Niagara Falls, part 2

When we last left our intrepid heroes, we were heading inside and then to get some lunch after a successful morning stalking the elusive huge waterfall. We emerged from Outback Steakhouse after lunch to find that the sun had come out and it was warmer than the predicted 30°. We headed back down to the falls area to explore some more.

With the sun out, we found the very elusive waterfall rainbows playing in the spray. The American Falls rainbow was easily spotted right out in the open.

 

The rainbow on Horseshoe Falls was a bit more shy, however, but we would locate it (and a surprise) before the afternoon was over.

The river itself was an interesting green color in the sunlight.

Before long, however, we were able to find the Canadian rainbow--and a friend! (That's the aforementioned surprise.)

We moved upstream to investigate some things we'd seen from the hotel, but we kept an eye on the frolicking rainbows, too.

The rainbows liked us. They even followed us above the falls. You can see in the shot below that the brighter rainbow is definitely standing in the river above the falls.

The plants were coated with ice, even upstream from the falls.

Below, I tried to take a really artsy shot through the ice plant. It didn't turn out quite as I had hoped, but it's not bad.

 

 One more rainbow shot, then we'll move to the next part of our tour.

When we were taking a break before getting lunch, we discovered that an attraction called "Behind the Falls" was open. We hadn't really thought it would be. Remember that viewing platform at the base of the falls that I mentioned in part 1? We got to go down there.

Our friend the rainbow came down there with us. It sure looks like it's having fun frolicking in the spray.

The view downstream from down there was pretty spectacular, too.

For some reason, they made us stay in the covered upper viewing area. We couldn't even go down and read the signs in the lower area.

While we were taking pictures, I saw some movement out of the corner of my eye and heard a strange sound down on the lower platform. Looking over the rail, I found that someone was probably on the cliff above squinting in the sun.

Now, this attraction was called "Behind the Falls" for a reason. There are tunnels leading to two viewports out of the rock behind the falls. Here's the view from the first one.

I guess the ice on the rocks behind the falls kind of filled it in. Ever optimistic, we headed off to the second viewport.

Oh, well. I guess it wasn't really surprising that these were completely blocked. I'll have to get back there some day when it isn't all frozen up. We were told by some locals that September is a great time to go because tourist season is over, but things haven't started freezing yet. Something to keep in mind.

At least we got to find out where we would have been looking out.

It was getting to be dinner time and the sun was setting, so we headed back up to the top of the cliff and said one last goodbye to the falls.

The trip home started out waaayyy too early (the train left at 7:20). We also got stuck at Penn Station for an extra hour and a half, as there were track problems in Virginia that delayed our train back home. Luckily, we were able to swap our tickets for another train and we managed to get home by 8:30 or so that night.

Niagara Falls, Part 1

A number of people have asked about our trip to Niagara Falls last weekend. For those who don't know, I have been a big fan of waterfalls since I was a kid. One of my favorite places to visit is Dry Falls, WA. (Granted, there's no actual falls there now, but imagining what it was like boggles the mind.) I had never seen Niagara before, though, so this was almost a sort of pilgrimage for me.

Rachel and I each took well over a hundred pictures of the falls and the surrounding area, so I'm not going to share all of them here. I will be uploading a photo album to facebook eventually which will contain photos taken by each of us. All of the pictures in this post were taken by me using my phone. Click on any image to see it at full resolution.

We started out pretty early on Saturday morning by taking a taxi to the train station and then an Amtrak train down to Penn Station in New York. That part was about 2 hours and we've done it before, so it was a little humdrum. After leaving the train and getting on a packed escalator, I suddenly realized that I didn't have my wallet, which meant that I had left it on the train which was going to depart in a few minutes.

As soon as I got to the top of the escalator, I found an escalator down to the platform, told the employee who was checking tickets before sending people down what was happening, and she let me go down. I searched near the area where I thought we had been sitting and found nothing. I returned to the up escalator just in time for it to turn into a down escalator. I found another way back upstairs.

We made a quick search to make sure I hadn't shoved it in my backpack somewhere. I hadn't. There was now someone manning the escalator we had originally come up, so I told her I needed to go check for my wallet again. She gave me more of a hassle than the other had, but eventually let me go down so I could check the route we followed off the car. No dice.

