Which Goal is the Biggest in a Hockey Game?

We intuitively know that not all goals are equal in terms of helping our team win. If we are winning 7-0, we already have such a massive lead that scoring an eighth goal is not going to increase the likelihood of us winning much. But how many goals will our team have to score to pick up a win? And which goal is the biggest?

From their listing of the 1230 games from the 2013-14 season, Hockey‑Reference.com can help us figure this out. We (er, Excel) can count the number of games in which each team scored X number of goals, which looks like this:

Games Per Goals Scored

This same info tells us that the average team scores 2.74 goals in each game. And while we’re at it, the standard deviation is 1.58. So teams are scoring 2, 3, or 4 goals in about 2/3 of their games. Not exactly breaking news.

Let’s get to the wins though. Unsurprisingly, as goals increase so too does win percentage:

Win Percentage Per Goal

I probably do not have to explain that teams who never scored, never won and teams who scored six or more times always won. That is the part we understand before looking at any numbers; we are after what happens in between. Teams who scored once only won 8.4% of the time; not surprising considering they would need to shutout the other team. Teams who scored twice—the most common goal total—won just under one-third of their games. Scoring that second goal increases our win percentage by 22 points (8.4 to 31.8), which makes sense given the added leeway; we can still give up a goal and get the W.

Our biggest jump in win percentage, however, comes in our third goal. Whereas two-goal teams won just under one-third of their games, three-goal teams won just under two-thirds. It is a 32-point jump in win percentage, which is a larger boost than any other goal will give a team on average. Teams that score four goals get another nice 19-point boost of, up to an 82% chance to win. Beyond that, teams win such a high percentage of the time that there is not much room for an extra increase and we arrive back with the intuition we began with—scoring six goals or more means you are going to win, at least for the 2013-14 season. Here is all of the data if you’re curious:

Goals Scored, Win Percent Data

All we have done is quantify what we already knew: Scoring more goals increases our chances of winning. Perhaps you will cheer a little more after that third goal from now on though.

A Guide to Good Graphs

There is a lot of data out there nowadays and whether it is an article or a PowerPoint, a good visualization helps to make sense of it. Unfortunately there are a lot of bad graphs out there too. There are a few reasons for that, the first is that few people really think about graphs (like we’re about to). The second is that most of the graphs people see are garbage, so they don’t really know how to make a good one even if they wanted to.

Here’s a few suggestions to hopefully fix that.

First, we have to pick what kind of graph we are going to use. Microsoft Excel gives you more than enough options to choose from. Bar, column, line, pie, area, and our old friend the scatter. Frankly, some of these should never be used (I’m looking at you Bubble with a 3-D Effect). I don’t care if you think your classmates will be blown away with a donut chart, column and line will take you pretty far and that is fine. Why? We don’t want your classmates to notice the graph.

Rule One: It’s not about the graph

Graph or otherwise, every time you communicate with another person you should have a simple task in mind. What is the point I am trying to get across here? When we are finished this should be as clear as possible.

The people who create the special effects in movies spend months working on computer-generated imagery. If they do their job well you will not notice any of their effects because they will look so real you will be absorbed in the story. We want people to see the information you are showing via the graph, not the graph itself.

Peyton Manning recently set a new NFL record for touchdown passes, so let’s make a graph to show how he compares to the other top TD throwers. If you put the info into Excel, highlight it, and click Column Graph it gives you this:


You can click on any graph to make it bigger.

I have a negative physical reaction to graphs that look like that. A few paragraphs from now I hope you will too. It’s vulgar. I don’t blame Excel, it needs some sort of default, but that doesn’t mean it is good enough for us to slap a title on and use. The onus is on us to know that this is a starting point and it will take some work to make it look good.

