken in that it provided vastly different levels of influence to different populations.  Following on that theme:

As of May, the Republican primary process has basically been over for more than a month.  Despite this, the process is technically continuing, including the district-level caucuses that are the second stage of determining state delegates in many states.  This of course includes states whose initial votes have already come and gone months ago.  The problem is that nobody cares about the process at this point.  If an insufficient number of Romney supporters show up to formally nominate the actual delegates for the convention, they still need to nominate delegates somehow, and Ron Paul’s fervent supporters have been quite willing to shoulder that responsibility.

Consider the following states have had two-stage caucus processes, and the difference in the timing would not be meaningful except that Ron Paul is still determined to collect as many delegates as possible.  Here are his results so far in several states:

State	Ron Paul’s Statewide Result (%)	Delegates	Delegate Proportion (%)
Maine	18	21 of 24	88
Massachusetts*	10	16 of 27 (11 remain to be allocated)	59
Colorado	12	17 of 33	51
Nevada**	19	22 of 28	79
Minnesota	27	20 of 24 (16 remain to be allocated)	83
Louisiana	6	17 of 33 (13 remain to be allocated)	51
*In Massachusetts, the delegates are obligated by law to vote on the first ballot according to results of the primary, but may participate as delegates of the candidate of their choice for all other purposes, including nomination of a VP candidate.  Paul has 0 votes on the first ballot. ** In Nevada, the delegates are obligated by law to vote on the first ballot according to results of the primary, but may participate as delegates of the candidate of their choice for all other purposes, including nomination of a VP candidate.  Paul has 8 votes on the first ballot.

Several other states are operating under the same rules and will likely have similar results to varying degrees, including Iowa, Alaska, Pennsylvania and Rhode Island.

While this system is not going to keep Romney from being nominated, it may give Paul some leverage at the convention.  It may also lead to a situation where Romney looks out on a sea of people waving Paul banners as he accepts his nomination, which could only be seen as embarrassing.