When I got off the train again, I spotted a couple of conductors and told them I'd lost my wallet on that train and asked if there was any way to find out if someone had found it before the train departed. One of the conductors returned to the car with me one more time, and while I crawled on the floor and looked, he announced to the passengers that I had lost my wallet. Someone found it at that point, because the next thing I knew, the conductor was tossing it to me.  That was a huge relief; I might not have enjoyed any part of the trip if I hadn't been able to find my wallet.

But the fun wasn't quite over. As the conductor and I went to exit the train, we found that the doors were already closed, meaning that the train was going to start moving at any moment. He grabbed his radio and told the train not to leave while he got the door open and we stepped out. I was nearly on my way south a bit further than I wanted to be. Thank goodness it hadn't taken any longer to find my wallet.

The rest of the trip to Niagara Falls was pretty uneventful. It included a 9 1/2 hour train ride, so it was also pretty boring. We arrived in Niagara Falls, NY at about 10:30, or 15 minutes early. Luckily, I had been able to call the cab that was supposed to pick us up and he was waiting for us as we got off the train. We stayed on the Canadian side of the river, so he had to take us across the border. We were amazed at how long the lines to cross the border were at 11:00 on a Saturday night in mid-March (and freezing temperatures). While we were on the bridge, Rachel spotted a colorful glow off the the left. We guessed (correctly) that it was the spray of the Canadian falls reflecting the colored lights that they shine on the falls until midnight. That was sort of our first view of the falls.

Our real first view of the falls was from our hotel room. Well, "room" is a bit of a misnomer; the hotel was pretty empty, so they upgraded us to the "Junior Presidential Suite". I didn't take any pictures of the suite and now I wish I had. I assumed that the hotel's web site would have some good pictures of it, so I could just link to that. Unfortunately, the picture they have labeled "Junior Presidential Suite" is very clearly not of the suite we stayed in. The suite we stayed in had a kitchenette, a dining area, a separate living room, a bedroom, and a large bathroom with both a shower and a two-person hot tub. The view was incredible; it was night when we arrived, so the all three falls (yes, there are three that make up Niagara Falls, not just the two) were lit up with multicolored lights. Personally, I'd rather they just used white lights, but that's me. No pictures at that point because our camera doesn't do well with that kind of shot, but here's an image of what it looked like in the morning:

The steaming cauldron in the foreground is, of course, Horseshoe Falls, which is the part of Niagara Falls on the Canadian side of the river. On the left is American Falls. For those of you wondering about the third falls, it is in this picture right next to American Falls. If you look really closely, you can see that the very right-hand edge of that part of the falls is separated from the rest by a bit of rock. The bit on the very right-hand edge is Bridal Veil Falls, and is the third part of Niagara. This image is looking roughly southeast with Niagara Falls, NY in the background. For some reason, neither Rachel nor I realized that the river was flowing north at this point, so we both had pictured the falls going the other direction for our entire lives.

The package deal we got included being able to ride buses all day, but we were close enough to the falls that we decided to walk down. To get there, we first had to walk north a bit so that we were straight across from American and Bridal Veil Falls. Coming down the hill and seeing the falls through the trees, I was amazed at how close it was; it seemed much further away to me from the hotel. The picture below was taken just as we finished going down the hill. You can clearly see Bridal Veil Falls on the right.

Looking downstream, you see a lot of ice blocked up under Rainbow Bridge. The "ice bridge" used to be much larger (and extend all the way to the base of the falls). People would go out on the bridge to take in the view of the falls. On at least one occasion, the ice bridge suddenly broke up and people lost their lives. These days, they block the larger chunks of ice from entering the Niagara from Lake Erie.

At this point, we turned south along the river. It wasn't long before we got to see Horseshoe Falls.

I was enthralled with the falls itself. Pictures do not do justice to the flow of water and amount of power those falls represent. And we were there in March, which meant that the flow we saw could be as low as half of what is flowing over the falls during tourist season! While I was staring at the falls, Rachel spotted odd lily pad-like bits of ice in the water. I guess they get rounded by their trip over the falls.

As we walked closer to the falls, we spotted a viewing platform very close to the falls themselves. We figured it was closed for the season, but as it turned out, we got to go down there ourselves before the day was over.

Being there in subfreezing temperatures (the predicted high for the day was 30° F) gave us an opportunity to see things that most visitors to the falls never do. The rock below is entirely encased in ice from the spray to a depth of up to an inch in places.

Of course, there were also interesting ice formations near the falls.

And man-made structures are frequently completely coated in ice, too. The railing that Rachel is leaning on here got coated with more ice as you moved closer to the falls. Right above the brink of the falls, one of the railings was so icy that the blank spaces between the bars were completely filled in with ice!

