With the usual caveats about sample size (as discussed in the paper), it seems that officials were systematically under-assessed and so carried a lower-than-expected property tax burden.

I don’t think it would. In each of three polls ending 2 October posted on NoDice.ca, the three-party left could take a majority of the popular vote with a fair margin of error in their favour. (The numbers are: 52% left coalition, 37 Conservatives, 9 Bloc; 57, 35, 10; and 54, 36, 9.) Of course, the caveat of distortion from taking the popular vote rather than the riding-by-riding vote applies. The seat projections at NoDice are nearly a month out of date.

So here’s a simple approach: I mapped (in OpenOffice.org Calc) the popular vote for each party, the number of seats, number of seats divided by percentage of the popular vote, and percentage of the popular vote per seat won. (I threw out the Conservatives’ 1993 number, since 2 seats and 16 percent of the popular vote skewed the numbers badly.) I then averaged the Seats/Percentage numbers over the last 5 elections to find the coefficient of the popular vote.

The coefficients are:

BQ:4.18

Conservative (plus Canadian Alliance): 2.76

Liberal:3.92

NDP: 1.52

Based on incumbency advantage, I’m going to arbitrarily adjust the Conservative coefficient upward 50 basis points to 3.26. I’m also going to arbitrarily issue the Greens 5 seats, because their lack of representation makes it impossible to find a coefficient. Thus distributed, I multipled the coefficients by averaged current support based on the 3 polls and rounded. The seats (accounting for 292 seats) are:

BQ: 40

C: 117

L: 97

NDP: 28

Green: 5

Under these numbers, a Liberal/NDP/Green coalition would have 130 seats – not a majority, even of the smaller number of distributed seats, but still more than the Conservatives.

This is NOT A PREDICTION, though. The numbers are utterly lacking in rigour. It was merely meant as a very rough demonstration that the Bloc would not be necessary for a coalition government by the left.

I originally designed this as a measure of anti-quality starts: six runs or more in three or fewer innings, with the team picking up the win nonetheless. There were fourteen of those this year alone (including one by my Favorite Pitcher of All Time, Sidney Ponson). Even Brad Penny had one. In fact, there were 485 instances of just such a thing happening in the history of baseball. Clearly I’m going to need to ratchet up the numbers on this one.

For 8 or more runs, the numbers get a little cleaner. Only 37 this time. There were still two instances in 2008, and John Garland had one last year and one this year. Hmm… looks like Garland may come out the winner of this little contest. Big ups to Sidney Ponson, though, for not having an 8-run, 3-inning game since 2005 (that was back when he was still talented). Sid gets an honorable mention, along with Nate Robertson from this year, for having all 8 runs be earned. (Garland had 8 earned runs but nine total.)

For 9 or more runs, we’ve cut it all the way down to 9 games. The eventual winner here is obvious, but I’d really like to point out how cool Andy Pettitte’s stats were for this game: a game score of 1, and an ERA of 72.00. (I can’t help but think that someone mixed up the two numbers.)

Finally, the winner: Sean Bergman of the San Diego Padres. Ending with an admirable game score of 7, Bergman pitched two innings and two thirds, allowing 10 runs, all of them earned, on seven hits and three walks (meaning that every last baserunner he allowed scored). What’s more, of the eight batters he retired, he struck out six! Once Bergman came out, a parade of relievers came to his rescue, shutting down the Colorado Rockies except for one inning later in the game, and his team rallied to 13 runs to get the win with a five-run 9th inning.

Sean also had a hit that night, wrapping up this installment of the “weirdest line” contest.

That raises the question: just how common an event is Jason’s productivity?

Marquis’ batting line:

J Marquis, P: 3AB, 1R, 1H, 5RBI, 0BB, 0SO

And his pitching line:

J Marquis, W (11-9) 6.2IP, 8H, 4R, 4ER, 4BB, 4SO, 1HR, 4.43 ERA

(From the Baseball-Reference.com box score). Marquis also hit into a fielder’s choice in the 5th that accounted for his 5th RBI.

