Page 3-4 Playoff: Sweden and Norway: do red rocks win more often than yellow rocks?

Preparing for today's game, I looked at the scoreboard and saw that Norway has the hammer. I couldn't figure out what was going on, why Sweden didn't have the hammer, so I asked the statisticians for CCA what was going on.

I turns out Sweden had the choice. But they decided they wanted the red rocks more than they wanted the hammer. Huh? Well, we were informed, the red rocks win more.

Alan and I were skeptical. So the statisticians ran off the data for us. No foolin' What a shock: in the 66 games of the round robin, 43 games were won with the red rocks and 23 games were won with yellow rocks! I don't think the powerful teams had the red rocks more often, so it is quite likely that this is both a statistically significant difference and, more importantly, an important difference for making the decision.

I'm astounded. I would have thought that giving up the hammer would be foolish and that preference for red rocks is just a silly superstition. I'm much more confused, now, and much more willing to look into what is going on.

We need a SHRCC grant to study this question!!!

[update] The father of Kraupp (3rd, SW) is sitting next to us on the media bench. He says that's not at all what happened. His explanation is that SW and NO were tied at 7-4 in the round robinm and because NO defeated SW in their round robin game, NO won the hammer, so then SW chose the red rocks.

But that doesn't refute the result concerning red rocks. We still need the grant!

Updating Doc's Attendance Model after Draw #10

Here are the data following the 10th Draw at the 2011 Men's World Curling Championship:

Drw PdAtt 50-50 Cumul C 8am?
#01 05595 10935 05595 *
#02 05748 10515 11343 *
#03 03948 01818 15219 - *
#04 05633 10765 20924 *
#05 04497 05635 25421
#06 02513 02280 27934 * *
#07 02585 03318 30519
#08 04185 09470 34704 *
#09 02431 01638 37135 - *
#10 03505 06173 40640 *


The implication from the 50-50 prize size is that there were slightly over 3000 fans in the arena this afternoon. It didn't look that way to me, but it might have been close. Also, I expect some of the fans spent a good deal of time in "Keith's Patch", a huge party room with music, alcohol sales, food, and visits from the Saskatchewan RoughRiders expected between draws. So maybe there were more people who bought 50-50 tickets but who didn't show up in the arena.

More likely, there are many omitted variables that are important, and the relationship between the 50-50 prize and actual attendance isn't perfectly linear.

We definitely need a grant to estimate the full model.

Updating Doc's Attendance Model

As of now [updated below to include the official stats from the ninth draw] the data are as follows:

Drw PdAtt 50-50 Cumul C 8am?
#01 05595 10935 05595 *
#02 05748 10515 11343 *
#03 03948 01818 15219 - *
#04 05633 10765 20924 *
#05 04497 05635 25421
#06 02513 02280 27934 * *
#07 02585 03318 30519
#08 04185 09470 34704 *
#09 02431 01638 37135 - *

The model would imply there were about 800 - 850 fans here this morning (not counting the students in the upper deck, who, presumably would not be allowed to purchase 50-50 tickets), no matter what the paid attendance figures are. As I looked around the arena, it looked as if more folks arrived as the draw proceded, and so that figure may not be far off. I expect many of them had day passes or week-long passes and didn't bother to show up until later in the draw. Too bad. They missed some pretty exciting curling.

Let's face it: morning draws are not big draws even if Canada is playing; but they're even worse when Canada is NOT playing. Time for the CCA to plan to sell or give more tickets to school classes for draws like these in the future.

How Many People Are Attending the 2011 Men's Worlds?

The Brandt Arena in Regina seems like an ideal place to host a major curling tournament championship. Saskatchewan is the heart of prairie curling; curling is the official sport of the province; and Amber Holland from here was the silver medalist just a few weeks ago at the women's world championship.

So how has the attendance been?

Through draw seven, paid attendance has been a bit over 30,000. But that's paid attendance, not actual attendance. Her are the data so far:

Drw PdAtt 50-50 Cumul C 8am?
#01 05595 10935 05595 *
#02 05748 10515 11343 *
#03 03948 01818 15219 - *
#04 05633 10765 20924 *
#05 04497 05635 25421
#06 02513 02280 27934 * *
#07 02585 03318 30519

The Paid Attendance (PdAtt) and the Cumulative Paid Attendance (Cumul) are official figures. "C" indicates whether Canada was playing, and 8am? indicates whether the game was an early morning game.

As you can see, more fans come when Canada is playing, but even then, they would rather not come to the early morning draws.