No, I don't know who the guy is in the next picture, but he wouldn't move and I wanted to get the shot while the sun was still back lighting the ice.

The plants were even completely encased in the ice. The shot below is from almost at the lip of the falls. All that separates these plants from the water is the wall you can see.

After taking that shot, it wasn't long before we got to where the walkway practically overhangs the lip of the falls.

 

After being amazed by this view for a while, we realized that it was after noon and we were both very hungry. The second part of this post contains pictures taken during that very sunny afternoon, including some from the viewing platform shown in the sixth image above.

How Can Hockey be Changed for the Better?

Putting aside any argument about whether hockey can be improved or not, I've been thinking about rule changes that could be put in place that at least some people would think improved the game. Some of the proposals below I think would be good for the game and some I don't, but I'm going to lay them out here without imposing my opinion as best as I can and I'd like to know what other people think. Please note: these are not my proposed rule changes, I'm just collecting several here that I've seen elsewhere.

Introduce a Goal Verification Line
This is one that was play-tested in the AHL a few years back. I think it was just as the NHL was getting back on the ice after the lost season, but I don't remember for sure. Basically, a goal verification line is a line drawn exactly one puck-width behind the goal line between the goal posts. The picture below is from the original article I read about this many years ago. I saved the picture because I thought it was interesting, but I have no idea who to credit. I think it was NHL.com.

The idea here is that if the puck is even touching the goal verification line then it is a valid goal. This is supposed to help on those goals that are too close to call even on replays because the goal line itself is blocked from view by equipment, etc.

Cease Allowing a Penalized Player to Return to the Ice After a Goal
The NHL has explicitly stated that many of the rule changes instituted since 2005 are intended to increase scoring (e.g., smaller goalie pads, the introduction of the trapezoid behind the net, and the moving of the blue lines closer to center ice). One thing that would greatly increase scoring would be eliminating the rule that allows a player serving a minor penalty to return to the ice after their team is scored on.

Believe it or not, the rule allowing a penalized player to return to the ice at that point was only instituted in 1956 (http://www.rauzulusstreet.com/hockey/nhlhistory/nhlrules.html). Prior to that time, a minor penalty lasted a full two minutes and the penalized team was a man short for that entire time (http://www.nhl.com/history/060656.html). The rule was modified to allow the penalized team to return to full strength because the Montreal Canadiens had gotten so good on the power play that they would regularly score several times in the two minutes (http://media.nesn.com/2011/03/top-10-most-important-rule-changes-in-nhl-history/5/).

Don't Allow a Shorthanded Team to Ice the Puck
As far as I know, a team  that is shorthanded has always been allowed to ice, or "rag" the puck. In fact, until 1925, play was not stopped regardless of whether the icing team was shorthanded or not (http://www.rauzulusstreet.com/hockey/nhlhistory/nhlrules.html). The idea behind taking that privilege away is once again to increase scoring. I've also heard that there are kids' leagues that don't allow a shorthanded team to ice the puck (this to encourage skill development), so it's not an unheard-of concept.

Institute No-Touch or Hybrid Icing
This one is a hugely hot topic. Many levels of play use a "no-touch" icing rule, meaning that icing is called as soon as the puck crosses the goal line, regardless of whether there is a player on the attacking team there to play the puck first or not. A lot of people have been supporting this idea because of the number of injuries sustained by players when they get knocked down during a fast race for the puck. The resulting crash is often quite awkward and results in the player slamming into the boards at 25 mph or so. Don Cherry has advocated no-touch icing for many years. (If you don't know who Don Cherry is, don't sweat it, but most hockey fans have at least heard of "Grapes".)

The argument against no-touch icing refers to maintaining the purity of the game and the excitement of the race for the puck (which is rare, yes, but exciting nonetheless). Those that argue this side are not ignoring the safety issue. The argument is that the key to preventing the often catastrophic, career-ending injuries is better enforcement of the rules about interference, checking from behind, and boarding. The idea is that if a player knows that he'll be called for a penalty if he so much as touches his opponent in that vulnerable situation then he'll lay off.

