I Just Love Baseball

So my girlfriend asks me the other night "How do you calculate games back in the baseball standings?" I give the standard, "well, if they've played the same number of games you just subtract the lower ranked team's win total from that of the higher ranked team" answer. Then, feeling smart and ready to flex my sports-fan chops, I started giving basic guidelines for determining the answer when the teams have played different numbers of games. It worked great, she accepted the answer and I got to move on and lay out the infield fly rule next.

Fast forward to this morning.

I'm looking at the standings after the O's comeback win in Tampa last night and something is nagging at me. It's not the standings themselves: "Baltimore" is above "NY Yankees" so all is right with the force there. I look around a bit and realize that the subconcious calculator and fact-checker is sending up chi-squared signals as it can't justify some of the "GB" (games back) numbers in the standings. See, there's been some kooky weather going around the Midwest and up the East Coast and a lot of teams have missed a lot of games. Two and a half weeks into the season and we have some remarkable games played deltas going on. Take a look at the AL Central where as of this morning, Cleveland is in first place with a 6-3 mark in 9 games played. Kansas City is sporting a 3-10 record in last place after 13 games played (and they were just rained out in Charm City on Sunday preventing the O's from going for a 4-game sweep)(Heh). Between those two bookends are Detroit (8-5), Minnesota (7-5) and the ChiSox (5-6) who have played 13, 12 and 11 games respectively. Despite the games played differential, the Indians and their 66.7% win rate are tied for first place with the Tigers and their 61.5% win rate. Again: the Tigers have a winning percentage 5.2% behind the Indians and yet are zero games behind in the standings. The mental alarm was going nuts for a good reason: I suddenly couldn't figure out the GB situation.

Now, I've been certain that I know how to do this calculation for years, decades even. I add in the half games here and subtract the losses there and I always came up with a good number. Well, almost always, I actually remember (after some soul-searching) just shrugging, blaming lack of coffee, and moving on to the box scores without a second thought when I've failed to produce a mental GB number to match the newspaper standings in prior seasons. It seems that I've been deluding myself, lying to myself, claiming credit for a skill I distinctly lack. I'm shattered, to be honest, and can't live with the situation. I need an answer, I need to retroactively fix this. To the interwebs!

My first find was a blag called Reinke Faces Life. This authoritative looking source showed me why I couldn't do this calculation mentally when it gave the answer (courtesy of the University of Toronto Mathematics Department) as: GB=-(w+L)/2 + √((w+L)^2 – 4wL + 4Wl/2). I'm good at math, really I am, but I don't solve modified quadratic equations in my head. I just don't. Of course, this makes me feel better about getting close but not quite right on my calculations earlier: that's hard stuff, not something I can be expected to do like some sort of particularly geeky party trick, particularly as the answer is completely useless for my fantasy team(s).

Relieved I sit back, relax, and curse as the mental alarm goes off again. I'd let my guard down and looked at the AL West (curse you, AL West! You produce things like 10:30pm EST first-pitches, a team named "the Los Angeles Angels of Anaheim" and A-Rod!). Seattle is in first with a 5-3 mark in 8 games (yeah, 8). Texas at 5-7 is in last (behind the LAAofA and Oakland, both at 6-7). A microsecond before glancing at the GB column my stupid brain reported that the LAAofA and the A's are 1.5 games back and Texas is 2 games back. I laughed ruefully at my presumption and looked at the actual numbers on ESPN.

They matched.

Now I know that I didn't run two quadratics in my head in less than a second without trying. Suddenly, in a flash of intuitive brilliance, it hit me: those damn Canucks screwed me! They're sitting around their University of Toronto Math Lab Bar and Grille giggling insanely and drinking Molson as I blindly accept their bloody complicated quadratic formula instead of the less complicated (and, coincidently, accurate) GB = ((WinsA-WinsB) + (LossesB-LossesA)) / 2. Yeah, that's it, two bits of substraction, one little addition, and then halve the product. Easily done by the subconcious. Just what I've been doing for decades without ever thinking about it. Stupid Sparky...

Lessons learned:
1. Don't trust people from Toronto or those who choose to live there;
2. Don't trust blags or the interweb without fact-checking every damn thing first;
3. Do trust my intuition and wait until coffee before wallowing in self-doubt;
4. The Yankees are in fourth place regardless of which formula you use, and that's always a good thing.

Puck Math

The Physics of Hockey
Alain Haché
Published by The Johns Hopkins University Press, 2002
ISBN 0801870712


I’ll admit it, I’m a bit of a math geek. I’ll also admit that I’m a bit of a sports geek. One look at the URL you’re at now should confirm that. One brief visit to the parent site of this blog, WashingtonHockey, will confirm that I don’t have the slightest shame about combining the two interests either. If I spot a chance to include a bit of regression analysis, or some economic theory to a hockey story, well, my day is made. Imagine my excitement, then, when my lovely girlfriend’s father sends me a book as a gift. Getting any book is a treat, but when it’s got the words "Physics" and "Hockey" both in the title, well, I almost made an honest woman out of her just to show him my appreciation!

Since I’m being honest here, I’ll flat out say that if you don’t like either physics or hockey you’ll hate the book. If you like hockey but can’t tell sin θ from Sins of the Father, you’ll struggle (unless you’re a young, hockey playing Canadian male in which case you’ll be glad to know that your chance of making it to the NHL is about 1 in 6,000). If you like physics but can’t tell a check from a Slovak, it’ll be interesting but nothing spectacular (unless you’re a young, non-hockey playing Canadian male in which case you need to consider the odds of making an NHL-equivalent salary if you stick with physics as a career). If you like both, though, this is a treat, and this review is for you.

You know physics, and you know hockey, so you’ve got a good understanding of the shooting motion. The wind-up, the swing, the release, the curvature of the stick, that’s all familiar. This book, however, explains all the motions and interactions involved in the process and there’s more than you might think. The same goes for goalie positioning, skating, accuracy, checking, and player quality. You can see how the author determines that Ray Bourque’s window of opportunity for a goal on a slapper from just inside the blue line, through traffic, with a screened goalie in a partial butterfly was 0.3° (aperture from 70 feet using Δθx = 2arctan (Δx/2d) as the determining formula for horizontal margin of error). Speaking of the butterfly, Haché uses Felix Potvin and Patrick Roy to demonstrate why that particular stance is so popular, while choosing Marty Brodeur for reaction times. He explains salaries as a function of probability, not relative or absolute quality (though I’d like to see him address that now that we’ve got a cap). Bobby Hull is the model in the discussion of shot selection in the crease. Jaromir Jagr shows off his skating power. The list goes on and on and on.

This book lives on my bedside table, with occasional forays to the bathroom bookshelf. I don’t pick it up every day, or even every week, but I never go very long without re-reading a chapter. I don’t play hockey, but I love to apply this kind of knowledge of physics to day to day activities, be it carrying things or playing golf. If you’ve got a puck-crazy friend who did pretty well in high school physics, get ‘em this book, they really don’t need yet another collection of crazy quotes from the penalty box.

Note: I am disappointed that, with all the academic vigor and attention to mathematical accuracy the author devotes, he described Mark Recchi giving "110% at every shift." That’s blatantly impossible. Dale Hunter, sure, but Recchi never gave more than 102% when I’ve seen him…