The column of interest for this post is the size of the prize for the 50-50 prizes held during each draw. 50-50 contests are simple: people buy tickets and at the end, whoever's ticket is drawn wins half the total amount paid for the tickets and the sponsor (ordinarily a charity or non-profit organization) keeps the other half. A 50-50 contest is held after each draw.

In the interest of honesty and transparency, the prize sizes, along with the names of the winners, are posted after each contest, making these data readily available for those of us who might want to look at them.

My hypothesis in this posting is that the size of the 50-50 prize provides a fairly good indication of the actual attendance at each of the draws (games). If the tendency to buy 50-50 tickets does not vary much with the types of people who attend games in the morning vs. in the evening, or for games featuring Canada vs. those draws when Canada is not playing, then the size of the 50-50 prize should be a good measure.

But maybe people who attend curling games in the morning are less likely to buy 50-50 tickets (you couldn't prove that by me, given the number of tickets I have seen sold at charity breakfasts). And maybe fans from other countries are less likely to buy 50-50 tickets AND are likely to make up a larger portion of the audience when Canada is not playing.

With these caveats in mind, and with the rough estimate I made on Sunday morning that there were no more than 1000 fans in the arena, I propose the following proxy method for estimating actual attendance at each draw:

Actual Attendance = 0.5 x (50-50 prize)

In words, take half trhe 50-50 prize and that will tell you roughly the number fannies in the seats.

I think we need a SHRCC grant to hire people to actually do the counts to test this hypothesis. 8-)

Margins and Statistics

In a recent posting at Econlog, my former student David Henderson writes about "at the margin" and the use of statistics. He's writing about the NCAA basketball tournament but everything he says applies equally to curling (see this, where I become mired in pedantry). David writes:

The economic principal is the idea that the margin matters. Think of how some of the outcomes would have changed had a few little things changed. I'm thinking, for example, of the close University of Arizona game against U Conn. (U Conn won 65-63.) What if Arizona's star, Derrick Williams, hadn't been called for just one touch foul? Then he would have been on the floor longer and Arizona might have won. Or, in some of the other games, what if two of a team's 3-point attempts had been a few inches shorter or longer and gone in? Again a different outcome. Margins can matter a lot. [EE: or in curling think how often an eighth of an inch one way or another affects the outcome]

And the statistical principle, which is related to the above, is how much randomness there is. One team can be a little off its game for most of a half and, although it is a better team generally than the team it's playing against, this can make a difference. There's always randomness. So much that happens in the world is random. So the moral of the story is that the degree of certainty otherwise-intelligent people have about their bracket choices is just not justified.

A related moral is that when you play a lot of games and win enough to get to be one of the 20 or so top picks in the choice of 68 teams, you've done a good job. What happens from then on is a mix of skill and randomness.

Gold Medal Game, Canada vs. Sweden: Intermission

Just to make clear: I see the statistics for the players and teams as indicative but not compelling. In stat-speak, and something I tried to say differently in my earlier postings, there's a pretty big variance around the averages, meaning pretty much anything can happen in any game or end. As I said, the stats are indicative of what might happen, and obviously I love looking at the stats, but the variance is just too high to have much confidence in using the stats to make predictions. In stat speak, the confidence intervals are pretty large.

Let me also note that the statistics for this game are consistent with the observations that Alan and I have been making. There seemed to have been a lot of misses, and the curling percentages are 68% for Sweden, and 71% for Canada. Both leads are curling only in the 70s, and the middles are all in the 60s!

So after all the action so far, Canada and Sweden are tied, but now Canada has the hammer.

The Dangers of Generalizing from Small Samples

Okay, okay. I was REALLY wrong this year. I saw a few draws early in the 2010 Scott Tournament of Hearts in which both PEI and Manitoba did not look all that good. I generalized from what I saw, and that led me to think these teams aren't very good.

Well those teams did pretty well. PEI ranked number 1 after the round robin, and Manitoba made it into a tie-breaker in the playoffs.

The thing I did get right, though yesterday I'd have thought even this was wrong, was the statement that Team Canada and the BC rink were both strong contenders.

Judging from their records mid-tournament, who'd have thought BC would place third and avoid a tie-breaker? Who'd have thought Team Canada would place 2nd and make the 1-2 page playoff? Probably lots of you readers. I was pretty skeptical, though.

Anyway, it will be fun. Unfortunately I'll have to miss a bunch of the draws: curling myself this evening and doing some acting for a film tomorrow afternoon. But I'll be checking scores as often as possible!