Let’s fix this up some. Our first rule was that it’s about the info, not the graph. In this situation, we are using the graph as a means to display the information in a better way than a list:

  1. Manning – 510
  2. Favre – 508
  3. Marino – 420
  4. Brees – 374
  5. Brady – 372
  6. Tarkenton – 342
  7. Elway – 300
  8. Moon – 291
  9. Unitas – 290
  10. Testaverde – 275

As we can see though, our default graph is not much of an improvement over the list. It is clear Manning and Favre are the top two, but we could have seen that on the list. Our graph does show that they lead everyone else by a pretty good margin, but it’s difficult to say by just how many (or how far apart the two of them are) so in some respects the list is actually a better way to portray the info. We can change that though.

Let’s make this big enough to see, without distorting the content. Make your screen look something like this:


Pro Tip: If you are making more than one graph for a project, keep them all the same size.

This also applies if you are putting your graph into PowerPoint presentation. It should not cover 100% of the slide, but you the graph should be the only thing on the slide, so make it big enough to see.

Next we’re going to delete the “Series 1” label. We only have one thing we are talking about here, touchdown passes, so we do not need to point that out anywhere other than the title. The second thing we need to do is add that title, which should be as brief as possible (we’ll be using the Layout options under Chart Tools a lot).

Like a lot of writing, the title should be as brief as possible without leaving out any key info. Rarely will you start with “The.” You do not have to say “top ten” because there are only ten names on the graph. Unless there is some meaningful threshold, it is implied. Abbreviations, like TD in this case, are fine. So let’s use “Most TD Passes, NFL History.” Also, the comma is your friend in graph titles.


Rule Two: Delete all irrelevant information

There is a reason why so many people love the design of Apple products: they get rid of everything they can. Jonathan Ive, one of Apple’s lead designers said of the iPad, “In many ways it’s the things that are not there that we are most proud of.” We don’t want people to spend time figuring out how the graph works, we want them to be absorbing the information, remember rule one.

Look at this bad graph I found:


Some guy thought adding a 3D effect would end up making his graph complex and him look smart. What it did was made the info in the graph impossible to read and him look like a dufus. Quick question: What was the profit made on hammers in February? If it takes you more time to figure that out than read this sentence, you fail. And you will fail, because the angle is such that you have no chance to figure it out no matter how long you stare at it.

It is easy to make a graph look 3D, to add gradients, to bevel edges, or use a drop shadows. Do Not Do That. I have nothing against drop shadows, but they do one thing on graphs: Distract the audience from the information. Let’s add some drop shadows:


Again, click on the graph to see it full size.

Does it make it look nicer? If you are saying yes, you have forgotten rule one. If there is drop shadow, people are going to be looking at drop shadow, and if they are looking at drop shadow, they are not paying attention to the information we are trying to show.

Same thing goes for 3D, only it is worse.


Not only does it make the graph more difficult to read, but again the perspective distorts how the columns line up—note that Elway’s bar looks like it is under 300, even though he has thrown 300. What’s the point of having the graph if it is not accurate?

But you might protest without any added effects it looks plain and boring. Does the iPhone look boring with its one button? Because they still are not struggling to sell those. This is not to say we are going to leave it like this, because it is difficult to read.


Brief Detour: Best Graph Ever

This is not to say we can never use complicated graphs if our audience is comprised of people willing to take the time to digest the info. (The 1% of the time your audience is this select you will know it, the other 99% of the time we should strive to make things as simple as possible.) One of the most famous graphs ever made was for a select audience, it is this one about Napoleon’s army:


A guy called Charles Joseph Minard came up with that in 1869 (he was probably not using Excel) and one guy said it “may well be the best statistical graphic ever drawn.” Another guy wrote a whole freaking book about it. A third guy made a video you can watch about it:

That’s a great YouTube channel, by the way.

On first look it can be confusing, but Minard knew that anybody into Napoleon enough would take the time to digest the info. Even with five pieces of info, he was still able to make it simple enough that most people could understand it after a few minutes of explanation. What if Minard had thrown a drop shadow on there?


