The Peril of the Baseball Wild Card Game

I didn't even realize it until this year with the Toronto Blue Jays. Apparently baseball expanded the playoffs to five teams from four. Previously it was the three division winners and a wild card. Then it seems in 2012 the playoffs were expanded to a second wild card team, which plays the higher wild card team in a 1 game playoff.

The addition of a wild card game definitely changes the dynamics of the playoffs. There is more emphasis now on winning the division and avoiding the jeopardy of a 1 game playoff. Anything can happen in one game.

Right now the Blue Jays are in good shape having swept their division series. But they were in a lot of danger in the wild card round. They were only 1 game better than Baltimore during the season, they were 11-16 in September, and Baltimore had won 2 of 3 off Toronto in Toronto just a week before. I'd say going in this game was pretty much a toss up or maybe with home field Toronto was at best a slight favourite to win this game.

It did get me thinking about the 1, 5, and 7 game series. The wisdom is that a longer series favours the stronger team. How much of a cushion does the 5 and 7 game series provide the better team. With a couple of reasonable assumptions it's not too difficult to actually calculate it.

Suppose x is the chance that the team we are hoping for will win any given game over the other team. So x then is a real number between [0, 1].

We know then that the other team's chance to win any game in the series is (1 - x).

For a 1 game series it's easy. The chance of our team winning the series is x.

For a best 3 out of 5 it is a bit more to think about. Our team can win the series in 3, 4, or 5 games. If you notice that our team always wins the last game, then you don't really care about what happened in the earlier games, you just count how many ways to get to that point before the decisive game. We only have to determine the number of ways to win the series. In any other outcome the other team wins and we lose.

So for a 3 out of 5, the chance of our team winning the series is
f(x) = x³(6x² -15x +10)

In a 4 out of 7, it's the same process, this time we can win in 4, 5, 6, or 7 games. In a 4 of 7, the chance our team wins is
f(x) = x⁴(35 - 84x + 70x² - 20x³)

Remember x is the chance that we win any given game.

With the formulas, we can plug them into a spreadsheet and see how much if any the longer series helps the better team.

This table shows the percentage chance that our team wins the series of that length for a given x.

x	1 game	5 game	7 game
0	0.0	0.0	0.0
0.50	50.0	50.0	50.0
0.55	55.0	59.3	60.8
0.60	60.0	68.3	71.0
0.65	65.0	76.5	80.0
0.70	70.0	83.7	87.4
0.75	75.0	89.6	92.9
0.80	80.0	94.2	96.7
1	100.0	100.0	100.0

So the longer series in fact does help the stronger team and there are fewer upsets. This is especially true when the better team is 60% or more to win a given game. There are a couple of things to note about this table.

Going from a 5 to a 7 game series doesn't help the better team a whole lot. Only about 3 times more per hundred series than they would win a 5 game series. So basically when the NHL and NBA made the first round 7 games it was just greed to have more games, not to help ensure that the better team advanced.

Also we can see why baseball changed the world series from 9 games to 7. The extra games don't materially affect the "discovery" of which team is actually better.

We can quick check the equations with the known cases of x= 0, 1, ½. When x is 0 the team has no chance and f(x) is of course 0. When we plug in x=1 the team is a lock and of course wins every time and the chance to win the series is of course 100%, as they win every game.

When x is one half, then each game is a coin flip. Playing extra games doesn't change anything. The result f(x) for the 1, 5, and 7 game series is exactly 50%.

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From this we can see that there are cases such as x=0, that the chances in a 5 or 7 game series is the same as a 1 game series. that is f(x) = x.


Now for f(x) = x then f(x) - x = 0. For the 3 of 5 series this is

x³(6x² -15x +10) - x = 0

This is a quintic equation so there are 5 roots. I was wondering about the other two roots. Since we know 0, 1, and ½, we can factor them out and with not too much work determine the remaining quadratic. It comes to

x(x - 1)(x - ½)2(3x² -3x -1) = 0

The quadratic formula can be plugged in to yield the other two roots (3 ± √21) / 6. The roots are all symmetrical about x = ½.

These other two roots are in decimal approximately -0.26 and 1.26. So real numbers, but outside the defined probability range [0, 1].

Hillary's deplorables

So Hillary considers half of Donald Trump's supporters to be deplorables. So if 44% of Americans support Trump then basically Hillary regards 22% of Americans with contempt.