In an effort to keep the race for the puck but eliminate the injuries incurred by crashing into the end boards, the concept of "hybrid" icing was developed. Many leagues have adopted this approach, including the NCAA, and it was play-tested in the AHL a few years ago. The exact rules for hybrid icing vary from implementation to implementation, but the basic idea is that there is an invisible line across the ice somewhere far from the end boards (frequently between the face off dots). Icing is called if the usual requirements are met and the first player to cross that invisible line is a defender. It is not called if the first player across that line is an attacker.

Institute Stiffer Penalties for Fighting/Ban Fighting
If no-touch icing is a hot topic then fighting is scorching. On the one hand, you have the people who want to ban fighting, who are pointing out head injuries that occur as a result of fights and that most 'enforcers' are really not skilled players and don't belong in an elite league. On the other hand, you have those who say that fighting is part of the game and that those who want it removed aren't real hockey fans (this is frequently stated using crude insults, which kind of undermines the argument  if you ask me).

Among arguments for keeping the fighting rules just as they are in the NHL, tops is probably "it's part of the game; leave it alone." The next argument usually points out that if pests such as Sean Avery or Matt Cooke don't know that they're going to have to fight the opponents' enforcer then they'll continue to make dirty hits and attempt to injure other players. (Different topic, but Matt Cooke has actually changed his ways. It would be nice if people noticed that.) Finally, the argument is frequently made that hockey is a rough sport and by removing fighting, you remove some of the 'manliness' from it. (Frequently, a reference is made to figure skating at this point.)

Arguments for banning fighting altogether include the injury argument mentioned above as well as opening up the spots currently taken by team enforcers for more skilled players. Fighting is not a part of the game, this side argues, because if it was then the game wouldn't stop whenever a fight broke out and there wouldn't be any penalties. Besides, look at international hockey (such as the Olympics and World Championships); fighting is banned in international hockey and you see some of the best hockey you ever will at that level. This side also points out that dirty plays exist now, so there's no basis for arguing that fighting deters dirty plays. In fact, many fights are started after a good, clean, solid check is made, so the argument can be made that fighting actually discourages good, solid checks, which are undeniably part of the game.

Eliminate the Shootout
The shootout is apparently very popular amongst fans, but there are those who don't like it because they feel that it's not really hockey. Hockey is a team sport, the argument goes, so something so individual as a shootout should not decide a game. Either allow for endless overtimes or accept ties. 

Replace the +/- with the Adjusted +/-
Okay, so I'm probably the only one who has ever put this forward as a 'rule' change, and it's not even technically a rule, just stats. Still, I think it would be cool to see it adopted.

There are many more proposed rule changes out there, some serious, some not-so-serious, but this is probably plenty to get any conversation rolling. Please feel free to share other ideas or to discuss those mentioned above in the comments section. Please note, however, that I do not tolerate name-calling in the comments. Any comments that include ad hominem attacks will be deleted.

A Few Hairy Thoughts about Evolution

Before getting into this one, I want to make it clear that this is not an invitation to debate the merits of the theory of evolution. For the purposes of this post, it is assumed that evolution, specifically that humans evolved from ancient apes (NOT modern apes--humans are not descended from any modern ape). As for the "it's only a theory" argument, a theory is as close to fact as you can get in science. We don't discount Einstein's theory of relativity or Newton's gravitational theory because they are "only theories", so neither should we reject the theory of evolution on those grounds. If evolution wasn't as close to fact as science will get then it would be the conjecture of evolution, not the theory.

Anyway, continuing on now from the assumption that evolution is a fact:

Do you ever wonder why, if our distant ancestors were hairy apes, we have lost almost all of our body hair? Even stranger to me is how long the hair on our heads grows; I know of no other animal that grows the hair on its head to such ridiculous lengths. (If there is one, please enlighten me.)

In pondering this, we must understand that natural selection does not select for any traits. In fact, it selects against traits that are reproductively disadvantageous. Two big words--maybe I should clarify: suppose there are two possible traits in a critter, a red chest or a brown chest. Further suppose that, all other things being equal, those critters with a red chest have a much worse time hiding from predators and, therefore, tend to die younger (some even before they have a chance to reproduce at all) than those with a brown chest. Natural selection is at work here, selecting against red-chested critters, giving you more descendants of brown-chested critters, possibly until there are no more red chests in the critter population.

Going back to body hair, the question I find myself asking is, "why was it a disadvantage for our ancestors to have thicker body hair?" All other land mammals seem to get along just fine with more body hair in all environments. What was different about human ancestors? There is the possibility that the mutation that causes less body hair just never occurred in any other evolutionary line, but that seems unlikely to me. And why is it that we still have thick hair in certain places? What's special about an arm pit that the "less body hair" gene left that alone?