The author regrets having to alter such a great graphic, but felt it was important for educational purposes.

Add much? Didn’t think so.

Rule Three: Details are important

It can take a while to understand the following: Font matters. It has a much bigger impact than you may think. The packaging of our graph is important—it is not just what we are saying, but how we say it. Trying to get cute by using a creative font often makes things more difficult to read. So let’s pick a clearer and larger font for our names and numbers. And we can do the same thing for our title (although it doesn’t necessarily have to be the same one).

This graph gives us more whitespace on the right side, so we can also move the title over a bit. It does not need to be smashed against the top of the box; give it some room on all sides. The title is going to be bold by default, but get rid of that because it is clearly the title and does not need any further emphasis. Having the title look good and in a better location than the default can go a long way in the overall presentation of the graph. Sweat the small stuff.


And now for our most drastic departure from the mainstream world of terrible graphs yet: Data Labels. We noticed earlier that it is difficult to see the real difference between Marino and Favre or even Manning and Favre, so why not actually include the actual numbers? You can find the Data Label button under the Layout tab (I almost always use Outside End because you are going to be looking at the top of the columns most of the time).

We have plenty of space to include these numbers on a chart with only ten columns, so let’s make them the same font as our names. More importantly, now that we can see specifically how many TDs each guy has thrown, our vertical axis is no longer necessary. Remember Rule Two. Let’s delete it and the horizontal lines. This gives the reader the option to look at the specific numbers or absorb then general comparisons as presented by the columns.


Now we’re getting somewhere. Look different than most column graphs you’ve seen? Good. Let’s make sure we include our source on this, which you should always have. While technically this is your source: http://www.pro-football-reference.com/leaders/pass_td_career.htm remember that brevity is key, so we can get away with Pro-Football-Reference.com. If your teacher wants you to include some absurd URL that’s three lines long use a URL shortener or grit your teeth and make it small; such criteria makes your graph look bad, but luckily does not exist in the real world.

This last suggestion may just be personal preference, but I usually make the background black and keep the bars a darker color. At this point, we can throw in a few final touches, like changing the color of the three guys on the list who are still active (football fans should pick up on this immediately), noting when we made the graph, and we have it:


Compare that to where we started and we can see that not all graphs are created equally:


It took some time for us to get to as simple of a graph as possible—when you think you are finished, it’s not a bad idea to ask yourself what the effect of deleting each element would be while remembering our first rule about having some. All of the text is brief and easier to read, we can tell exactly how many TD passes each guy threw, the addition of our data labels allowed us to remove the vertical axis, and our columns still allow us to view the comparison of QBs visually.

Line Graphs

Congratulations, you have made it through column graphs! Let’s move on to line graphs, although the vast majority of things we discussed already will apply to every graph you make regardless of what type it is. To reiterate the three rules: It’s about the info not the graph, get rid of anything that isn’t a must-keep, and make sure it looks good.

We’ll switch to baseball for our line graph (sorry if you don’t like sports, but they’re full of stats that can be used to practice graphs with). You have probably heard of Ted Williams who was one of the best hitters ever for the Boston Red Sox. Let’s make a graph to see just how good.

We often evaluate baseball players in terms of averages, rather than absolute numbers like our touchdown passes, so let’s compare Williams’s yearly On-Base Average (aka the percent of times he hit and did not make an out) to the league’s average OBA from each season he played. Williams missed the three seasons to fight in World War II and two more to fly planes during the Korean War.


Here is another spot that we can immediately see where size makes a difference.


I also have used the Line with Markers chart, which I prefer when we’re only looking at less than 20 points. You can see without the markers, it becomes difficult to tell one year from the next.


