Hockey

As some of you may or may not have known, I've been punching numbers into a spreadsheet recently to try to analyze some of this NHL madness that's been going on. Now that the LA Kings have officially won the Cup, I'd like to take a quick moment to celebrate, because my model has said they would win ever since April 28th (nearly 6 weeks ago).

Yay!

Naturally some of you should be wondering, "Is this a fluke? Is he onto something or is this just luck?" My only response to that is that I believe that my model is indeed better than chance, but I'm not quite positive if the difference is enough to be particularly significant.

Now I'm going to show you some pretty pictures to confuse you:

This was a visual representation of my day-to-day analysis results. The height of each bar (y-axis) represents that team's chance of winning for a given time (x-axis). At the beginning of the playoffs I had the Blues picked as the most likely winners (20.32% chance) with the Kings as the second-most likely (13.54%). Once it looked less likely that the Blues would beat the Coyotes, however, the model began to side more favorably towards the Kings, and never looked back.

Unfortunately the model was a little off the mark for the Devils - they were only ranked as 6th most likely to win from the Eastern division. Of course, the most likely Eastern team (Rangers) did make it pretty close, I suppose. Interesting to note, though, is that the whole way throughout this analysis teams from the West were favored over teams from the East.

So I picked the right team from the west and the wrong team from the east - does that make this right or wrong? Well, that's where math comes in. Technically I got 9/15 series predictions right, which is just better than what you'd expect if you were guessing randomly.

A better way of looking at this is with a statistic called a p-value, which is a statistical test for how likely it is that your model explains the results. In a basic example, a p-value test could be used to check if a coin is fair or not by flipping it 10 times. Say we get 9 heads - the chance of a fair coin getting 9 more more heads is 1.07%, which is quite unlikely. Depending on how sure you want to be, this is around the point where scientists would reject the hypothesis that the coin is fair. This 1.07% is the p-value for the test - the chance that a null hypothesis could explain the data. Commonly a p-value of less 5% is enough to reject a hypothesis (in this case, the hypothesis that the coin is fair).

P-values don't tell you, though, what the chance is that a model *is* correct, but in general they are a good indicator for how strong a model is. A model that is giving precisely the same output as expected (on a very large number of games) would expect a perfect score of 0.5.

Check out this graph of p-values from my model:

Using similar calculations as with the p-value, these are scores for my model over the most recent playoffs (86 games). I broke each game down into the chance for the home team to win in regular time, the chance the visitors would win in regular time, and the chance of going into overtime. The lines are the results from my model, whereas the points are what would be expected from just chance.

In general, my model's predictions throughout a game got better as the game progressed (yay!), and my p-value scores were higher than chance in terms of which team would win in regular time. On the other hand, when looking at just which team would win any given game (disregarding overtime), my model scored 0.3499, whereas chance would give only 0.2253. I am incredibly please with this result, as it suggests my model may in fact be significantly more likely to be correct than just randomly guessing.

However, my model severely under-predicted the frequency of games going into overtime (which was higher than average anyway, resulting in a relatively low score for chance too). These results are going to be used in my infinitely more massive iteration of this spreadsheet next season, which is going to track the chances of winning the playoffs throughout the regular season too! Stay tuned!!

Electability

Hey there!

Another short post just to keep this blog active-ish. Please enjoy!

Using the formula I developed from analyzing last election's results, I've come up with an electability index of sorts for members of the current Students' Council at the University of Alberta. It's never too early or too late to think about running for an executive position, right?

Most Electable Members of Council:
Petros Kusmu: 0.903
Colten Yamagishi: 0.793
Saadiq Sumar: 0.658
Joshua Le: 0.616
Andy Cheema: 0.586
Brent Kelly: 0.521
Navneet Khinda: 0.478

Least Electable Members of Council:
Wen Yu Liang: 0.137
Leon Milner: 0.189
Cory Hodgson: 0.197
Tim Holt: 0.199

Now for those of you on the "least electable" list, don't despair - the formula depends largely on years spent on Council, and Dustin Chelen famously broke the mold last year.