Along the same vein, why do women tend to have less body hair than men (even when they don't shave it off)? Clearly, some evolutionary force selected against women with much body hair. Nowadays, that could be seen because most men (in our culture, anyway) are more attracted to women with little body hair, but is that what started it all? If that was the selective factor, where did that attitude come from in the first place?

A similar question goes for head hair: "what was the disadvantage for not being able to grow long hair on the head?" Those who have had long hair can tell you the disadvantages of same: it takes a long time to dry; it gets tangled and is hard to maintain; it can get caught on things (which seems like a distinct disadvantage to a primitive ape to me); etc. Perhaps the two things are related; longer head hair had to come with less body hair for some reason (or vice versa).

Finally, why do men tend to grow facial hair, but women don't? (I'm speaking in generalities here, and not talking about a little "peach fuzz" on the upper lip.) What possible evolutionary factor could there have been to select against males with no facial hair, but against females with facial hair? Perhaps, again, we're looking at what specific mutations did or did not occur, but why affect males and females differently? Maybe it has something to do with the second X chromosome, seeing as the Y chromosome doesn't have as many genes on it. (I do know that this is the source of some male-female differences, such as pattern baldness, which is a recessive gene but occurs on the X chromosome and not on the Y. A woman with the gene might well have the dominant gene against pattern baldness on the other X chromosome. That's an oversimplification, I'm sure, but it's the basic idea as I understand it.)

I'm afraid I don't have the answers to any of these questions, but they have been occurring to me off and on for years. Please feel free to educate me if you know, or even share if you have a theory. I'd love to know what other people think, especially about the reduced body hair question.

Hey, not all my posts can be deep and meaningful. :-)

The Adjusted Plus-Minus

With the start of hockey season (though no NHL season just yet) upon us, my thoughts have turned towards the sport I love. This post may not be of much interest to those of you who aren't hockey fans (and maybe even to those who are but couldn't care less about stats). You have been warned.

The plus-minus; what it is

The plus-minus (or +/-) is relatively new in the hockey statistics world. It was first employed by the Montreal Canadiens in the 1950s and started being tracked by the NHL in 1968. That's over 40 years, but most fans had never heard of it until the last 15 or so (if ever). These days you hear it mentioned several times in most broadcasts, but what is it?

As with many sports, the most well known hockey statistics (goals and assists) are geared towards measuring a player's offensive ability. The plus-minus is intended to be a measure used for defensemen and defense-minded forwards. The statistic is calculated by taking the number of non-power play goals scored by the player's team (so even strength and shorthanded goals) while he/she is on the ice and subtracting the number of non-power play goals scored by the other team while he/she is on the ice. For example, suppose Roy was on the ice for 3 goals scored by his team, one of which was a power play goal. This gives him +2 (since the power play goal doesn't count).If the other team also scored 3 goals, none of them on the power play, then his plus-minus for the game is +2 - 3 = -1.

Once you get used to it, this is pretty straightforward. The idea is that a better defensive player will have a higher plus-minus since the other team will score less when he is on the ice and the offensive players on the team will likely score more since they can be confident that the defense is being taken care of.

What's wrong with the plus-minus

The plus-minus has a number of issues, but there two that I want to address here:

The first is that the plus-minus does not take into account the amount of time a player spends on the ice. A player that spends 20 minutes playing and earns a +1 is seen as contributing the same as a player who plays just 1 minute and also happens to earn a +1. This is not equitable.

The second (and, in my opinion, bigger) problem is that there is no baseline. Suppose Roy's team in the example above lost that game 14-3. Roy's -1 is actually quite good. On the other hand, if Roy's team won the game 14-3 then Roy's -1 is really bad. This becomes worse as you look at season or (shudder) career plus-minus. Someone who is very bad but plays for a very good team can have a season plus-minus that looks great, while someone who is very good but plays for a very bad team can have a plus-minus that looks horrible. (Take John Tavares, for example. His season plus-minus in 2011-12 was -6. That's on the minus side, so looks bad, but when you take into account that the Islanders were 26th in a league of 30 and that they were outscored by their opponents by 55 goals (251-196), his -6 is actually pretty decent. It's not great, but he's also a very offensively-minded player and it is 5th place on the team among players who played at least half the season.)