Before we get too far, we should look at why we didn’t we use another bar graph. You can show the same info in multiple different ways, after all, so there is some subjectivity as to which type of graph looks the best given certain information. It is never a bad idea to look through the different styles (Excel makes that easy enough) before you go too far. Here is the same info in a column graph:


It is quickly obvious there are more columns than we had in our first graph, which makes things much tighter and tougher to read. We can still tell that Williams was always an above average hitter. This is helped by the fact that the League average OBA stays steady the whole time. If it were going up and down, it would be much tougher to keep the two straight, especially if Williams had a few below-average seasons. There is not always a clear-cut way, but what we are trying to portray to our audience is the key to deciding: Which style makes it easiest to see Williams’s stats compared to the League average?

Now that we have established a line graph is the way to go we can make the changes that we did with our column graph: Larger, more readable text. Let’s only include every-other-year on the horizontal axis, because that’ll make it less jumbled and it’s still easy to understand. Let’s also change the vertical axis units to the standard way OBA is portrayed (i.e. .400 rather than 0.4). We can make our lines thicker while we’re at it.

Since Williams played for the Red Sox his whole career let’s change our color scheme to match their dark blue and red. If we were working with fewer years I would use data labels and eliminate the vertical axis, but they become too chaotic at some point. The title looks nicer below the lines where there is more space too. Don’t be afraid to move something from where it usually is, people will recognize the title from its font size and style no matter its location.


Our goal here is to show a general overview of Ted Williams’s career and we have done that: Anyone can take a quick look and see that he was far above average every season. If we don’t just want to inform, like we did with the TD graph, but persuade our audience that Williams is the best hitter ever we can make a few slight changes to drive that point home.

First, we can use black markers on the years in which he led the league in OBA. We can also switch the horizontal axis to show his age to make it more personal. This helps us notice that he was 24, 25, and 26 years old during the three seasons he was fighting in WWII—these are prime years for most ballplayers. Not only did Williams miss those seasons, but he returned in 1946 and did not miss a beat. The legend also fits in nicely at the bottom, rather than relegating it over to the side.

One feature that you may think is missing is the vertical axis title. We have the horizontal axis labeled as Age because there may be some confusion over those particular numbers. I would not have added a label for the year, for instance, people assume it is a year when they see “1948.” Because the title of the graph states that we are looking at Williams’s OBA though, I see no reason to repeat that same info in an axis title.


Don’t Do This: Skewing Info

There is an element to both of our graphs that might look better if changed, particularly to someone new to graphs. For example, what if I changed the vertical axis of our TD Pass graph so this happened:


By making the minimum of the vertical axis 250, our column heights have a much larger range. But even while all of the number remain the same, our information becomes skewed. Peyton Manning’s column becomes four or five times the size of John Elway or Vinnie Testaverde’s columns, but he has not even thrown twice the number of TD passes they did.

For some reason FOX News has become known for this type of skewed graph, like this one about people apprehended at the border between the US and Mexico:


Based on the size of the bars, it looks like the number of apprehensions has tripled from 2011 to 2013, but if we look at the numbers we see that is not even close to being the case. You might argue that this is why the numbers are there, but I would counter that if you want to give the numbers, then the graph becomes unnecessary. The purpose of the graph is to give a visual of the numbers relative to each other, which when done properly looks like this:


Obviously the numbers have still gone up, but they have not tripled. It is common to skew graphs (or data in general) like this on purpose to make an argument look better. There is always some balance: We did not, for example, have a vertical axis that went all the way up to 1 on the Williams graph. By making the maximum .600 were we artificially inflating his numbers? Because nobody ever has an OBA above .600, I would argue that we were not. The point of that graph was to compare Williams against the League average, which we did.

The border patrol graph is comparing the yearly numbers to each other though. Each column’s size relative to the others is what matters and what was skewed. You should never purposely skew a graph to make an argument look better. To the contrary, if a graph helps you to see an argument is weak, then maybe you should reevaluate your position.

More on Graph Goals

We looked at using data labels to make specific numbers more clear. Sometimes we can improve a graph by not using them though. Check out this graph that shows the Pittsburgh Steelers’ points for and against over the last decade:


I forgot to note that this was only through the first few weeks of the 2014 season, an element that should have been included.