Happy election planning!

A small distinction...

Some people seem confused about this. Here's a quick example:

This is what democracy looks like:

This is a fire:

Now you know!

Open Letter to Elections Alberta

Dear Mr. Fjeldheim,

I had the privilege today of voting in the Alberta Elections at an advanced poll in Edmonton-Whitemud. I was very pleased to hear that the voter turnout in the advanced polls had already eclipsed the results from last year, and I am impressed as always with the quantity and experience of volunteers that worked at the poll.

I was disappointed, though, when I saw the following sign at the polling station that laid out the conditions for voter eligibility:

Though the quality of the photo is poor, the instructions are listed in six languages. I recognized English, German, and Spanish, but I was unfamiliar with the other three (though I believe one to be mandarin). Notably absent from the poster was French.

According to the 2006 Census of Canada, the most common mother tongues in Alberta are as follows:

• English: 80%
• Various Chinese Languages: 3.0%
• German: 2.6%
• French: 1.9%
• Punjabi: 1.1%
• Tagalog: 0.92%
• Ukrainian: 0.91%
• Spanish: 0.90%

 Though I understand that at some point the number of languages included on informational posters must be limited for practicality, I must admit that I am confused and upset that French, which is both the fourth most common language in Alberta, and more importantly an official language of Canada, is not included on informational posters present at voting sites. As far as I can tell the inclusion or exclusion of languages from this poster appears to be arbitrary for languages other than the three most common.

I hope that you address these concerns in future elections.

Thank you very much, and I wish you a smooth election day on Monday.

Michael Ross
April 21, 2012

SU Elections Aftermath: Part 2

If you've actually bothered to read this, I must applaud you. I wouldn't have. Trust me. This is going to be more stats about the SU, but less interesting than last time. Yippee.

With that lovely disclaimer aside, check this out:

This first graphs I've lovingly whipped up is for SU elections turnout. RIVETING. These are the results of the voter turnout by year for the last three years:


Ooh. Aah. Exciting! What's REALLY interesting, though, is how similar the 2010 and 2012 results were. I mean, they're almost identical. That prompted me to take a look at the hour-by-hour results for 2011 in a more normalized capacity, and this is what I got:


This is way cooler, because it turns out that all three years follow a very similar pattern, regardless of final voter turnout or campaigning restrictions on voting days. An R2 value of 0.994 suggests that if you were to know the turnout by the afternoon of the first day of voting, you could be fairly confident in a final prediction for voter turnout. Nifty!

What do these graphs say? You'd think that I'd be sitting on at least two thousand words of awesome explanations and analyses (two pictures at 1,000 each, right?). I guess one thing that's easily noted is that two-thirds to three-quarters of students vote within the first day, and (surprisingly?) almost nobody votes between 2 and 5 am on the second day. What *is* surprisingly is that the rate of voters per hour stays fairly constant leading up to the close of voting on the second day, and that it isn't significantly lower than the voting rate on the afternoon of the first day. I would have anticipated that it would plateau before the end of voting as everyone who wanted to would have already voted, but instead we have ~150-200 people voting each hour leading right up until the end of the election. In fact, I would suggest that up to another couple hundred votes could be obtained simply by keeping the election open a bit longer.

Interesting indeed.

SU Elections Aftermath

Well that was fun!

On the off chance you don't already know, the winners of the 2012 SU Executive and Board of Governors Elections are as follows:

• President: Colten Yamagishi
• Vice President Operations and Finance: Andy Cheema
• Vice President External: Petros Kusmu
• Vice President Academic: Dustin Chelen
• Vice President Student Life: Saadiq Sumar
• Undergraduate Board of Governors Representative: Brent Kelly

This is of course pending the results of a few DIE Board rulings, with one in particular against a candidate who won one of the races. Stay tuned!

That aside, I've found an interesting feature from this election. I was interested in how easily someone could actually predict the nature of an election, and what the effect of campaigning was on the outcome. So, naturally, I decided to look into it.