To make matters worse, stats pages and commentators compare plus-minus values between players on different teams as if that means anything. Is Chris Kunitz's +16 (5th among the Pittsburgh Penguins for players playing at least half the games in 2011-12) really better than John Tavares' -6? That's debatable since the Penguins outscored their opponents by 65 goals (273-218).

To make the plus-minus more comparable between teams, we need a baseline to work from. That's where my proposal for the adjusted plus-minus comes in.

Proposed solution: adjusted plus-minus

The goal behind the adjusted plus-minus is to create a statistic with a known baseline which is therefore comparable for players on different teams. The formula is below, but the idea is simple: adjust everyone's plus-minus so that a player that is neutral (in the sense of not directly affecting which team has more goals in the end) will have an adjusted plus-minus of 0. A positive adjusted plus-minus will show that the player is contributing to the team's success and a negative adjusted plus-minus will show that the player is not (or may, in fact, be contributing to the team's failure). The formula takes into account the player's time on the ice (TOI) as well as the overall performance of his team, thus addressing the two issues described above.

First, some notation:

EVTOI = the player's time on the ice when the teams are even strength. This includes 5 on 5, 4 on 4, 3 on 3, as well as times when one team has pulled the goalie in order to gain a one skater advantage. If either team is on a penalty kill then that time is not counted in the ESTOI.

EVTOT = the team's total time playing at even strength. (Obviously, this is the same for both teams in a single game, but not over the course of many games against differing opponents.)

TPM = the player's team's plus-minus. This is a total of all even strength and shorthanded goals scored by the players team minus all even strength and shorthanded goals scored by the opponent. In short, compute the traditional plus-minus for the entire team as if it was one person.

PPM = the player's traditional plus-minus.

Okay, here's the formula:

Adjusted plus-minus = PPM - (TPM * ^EVTOI/_EVTOT)

The logic is as follows:

^EVTOI/_EVTOT gives you the fraction of the team's even strength time during which the player was playing. Shorthanded goals for or against wind up acting as a bonus or penalty for the player, but power play goals either way do not affect them, so that time is not included in the ratio. In this way, the time that the player spends on the ice is taken into account in the statistic.

Multiplying ^EVTOI/_EVTOT by TPM gives you the player's "expected" plus-minus. This is the plus-minus that would be earned by a player who is neutral in the sense described above. This is very likely to be a fractional amount; I've been rounding to two decimal places in my personal calculations, but any number of places could be chosen.

Subtracting the expected plus-minus from the actual plus-minus gives a statistic with a baseline of zero. A neutral player would be "even" (an adjusted plus-minus of 0), no matter how good or bad his/her team was.

Example with full statistics available:
Let's get some more information about Roy's game. The actual score for the game was 9-4, Roy's team lost, scoring once on the power play and giving up two power play goals against. The team's total plus-minus, then is TPM = 3 - 7 = -4. (3 because they scored 3 non-power play goals and 7 because they gave up 7 non-power play goals).

During the game, Roy played a total of 17:30 of ice time: 0:45 on the penalty kill, 1:15 on the power play, and the rest at even strength. That makes Roy's EVTOI = 15:30 (17:30 - 0:45 - 1:15).

During the 60:00 game, the team spent 4:30 shorthanded and 5:15 on the power play. Thus the teams even strength time is EVTOT = 50:15 and Roy's ^EVTOI/_EVTOT = ^15:30/_50:15 = 0.31 (approximately).

Multiply that by the TPM and you get 0.31 * -4 = -1.24. This is Roy's expected plus-minus. His adjusted plus-minus, therefore is -1 - (-1.24) = +0.24. Roy was actually a little bit of a help to his team in this game, in spite of the -1 rating.

How to adjust for rec league:
Of course, most of us don't have that detailed TOI data to refer to. In my rec league, I've simplified the calculation to simply take the approximate fraction of the game I play based on the number of people playing my position. If I'm one of three centers, for example, then I make the fraction 1/3. If I'm one of 5 defensemen, I make it 2/5 (two defensemen on the ice at any time divided by 5 total). Other than that, I compute it just as described above.  

Update 9/24/2012: As an example of what a difference it can make, I offer my own stats from the SCHL for summer 2012. That was a rough session for my team; we went winless and were completely blown out multiple times. My plus-minus for the summer was -21. My adjusted plus-minus was -0.70. I was still on the minus side, which doesn't please me, but at least it shows that I wasn't a complete drag on the team, which a -21 might seem to imply at first.