Very well, she is entitled to her opinion. One one level, at this point what difference does it make? Those 22% weren't going to vote for her, and nor will any of them vote for her in 2020. So whatever. In that sense she loses nothing by discarding them and speaking her true feelings.

Still it's disappointing. Looking across America, a great and beautiful country. And for her to feel that way about 1 in 5 Americans. A president is supposed to lead all the people, including those who voted for someone else. And she just outright discards 1 in 5. The lack of civility, and open disrespect to 22% of the citizens of that nation is not presidential.

We can only speculate who these 22% deplorables are

• live in flyover country
• make a living working outside, working with tools, or industrial work
• your car is a truck
• gun owner who enjoys hunting and fishing
• shop at wal-mart

Hillary's health from 3 AM to today

Remember 2008 and Hillary's 3 AM phone call ads. In those ads the phone rings at 3 AM, it's some kind of national crisis. But no worries, Hillary is there to respond. Up and alert and ready for action at 3 AM.

I also remember the informal campaign theme song. I am woman hear me roar. It seems such a long time ago now eight years. Recently I chanced to see a 2008 photo of Hillary. She was noticeably thinner and still had blonde hair then. 

Today there's no talk of roaring, late night phone calls or anything about Hillary's vigour and energy. Walking pneumonia and needing considerable assistance getting into the van. Well she is 68, and basically looks and seems 68. Hillary's moment, her pinnacle, really was hear me roar in 2008. Then somehow something happened and here we are today eight years later. This really should be Hillary's sendoff into history after completing her historic term. But instead she slogs on, spurred ahead by her vanity, ego, and oversized sense of entitlement. Remember it was not that long ago she promised she would not seek public office again?

Consider the decline in Hillary's health and vigour between 2008 and today. Then she wants to be president, a very demanding role. Now apply even 4 years of the demands of that office to the projected decline that would have happened anyway in the next 4 years. Doesn't look good or inspire confidence.

Ben Johnson former Windsor Spitfire New Jersey Devils prospect case

I noticed a couple stories go by about a pro hockey player Ben Johnson link  link being convicted of sexual assault.

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The first thing I thought was, what's a 16 year old doing in a bar? I've mentioned before the drinking age is 19 for a reason. Bars are not safe places. Hard people, criminals, and smooth operators frequent them. She should not have been underage drunk in a bar, especially when she was on medication to begin with. Her sister and the others with her should have kept a better eye on her, especially around the more worldly and sophisticated big time OHA players.

Ben Johnson was convicted of a crime so he is responsible for what he did. Still these are crimes of opportunity and it's important to avoid being vulnerable and in situations where bad people can do bad things.

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I was a bit surprised at the line the defence took in this case. They seem to agree that Ben Johnson and the victim were in the bathroom together and some kind of encounter occurred. But to say that it was unsuccessful oral, while offering no credible explanation for the physical evidence seems a hard case to prove.

I'd have thought if the defence was going to agree that an encounter had occurred in the bathroom, they should have just said yes we had sex in the bathroom. Then with the act out of the way, focus on whether there was consent to what they agree happened in that bathroom or not. If there wasn't consent that would mean that Ben Johnson basically followed her to the ladies bathroom without her knowing and pounced. That would have been a tougher burden and a less believable story for the prosecution to sell.

After all, name OHA hockey players are propositioned all the time in bars. Johnson would not have had to just randomly sneak up on an unsuspecting young lady when someone like Johnson would have had opportunity to "pick up" normally in a bar. So it would give credibility to a defence line that she either suggested or at least agreed to the encounter.

With the line the defence took they seemed to put the burden of proof on themselves to prove their story that came across as less believable. It also implicitly validated the prosecutions line that if there was sex in the bathroom then it was criminal. Anyway the defence knows more about the case and the facts then I do so they took the line they did. It was unsuccessful and Ben Johnson was convicted. I think Ben Johnson's chances on appeal aren't bad. The Lyle Howe conviction was overturned.

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The line the Ben Johnson defense took did make me wonder a bit though, if there already is or is very close to some kind of precedent and case law about consent. Specifically this

Is it possible to consent and be too drunk to consent?