I purposely left off the markers and data labels on each year because my goal with this graph was to show trends more than any specific numbers. And with a quick glance you can see that it is the defense that has dropped off more than the offense.

This is one of my favorite graphs from the most recent baseball season:


Two things to note: The title is in the form of a question, which makes it longer, but immediately more engaging than “Pirates Chase Percentage.” The second thing is that including the league average line gives it much more context. A single line immediately answers the question “OK, is that good?” in a case where most people will not know what is good or bad.

So one more time: Have a specific goal as to what you want your audience to learn from your graph, delete all info that does not lead to that goal, and make what is left look good. Happy graphing!

Song and a Quote

The effect of music is so very much more powerful and penetrating than is that of the other arts, for these others speak only of the shadow, but music of the essence.

- Arthur Schopenhauer

How a Hundred Year Old Finding Picks NFL Games As Well As the Experts

In 1906 Sir Francis Galton came across a contest at a fair in which people were guessing the weight of an ox that had been chopped up to eat. The person who produced the closest guess would win the meat and presumably not go hungry for a long time. Galton believed that, for the most part, people were stupid and he could prove this by showing how far off their guesses were. Somewhat ironically, while nobody guessed the weight, Galton found that the average of all 800 guesses was only a few pounds off the 1,198-pound weight of the ox.

We now call what Galton had found the Wisdom of the Crowd, and while it only applies to certain topics, we are better off taking opinions from as many people as possible, rather than just asking one person, even if that one person is an expert. Regis Philbin said when somebody on Who Wants to Be a Millionaire? asked the audience, it was extremely rare that the majority would give the wrong answer. So even while most people in the audience will give the correct answer, we would much rather have the option to ask the whole audience than to ask one random person in the audience.

Predicting the NFL

With this in mind, let’s look at the accuracy of betting lines and their ability of correctly predict the outcome of NFL games. Point spreads exist because they make betting on single games tougher. However, if we are predicting the winner straight up, we can use the point spread as a helpful tool (we’ll get to picking against the spread in a bit).

Remember that the guy setting the line is not making a personal prediction on the game. He wants to choose a number that will evenly divide bettors (which is how he earns his money). He can allow the market to guide him and readjust the line if the bets become too one-sided. The crowd will ultimately dictate the line.

The Data

From 2009-2013, the favorite was victorious in 857 of 1269 picked games, which is a 67.5% success rate (even games were not included). Things fluctuated over the years with the success ranging from a low of 64.4% correct in 2012 to a high of 71.3% the following year.

Compare this to the best picker on ESPN’s Pigskin Pick ‘Em Game in 2013, who predicted the winner in 75% of the games. In other words, he picked just ten more games of the 256 correctly than the spread did. The technique of the winning picker is unknown, but going with the odds on every game means putting in virtually no work. Copy and pasting selections would have tied for the 47th overall rank on ESPN, which is still in the 99.9th percentile.

On the other side of the spectrum, in 2012 the favorite picked 163 games, or 64%, accurately. The top picker on ESPN correctly choose the winner in 188 or 73% of games. But even in a down-year, the line still beat over 500,000 guessers.

Accuracy of picks over the years

Wiser Crowds

Using a crowd to pick a game can change depending on which crowd you go with. Ask a bunch of fifth graders and you will not get the same results as bettors who are putting money on a game. The line differed from the majority’s pick on ESPN in 60 games in 2012 and 2013. The line favorite in those games won 37 to ESPN’s 23. This is too small of a sample to draw any conclusions from, but one possible reason being that ESPN’s users are more likely to make risky picks without money on the line.

Degree of Certainty

While every game has two teams, not all are equally difficult to predict. Favorites in games with a point spread of less than three won just 52% of the time, while teams favored by 11 or 11.5 points won 90% of the time. As the spread increases, we find that the chance that team will win the game steadily increases as well.