Please feel free to ask any questions and/or offer any critiques of this proposed statistic. I've been using it for myself for years, but I'd like to know what other people think.

Dear FedEx

The following is the actual text (copied and pasted) of an email I sent to FedEx.

Dear FedEx,

I regularly ride my bicycle from my home in New Haven, CT to my work in Wallingford, CT. My usual route takes me past the FedEx Ground location at 29 Toelles Rd in Wallingford. That particular part of my route is not the best for a bicycle and I'm frequently annoyed (and occasionally frightened) by the many commuters driving along that road in the morning. One thing I don't have to worry about, however, is the drivers of the many FedEx vehicles I see. The drivers are always polite and respectful of my right to be on the road and never do anything that I feel places me in danger in their presence.

Nearby Mt Carmel Ave/Kings Hwy is the only direct route between that part of Wallingford and both the bike trail that half of my commute is along and a major north-south artery used frequently by your drivers. It is a narrow, winding, two lane road with no shoulders which climbs up and over a small ridge just south of Sleeping Giant. I frequently encounter FedEx delivery vans along that road. Even on that cramped road, FedEx drivers have been the most courteous and safest drivers I have encountered. They never pass me as I'm attempting to finish a steep climb with no shoulder and never pass when approaching a corner, something that other vehicles do along there almost every day. I feel bad sometimes because I do slow them for up to a minute or so as they wait for a safe place to pass, but I want them and you to know that I appreciate their courtesy and that they always give me plenty of room when passing.

Connecticut is not the home of the country's best, most courteous, or safest drivers, but the FedEx drivers I have encountered have always been respectful, courteous, and safe around me on my bicycle and for that I am grateful. I want others to know how much I appreciate your drivers, so a copy of this email will be posted to my blog (http://twocatsonabike.blogspot.com).

Thank you,

Scott MacDonald

 Google Street View of the FedEx Ground location.

A Driving Primer for Connecticut Drivers, Part 3

This primer is presented somewhat tongue-in-cheek, but it is inspired by the actual activity I've seen on the roads since moving to Connecticut. To be fair, it may just be the greater New Haven drivers that really need this primer, as I hear that even Massachusetts drivers think New Haven area drivers are terrible. One legal-ish note: none of the images used here are mine. Click on an image to see where I've linked to it from and any copyright information that may be included.

Part 1 of this driving primer focused on the confusing lines in the road that run parallel to the road itself. Part 2 focused on those weird color-changing "traffic" lights and two types of lines that run across the road: stop lines and crosswalks.

Part 3: Stop Signs and Unmarked Intersections
If you've driven much at all then you're probably come across one of those weird 8-sided red signs with the enigmatic message "STOP" written on them in white letters. Though many feel that these signs are ambiguous at best, we'll unravel the mystery of what they mean here. We will also tackle the difficult problem of what to do when two streets cross each other but there are no "traffic" lights and none of these "STOP" signs.

• Stop signs "STOP" signs (or simply, stop signs) seem to be everywhere. To many drivers (and to even more bicyclists, but that's another post), they simply have no meaning and can be ignored. Here's a typical stop sign in the wild:
  
  
  
  To begin to unravel the mystery of what to do when confronted with one of these signs, I started by trying to find out what the acronym "S.T.O.P." stood for. Much to my surprise, I discovered that it is not an acronym, but an actual English word! The word has many definitions, but the one that seems the most relevant in a driving situation is this: "To cease moving, progressing, acting, or operating; come to a halt." This makes it clear what one must do when confronted by a stop sign; one must come to a halt. But where? Most stop signs come paired with a stop line (see part 2 of this primer).
  
  
  The stop line in the above image is a bit worn, but it's there. When a stop line is provided, treat it just like a stop line at a traffic light: stop there. Not 15 feet before you reach it. Not after your car has crossed it (and therefore entered the intersection). Stop so that the front of your car is at the stop line and the rest of the car has not yet crossed it. If there is no stop line then stop before the front of your car enters the intersection. (I placed emphasis on the word "before" because so many people seem to miss it.)
  
  Once you have stopped your vehicle, it is not necessary to remain stopped indefinitely. Instead, carefully look for the following: (a) other vehicles approaching the intersection whose route will intersect yours and who do not themselves have a stop sign and (b) pedestrians. As much as I joke about things being difficult, this looking for pedestrians bit is extremely important, yet seems to be missed by many, many people. I don't know how many times I've seen a pedestrian hit or nearly hit by a car because the driver was so busy peering around the pedestrian for traffic that they never even saw the pedestrian.
  
