LogFAQs > #935400460

Greetings! This topic is a new project I've made that should be interesting to all of you stat nerds.

This idea came up about a week ago, when I saw people discussing the need to take risks and avoid making their bracket too close to the cookie/chalk, and "get away from the pack". WHile that is usually seem as common board knowledge, I wondered if it actually held true in practice or if it was just a cultural thing that didn't actually increase an user's chance of winning. Then I realized I could investigate the results of the Guru Contests, since those almost always come with the risks for each player calculated, and see if I could find some pattern that justifies, or denies, the pursue for risks among bracket makers.

In case you don't know, a "risk" is when you make a pick that goes against the board consensus. If most people take Link to beat Cloud, and you take Cloud, that's a risk. You can find out how many risks you took, during the contest, by checking the Guru page. Before the contest, you can do it by counting your risks in the Board Odds Project. Now let's move on.

Objective: to find out if there is a correlation between number of risks taken and bracket score, or chance of ending in 1st place. If there is, figure out the optimal number of risks to take to maximize one's Guru winning chances.

Hypotheses:

1) Following the cookie is good. People who follow the board consensus tend to score high compared to most of the board. People who make tons of risks tend to finish far away from the first place. The board knows their stuff, after all.

2) If you are close enough to the cookie, it doesn't matter how many risks you take, because each individual pick is not more or less likely to get matches right than the cookie pick.

3) However (and this point denies #2 to an extent), there is the matter of bracket eliminations. If your pick is different enough from the cookie, you get a little more room to make mistakes without being eliminated by another bracket who was too similar to yours but didn't make that specific mistake. If you are almost identical to the cookie, you might not get that room, as there will be multiple people to capitalize from your mistakes. In this sense, while the cookie is not more or less likely to be 100% right than any other random bracket, it is less likely to score more points if it gets a few things wrong.

To test those hypoteses, I put all the rankings from the 12 guru contests onto a spreadsheeet, as well as each players' respective scores, and number of risks taken. Special thanks to @Ngamer64 for providing me with data on Best Series Ever, which allowed me to calculate its risks myself since those weren't in the guru site.



The first two lines present the total number of picks each user had to make, and the maximum number of points someone could make in each contest. Winner Risks shows how many risks each guru winner made, and the following line calculates its % on Total Choices, in order to compare different-sized contests. Average Risks gives you the average of risks taken for all users. Finally, Winner/Average compares the winner's risk taking to the rest of the field.

Looking at Winner Risks (%), we can see most guru winners take a number of risks in the 10-20% range, which seems to be a trend. The average for all contests is 14%.

There are three major outliers: Years, with 3%, Rivals, with 6%, and Characters 2008, with 29%. The first two were gimmicky contests that probably explain the higher level of chalkiness. Personally, I was here for Years, and I remember there were very few debated matches at all, so there just weren't many viable risks to take. Rivals was probably a similar case.

2008 is a weirder case, with the winner taking a grand total of 36 risks. It gets wrider when you look at the ranking, and realize the 2nd place also took a huge number of risks (37), but from the 3rd place onwards, the gurus took risks closer to the global average, although if you keep going down, a lot of brackets above 20% can be seen. It's hard to say if there is some meaning to this or if it's some statistical anomaly. If I recall correctly, 2008 isn't exactly known as a wacky contest, since it ended with a Link win and had no major rallies. Its counterparts in the 4-ways format, Characters 07 and Games 09, had their winners take 18% and 13%, respectively, so I'm not sure if it's the format either (though Characters 13, which was 3-ways, had a rate of 20%, which suggests multi-way contests favor risk takers a little more than the average, if you ignore Games 09).

The lack of gurus going below 9% except for those two gimmicky mini-contests suggests there is an optimal floor to be pursed, which gives strength to the Hypothesis #3 I outlined in the beginning. But then I decided to compare the winner risks to the average guru risks and the results were... not very meaningful. It seems the ratio between the winner and the average risks is all over the place, and the average of the averages gave me 16%, which is not much different from the 14% of the winners. All of this suggests a lack of correlation between risks and bracket performance.

So I decided to dig deeper. I put all the guru picks on graphs, to see if there were any visible trends.

Note: the graphs below don't actually show every single bracket. Each point corresponds to 7 brackets, with their values averaged. This is to make the lines easier to see, but does hide some points, most notably the guru winners. I believe this level of smoothness did not compromise the results very much, as long as you use it along with the table above.



The values for both bracket score and risks are averaged to each contest's available points, and total picks.

First, we can see a common trend where each graph starts at a high point, then drops down. This confirms Hypothesis #1: people who take too many risks lose. But, after you reach the top part of the guru rankings, the trend becomes less pronounced. That usually seems to hapen below the 20% risk mark.

For Series 06, there is a large number of people with similar risk levels, then it goes down, but then the winner then spikes again to 19%.

For Chars 06, most of the field has risks below 10%, but when you get to the top 3, they go above that mark.

Chars 07 has a number of risks actually above 20% in most of the list, stopping at 18% in the 1st place. The 2nd place, btw, had a whopping 29% risks, so this came close to being a very different story. But in the end, the win went to the one who stopped below 20