I picked a few parameters that are easily quantifiable and can be determined before the votes are all cast. My original list of parameters included amount of money spent on campaign, amount of money spent on penalties, number of years on council, and number of personal friends on Facebook. Naturally there are many other parameters that are important to a campaign that cannot be accurately quantified or known beforehand, such as number of hands shaken, classes visited, or babies kissed, but I thought these four parameters would be fairly important and were the easiest for me to find.

I then compared these four parameters to the percentage of vote obtained by each candidate on the first round (even though our system isn't first-past-the-post, every candidate in this election who was leading in the first round went on to win their election). I wasn't positive if I'd get any sort of correlation, but hey - sometimes you just have to throw stuff against a wall and see what sticks (that's a completely legitimate form of science, by the way).

Surprisingly, though, there was a correlation. A pretty decent one too - I got an R2 value of 0.914 (where 1.0 is perfect fit). In fact, the data I input can be summed up in a nifty little formula:

First Round Votes= (12.7%)*C+(11.2%)*Fb+(54.4%)*B+(2.8%)

In this equation, C is a normalized value for number of years on Students' Council, Fb is a normalized value for number of Facebook friends, and B was a normalized value for the relative amount of money spent on campaign materials.

At this point I would like to remind you that correlation does not imply causation, so take what I'm about to say with a grain of salt. I'm not trying to present this as a fact or the truth, simply an interesting finding.

This formula suggests a few things. First of all, it suggests that the number of penalties taken by a candidate has very little impact on how well they do in the election (unless, of course, they get so many they're disqualified). This is interesting because penalties are supposed to offset relative gains for a candidate, and so one might almost expect a candidate with lots of penalties to have an edge. It would appear, though, that for these elections that wasn't the case.

Secondly, having more Facebook friends than your opponents is fairly important in an election. A plausible explanation for this is two-fold: having lots of Facebook friends suggests that a candidate is some combination of interested in social media, and popular and/or out-going. Though of course the number of friends isn't necessarily proportional to presence on campus, it has become increasingly apparent that social media is important in races of all sorts, and so it is not unrealistic to expect that number of Facebook friends plays a role.

Thirdly, having been on Students' Council is slightly more important than social media presence. Cool. I'm not particularly surprised that having been on Council helps people out in Students' Union elections, though I could see that if this had been a different set of candidates in a different set of elections, with fewer returning executives and a stronger pure Lister group, this factor could change quite a bit.

Last observation from this formula is that how much you spent on campaigning from your budget plays a huge role in how well you do. Some candidates spent significantly less than others in their races (for instance, Adam spent less than 30% of all campaign materials in the VPX race, resulting in Dorothy and Petros splitting the rest), and it (apparently) cost them big-time. Moral of the story is go big or go home when it comes to materials, I guess.

Of course, this model isn't perfect:

Great predictions:
Saadiq Sumar: 81.18% (Real: 80.60%)
Andy Cheema: 33.04% (Real: 31.74%)
Jessica Nguyen: 19.93% (Real: 21.17%)

Really bad predictions:
Murtaza Jamaly: 18.28% (Real: 9.94%)
Farid Iskandar: 26.41% (Real: 19.68%)
Mike McGinn: 18.38% (Real: 27.88%)

But hey, what can you do?

Voting

Voting is important.

When your country/province/city/university/bridge club holds an election, they are asking for you to determine who is going to be representing you for the next term. The Governors at the Board are going to be told that the two undergraduates that the U of A student body sends to them were elected from the masses to represent the masses, and so it's important that you vote for the two that best reflect your opinions.

However, in the Students' Union, we don't use a first past the post system. Instead of saying, "I like candidate A!", you get the option of deciding your second favourite, third favourite, and so on. At some point, you can even rank None of the Above as if they were a candidate! The options are limitless!

The long-lasting problem with systems like this, though, is that most people simply will not understand how their vote is counted. It's a fact that all voting systems can be played strategically, and really die-hard supporters will want to know the ins and outs of how best to vote in order to guarantee their candidate's success.