  Pedestrians have the right of way at intersections whether there's a crosswalk painted there or not. If someone is crossing the street, don't just stop right in front of them and figure they'll go around you. Stop far enough back that they can safely pass in front of your vehicle, let them do so, then move forward to where you can see oncoming traffic and stop again to look for traffic. (True story: I was crossing a street when a woman pulled up to the intersection, stopped before entering the crosswalk, looked me in the eye, then pulled forward inches in front of me to look for traffic and stopped. She was so close that I lost my balance trying to dodge around the back of her car and accidentally hit it with my hand as she started to drive off. She stopped (in front of oncoming traffic), rolled down the passenger window, and yelled, "That's how people get shot!" By getting cut off by a rude driver and losing their balance? Whatever.)
• All way stops Many people are honestly confused about what to do with they approach an all way stop (frequently referred to as a 4 way stop, since most intersections have traffic traveling in four directions).
  
  
  All joking aside, all way stops are clearly very confusing for people, so here are the rules on how to handle an all way stop.
  • First, come to a stop just as you would with any other stop sign.
  • Look for traffic (and pedestrians!); if there is no other traffic then proceed on your way.
  • If another vehicle arrived at the intersection before you then they have the right to go first, so you must wait until they have gone before you go.
  • If two (or more) vehicles arrive at the intersection at the same time, then right-of-way is determined as follows:
    • The vehicle immediately to your right has right-of-way over you. You must wait until that vehicle has gone before you go.
    • It follows from the above that you have right-of-way over the vehicle to your left. Make eye contact with the other driver (if possible) and make sure that they are yielding that right-of-way to you, then proceed if it is otherwise safe.
    • If the other vehicle is coming the other direction then right-of-way only matters if one or both of you is turning left (or otherwise crossing the other's path). In that case, any vehicle going straight or turning right has the right-of-way and the left turner must yield.
  • Sometimes you come to an all way stop to find that there are lines of vehicles waiting in all directions. This is a situation in which many drivers are confused and don't know what to do. The important thing here is to take turns. To determine who goes next, figure arrival time at the intersection to be when each vehicle reaches the front of the line and use the right-of-way rules described above.
  
  One final important comment related to all way stops: if you come to a traffic light that is either completely nonfunctional (dark) or which is flashing red in all directions then that traffic light is an all way stop. These can be difficult to navigate if it is a large intersection with multiple lanes going in each direction. Here, again, turns should be taken, with all vehicles traveling in a certain direction going at the same time. One vehicle from each lane should go with each "turn". There should not be multiple vehicles from the same lane going through the intersection at the same time, I don't care how frustrated the drivers are or how long they've been waiting; others have also been waiting and are probably just as frustrated. You're all in that situation together, so cooperate to get through it safely.
• Unmarked intersections Also known as "uncontrolled" intersections, these are intersections with no stop lights or traffic control signage whatsoever.
  
  
  Having learned the rules for all way stops above, unmarked intersections should be a breeze: the only difference is that you don't have to stop before going through the intersection if there is no other vehicle with right-of-way over you. That emphasized part is the part that a lot of people don't seem to realize. You do need to slow down enough when approaching an unmarked intersection to determine whether or not (a) you have the right-of-way and (b) if it is, in fact, safe to go through the intersection. Not checking for both of these things leads to this:
  
  
  This accident occurred in an unmarked intersection. None of the three drivers involved was paying attention to cross traffic. Luckily, no one was seriously hurt, but the drivers of the Cavalier and Jeep got free trips to the hospital and the driver of the truck got to explain to his boss why he totaled a company car when he could have prevented the whole accident just by glancing to his right.
  
  There is one important situation in which an unmarked intersection does not have the same right-of-way rules as an all way stop. This is at a "T" intersection (i.e., one of the roads ends at the intersection while the other continues on).
  
  
  In this situation, the car on the road that ends (the red car above) is required to yield to all vehicles on the road that continues through (the blue and yellow cars above).

Thus ends my driving primer for Connecticut drivers. Since this is just a primer, I haven't touched on more advanced topics such as yield signs (HINT: they are not the same as stop signs, but the right-of-way rules are the same) and merging into freeway traffic (HINT: it is very dangerous to try to merge at 40 mph when the traffic is traveling 60-80 mph--ramps and acceleration lanes are there for a reason). We now return you to your irregularly unscheduled blog posts.