You're tipsy in a bar talking to a lady you met that evening who has also been drinking. Out of nowhere she or maybe it was you suggests you sneak into a nearby broom closet for an encounter. Both drunk, you two foolishly agree to this crazy idea and it happens. The next afternoon you have a hangover and a bit fuzzy memory but you're pretty sure it did happen. Could you be arrested by the police if the lady claims she was so extremely drunk and does not remember consenting and in fact was too drunk to consent (even if she actually did in her drunkenness, but does not remember doing)?

If so, that would seem to create a secondary requirement around consent. First is to get consent. Then to somehow verify that the consent is "valid", that the person is not excessively drunk or medicated or whatever. Looking at the Ben Johnson case I'm not sure what that could mean. Carry a pocket breathalyzer and somehow measure if a lady is actually "too drunk" to consent? Johnson was not a doctor and could hardly have known about factors such as the medicines she was taking before hitting the bar. Also in a bar a man typically would be drinking himself so is hardly qualified to determine if someone else who has given consent is actually too drunk, medicated, etc. to be capable to give valid consent.

If I get a chance I should ask a lawyer who knows about that "too drunk" consent where a person has become voluntarily drunk/high/medicated by their own actions and if there is a thing such as "invalid" consent. This is outside of say a drink being spiked unknown to the victim, that is of course invalid consent and a crime. For guys in bars, a wise rule for our times is to avoid being excessively drunk. Avoid encounters out of bars with ladies you just met who you do not know.

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I know in other situations "I was too drunk. I don't remember" doesn't hold. You're still responsible. For example if you drive drunk and wrap your car around a tree you will still be convicted of drunk driving. A judge will not accept that you were too intoxicated to "agree" to drive the car, and you have no memory of driving it or the accident. Whether you remember it happening or not you are still responsible for your decisions and actions while drunk though you may regret what happened.

Submission by Michel Houellebecq

Continuing on the theme of French culture I read Submission. Another title I'd heard of here and there and had been meaning to read. After a short wait it appeared at the library. It was pretty cool of the library with Camp of the Saints. They didn't have it but special borrowed it from a university. I hadn't even asked them to to that. +1 for Halifax regional library.

Anyway Submission is modern, published in 2015. So there's Internet and all that. And lots of French culture. Delicious food, fine wine, beautiful architecture. The author Houellebecq describes the classic French culture in an inviting way. It made me want to go to France and take in the culture firsthand. oh well, perhaps someday anything is possible.

The protagonist is a mid 40s tenured literature professor in Paris. His specialty is Huysmans, a 19th century French literary figure I personally have never read and know nothing about. The professor is tellingly unmarried and childless. He has something of a love interest, Miriam, a graduate student about 20 years his junior. Miriam is Jewish and decides to leave France for Israel in the face of a rising Muslim Brotherhood. In the book Miriam professes her love for the professor, but what she loves is in her words France. The professor is, France. The literature, the cheese, the meats, the wine and brandy, the secular humanism.

The author goes on a spiritual journey of his own, learning about Islam and exploring his own post Christian identity, spending time at a monastery. I did find a really interesting passage in the book defending polygamy that made me think. The argument is science-based, natural selection. The most successful males would naturally attract more female mates who would want to settle with him, even if he has one or more wives already. If this leaves the less successful males unattached and without children then that's the market, natural selection, which is consistent with nature. It was certainly a thought provoking argument. I'd never thought of polygamy that way I must say.

It was a good book. I recommend it. I think there are more themes in this book the author is getting at that I likely missed. So that makes it interesting as well. It would be cool to discuss the book with other readers.

The Camp of the Saints by Jean Raspail

I finished another book. I'd had Camp of the Saints on my list for some time. It was an interesting book. I'm glad I read it. I found the ending satisfying.

The book is about a group of about 1 million refugees from Calcutta who board a ramshackle flotilla of 99 boats and make their way to Europe. After a long journey they eventually land in the beautiful south of France on the Mediterranean.

At times I found it remarkable that this book was written in 1973. Considering current events and the voluntary mass migration from the Middle East and Africa into Europe. Life imitates art and a number of events in recent months have unfolded pretty similar to in this book. The author touches a number of themes including demographic decline, and the erosion from within of Western confidence.

I gained an appreciation of French culture and food from this book. It would be cool to go to France some day and experience it firsthand.