Unfortunately, to most people the process works something like this:
It doesn't.

I'm going to talk about four different methods of determining the winner of elections. This post is about to get super fun! Before I do that, though, I want to quickly mention a few of my favorite electoral system criteria that "expert political scientists" have come up with:

Absolute Winner: May seem obvious, but if one candidate gets more than 50% of the votes on the first round, they should win.

Independence of Clones: The election outcome should remain following the addition of an identical candidate with an equal chance of winning.

Condorcet Winner: If a candidate wins a head-to-head competition against every other candidate, that candidate must win the election.

First Past the Post

This one is pretty easy:

Everyone votes.

The person with the most votes wins.

Pros: Dead easy.

Cons: It kinda sucks in terms of figuring out the best candidate. If five people run, you could expect a candidate to win with only slightly more than 20% of the popular vote. Also, it only examines the first choices of voters.

As a voting system, it only satisfies the absolute winner criteria. It fails the independence of clones criteria as vote splitting is a very common issue amongst similar candidates, and it fails the Condorcet criteria because it doesn't even consider the subsequent choices of voters.

Borda Count

Second easiest:

Everyone votes.

Each candidate gets a number of points for each first place vote, a smaller number of points for each second place vote, an even smaller number of points for each third place vote, etc. The candidate with the most votes wins!

Pros: Still pretty easy. It also takes into account the subsequent ranking of candidates by voters, and tends to give a winner that most people are generally ok with (as opposed to FPTP where a majority is likely to have never voted for a winner).

Cons: Fails pretty much every other test in the book. You could have 50.1% of first place votes and still lose if another candidate has a VERY strong second place showing.

Instant Runoff Voting

A little bit more complicated:

20% of students vote (sad fact).

All first-ranked votes are examined. If someone has more than 50%, they win! If they don't, the last-ranked candidate gets kicked off the island, and their second-ranked votes are redistributed to the remaining candidates. This process continues until, at the end of the day, someone finally has more than 50% of the votes (often through borrowed votes from other people).

Pros: Vote-splitting doesn't happen in this method: if one candidate pushing for a waterslide in Quad is expected to get 60%, and another candidate comes forward with the same promise, we're still going to get a waterslide in Quad. This assumes, of course, that people would rank both candidates numbers 1 and 2 on their ballot if they really want that slide. By the time that a winner has been determined, more than half the voters will have indicated in some way that they support that candidate more than anyone else who's left, so a majority will be (begrudgingly, at least) satisfied with the results.

Cons: It can be complicated. If you didn't understand the SU's system before reading this post, you weren't alone. If you don't understand it after reading this post, please tell me and I'll try to make it clearer.

This method satisfies all the above criteria apart form the...

Condorcet Method

Way more complicated:

Everyone votes.

For every possible pair of candidates (that's 10 if there are five candidates in a race), the candidate who is ranked higher more often is declared the winner in that head-to-head contest. If one candidate wins against all the other candidates, then they win the election. If there's a tie in the number of victorious head-to-head contests, then a complicated method based on vote differentials is used to determine the winner.

Pros: It's awesome. It's actually by a mile the coolest way to count votes.

Cons: It takes a while to explain to people, and for large races it basically can't be done by hand.

Now you know! The SU uses an Instant Runoff Voting system for its executive, and a variant iterative IRV system for its council elections. What's especially fun about electoral systems, though, is that different systems often change the results of an election. Take a look at this example:

42 Voters: A, B, C, D
26 Voters: B, C, D, A
15 Voters: C, D, B, A
17 Voters: D, C, B, A
Total voters: 100

What's really fun (and I'll let you do the math) is that the winner of this election depends on the method. First past the post simply says that A should win. A Borda Count or the Condorcet Method would let B win, and an Instant-Runoff Vote would elect candidate D. Go figure, right?

At the end of the day, what I'm trying to say is that the order in which you rank your candidates in this election really does matter.

Stay tuned for an analysis of the election results after they're revealed!