Grand slams by the pitcher are… well, not common, per se, but they happen with some degree of regularity. The last one was earlier this year, also against the Mets, by King Felix Hernandez of the Seattle Mariners. That was also Hernandez’s first and last at-bat of the 2008 season, giving him the coveted OPS of 5.00. Hernandez also had a sacrifice hit in the game, but didn’t score a runner, leaving him at a paltry 1AB, 1H, 4RBI. Since he pitched 4.2 innings, he also didn’t get the win, although his team did. He’ll have to do better than that to compete with Marquis.

Meanwhile, in 2006, Micah Owings had a 4-for-4 game for the 2007 Diamondbacks as the starting pitcher. Owings had 4 hits and six RBIs, including one home run. He also got the elusive win, pitching 7 innings, 3 hits, 3 runs (all earned), and struck out 7. That left him with an impressive game score of 66. Sadly, Owings’ home run was a leadoff, so it was only a one-RBI strike. Still not quite what we’re looking for.

So, let’s see… We can whittle this down from stats in which the team wins, the pitcher has 1 at-bat and at least 5 RBIs, using starting pitchers. We have to go all the way back to 1977 to find a similar line, with Larry Christenson of the Phillies hitting his grand slam against the Cubs. In the top of the second, Christenson sacrificed Bob Boone in, and then hit his grand slam in the top of the 7th. Christenson pitched 7 innings, giving him the all-important win. After facing two batters in the 8th, he was relieved by Tug McGraw, who would walk in his only plate appearance and score, giving him a weird line of his own.

I guess when one pitcher has a weird night, his reliever has to follow suit.

My third through nth thoughts involved my standard method of creating a needlessly complex spreadsheet using data culled from ESPN.com. The results were quite surprising.

I ran the usual 1.81 version of Wins Above Expectation numbers (Holy cow, Tampa and the Angels are way above!), and in addition I ran the Beane Count and checked how it correlated to the standings.

The Beane Count is the sum of ranks-in-league for home runs, walks, home runs allowed, and walks allowed (with lower obviously being better for the last two categories). The theory, according to Rob Neyer, is that teams that walk and hit home runs, and do not allow their opponents to walk or hit home runs, will do better on the whole than teams that fail to walk and hit homers, or allow their opponents to do the same.

According to the data (stored here in handy dandy PDF format), Beane Count actually correlates very strongly with league rank. In the American League, the correlation to actual wins is .658; in the NL, .736. The correlation to Pythagorean expected league rank was even stronger: .755 in the AL and a whopping .845 in the NL. I’m prepared to eat my words on this one: Beane Count is a solid stat, particularly when measured against highly predictive stats.

Today’s project: find Pythagorean expectations for each team, then find the difference between the actual and expected win percentages (“pythagorean difference”). Apply the pythagorean difference to the total number of games played to determine a team’s Wins Above Expectation by multiplying the total number of games by the pythagorean difference.

Practical application: none.

Discussion and numbers behind the cut.

I’m using OpenOffice.org Calc and numbers that I copypasted from ESPN.com, cited above. The formatting is a little wonky because this was just a play session for me, but here are my data in handy dandy PDF format (original spreadsheet format available upon request).

Wins Above Expectation is a measure of the economy of a particular baseball team – the ability to win more games than the number of runs scored would predict. I would therefore hypothesize it to be useful as a measure of defensive ability, though of limited use from a predictive standpoint because anything it would predict could be more elegantly but less surely predicted using other measures.

Speaking of elegance, I can’t help but notice that the pythagorean expected rank and the rank by run differential are the same in all cases. The elegance of run differential as a method of ranking teams’ performance hadn’t occurred to me before, but I’ll probably continue to use it. The use of pythagorean expectation is to predict a number of wins given a particular number of games. (The correlation between expected rank and rank by run differential is obvious after thinking it through, since pythagorean expectation is basically just a special case of differential.)

The Rays’ exceedingly economical performance isn’t surprising, since they’ve been squeaking out wins regularly all season. As a team, they rank second in MLB in the teams’ number of saves (a stand-in variable for close wins), behind only the LA Angels (who beat them in terms of WAE as well). There’s also no surprise that one of this season’s biggest punching bags, Toronto, is last in the league in negative WAE (that is, wins below expectation).  This is what happens when you lose tight games and get your wins by enormous margins. Lesson to be learned: consistent performance creates measuring statistics that closely match performance.

Edit to Add: I added an additional page of stats using the 1.81 exponent cited in the Wikipedia article. The numbers changed; the ranks didn’t.