For simplicity's sake, games with similar spreads (ie. 9 and 9.5pts) have been combined.

For simplicity’s sake, games with similar spreads (ie 9 and 9.5pts) have been combined.

Picking Against the Spread

Picking a winner is one thing, but Galton’s hunch about people being dumb (we’re talking about beer drinking football fans here, not rocket scientists) must fall apart when they come up against the spread, right? Not exactly.

Picking against the spread is tougher: The guy who won Pigskin Pick ‘Em against the spread last year picked 159 games right compared to the straight winner who got 191. Still the masses guide the betting line, which will shift over the week. ESPN sets their lines on Tuesday, but you don’t have to make your pick until game time, which allows a few more days for the crowd to work their magic. And unlike ESPN, virtually all betting sites do adjust their lines as the week goes on.

If the line increases from Tuesday to Sunday (I usually take the average line from multiple sources, thus increasing the crowd size), even if it’s not by much, it would be wise to bet the team will cover. On the other hand, if an injury leads to a decrease in the crowd’s confidence and a shrinking spread, we would be wise to go with the underdog. It is not complicated (nor is taking advantage of “soft lines” new strategy), but it has been right 52 out of 90 times this season, which is better than 94% of about 100,000 entries on ESPN. If you don’t think a day or two will make much difference, note that it has only worked 44 times on Yahoo! where lines are set on Thursday.

How do the Experts Stack Up?

The remarkable thing about the Wisdom of the Crowd is not that the crowd is better than any given analyst, but that the crowd even comes close. When we step back and consider what exactly the crowd is—in Pigskin Pick ‘Em it is anyone with internet access, in Vegas lines it’s anyone with a few bucks—we would probably think most employees of sports networks would be much better than such a motley crew.

PunditTracker.com looked at predictions made by 13 analysts from ESPN and Sports Illustrated from 2009 to 2012, and found that only two, Jim Trotter and Kevin Seifert, were better than the Vegas odds. In a separate 2012 study, they found that on average 23 analysts from ESPN, CBS, and Yahoo (a mini-crowd of analysts) picked the right winner in two more games (165 to 163) than the odds. Recently they looked at 24 analysts from ESPN, CBS, and Yahoo and found that none of them have picked better than Vegas from 2012 through the first five weeks of the 2014 season. As a group they’re 4% worse on average.

As we saw earlier though, the top finishers in Pigskin Pick ‘Em are often as good or better than the experts, so clearly somebody has figured out how to outsmart the masses, right? This really comes down to how many games you are picking. Somebody will win Pigskin Pick ‘Em with a high total, but unless they can perform at such a high level for multiple years, it’s possible they were just lucky. I could accurately pick every game over the whole season with a coin-flips, but that should not make you want to ask me for advice on who to pick (more likely you’d beat me up and steal my lucky coin). Lots of people have perfect weeks, but most cannot maintain that level for more than one week, let alone 17.

Remember when I said that ESPN and Vegas differed on who would win 60 games over the past two years and Vegas has been right in 62% of those? This in no way guarantees that Vegas will be more accurate every season. In fact, ESPN got 13 of the 22 games right in 2012, but Vegas got 28 of 38 right in 2013. So in a dispute who are you better of going with? Obviously we don’t know who is more accurate this season until it is too late.

So Far in 2014

Through the first six weeks of the 2014 NFL season, the line has picked the right team to win in 60 of 90 games, which is right about where it should be based on the last few seasons. The majority has correctly chosen 61 games in Pigskin Pick ‘Em.

The contest has hundreds of thousands of entries coming from people of all walks of life, with all sorts of levels of knowledge about any given football game. Given the choice between them and someone who covers football for a living, you may be tempted to listen to the later. What we find in the numbers though is that the crowds (on ESPN) are actually as good or better than all 13 of ESPN’s NFL experts, all seven of CBS‘s, both of Yahoo!’s, and all four of Fox Sports’ (and their projection software).

The crowd may not help you win your office pool, but surprisingly its track record has shown that if you put aside your ego and stick with the majority every time, you will finish ahead of almost everyone in the crowd individually.

Author Note: I don’t gamble or claim to know anything about it. The preceding is not intended to help you win money, and I’m not sure it even can.

Caption Poetry

Like most single, American men in their mid-20s I spend my Friday nights watching Slavoj Žižek videos. These are only enhanced more by watching them with YouTube’s caption feature, which automatically translates language into words.

The accuracy of the captions is not very good, but when combined with Žižek’s near-impossible Slovenian accent, they are beauty. Here he is talking about movies:

Then that hurt.
Shocked God a chink Egypt pretentions Craig.
Dreams a document that he owned,
A making coffee.
Let ‘em around a movie,
How close we rebuked rich right.

You let him bat about, ok.
Good visual problems making coffee,
Or some freshman she said amish, I think.
Bitch, I like got the Italian because I’m totally theoretically crap.

Gotta go I think it’s much better than the movie.

Introducing Salary+

A few days ago, we found that that the relationship between wins and salary among MLB teams in 2014 was not that strong. Today we’re going to see if that was a fluke or the norm.

Salaries Over the Years

Graphs get bigger with one click!

Because the average team salary has increased by about $40 million over the past decade (and $80 million over the last two), we can’t compare wins to money spent straight up. To address this I have created Salary+, making the league-average salary for each season is 100. If you’re familiar with stats like OPS+ and ERA- you probably get it, skip the next paragraph. If not:

Like salary, most stats change over time. The average hitter in 2000 had a .345 OBP, but the average hitter in 1968 had a .299 OBP. In order to better compare players from those years, we take the player’s OBP, divide it by the league average for that season, and multiply it by 100. So if your OBP+ is 100 you were an average hitter for that year. If you’re above 100 you were above average, if you are below 100, below average. That goes for any stat you see a + after. Conversely we have ERA- because the lower the better, so an ERA- of 100 is average, but 60 is awesome.

Salary+ keeps things proportional, so the R-squared value is the same for each season whether you use the actual dollar value or the Salary+ value. In 2014, the R-squared for salary compared to wins was 0.087, which is not all that strong of a relationship. If we expand our pool back to 1988 (that’s all USA Today had in its database), that gives us 724 team seasons and an R-squared of 0.163. So this season was below average, but clearly there is more to a winning team than spending a lot of money. I left out the 1994 and 1995 as they were shortened due to the lockout.

Salaries vs Wins, R-sqared

I wanted to see how much the relationship fluctuated from season-to-season, so I found the R-squared of each season and plotted them out. In the early 1990s there was virtually no relationship, but it rose sharply toward the end of the decade.

Yearly Salary R-squared

Part of that I would credit to the increasing range of salaries, which doubled from 1992, when the R-squared was at its lowest, to 1999, when it was at its peak. This would seem to lend credence to the thinking that the Yankees (who won the AL from 1998- 2001) bought their way to the top. Since 1988 the Yanks’ R-squared for salary and wins has been stronger than the League-average at .295.

Over the past decade though, the relationship between salary and wins has again been on the decline. Teams with smaller budgets have been able to compete by minimizing their cost per win. Oakland has managed to average 88 wins on an average Salary+ of 66 since hiring Billy Beane. Still, in 2014, five playoff teams in 2014 came from the League’s top third, three from the middle, and two from the bottom. Spending money helps, but it does not guarantee anything: Four of the five highest salaries did not make the playoffs in 2014.

While we’re at it, here are a few more graphs using Salary+. Everyone knows the Yankees like to spend a lot of money, but I never realized it was this much.

Highest Salary+ Teams

And in the interest of symmetry, here are the lowest spenders.

Lowest Salary+ Teams