Maybe not cheap but they (the Bears) do kinda suck

The issue

This little tidbit was inspired by a party conversation during which I was engaged mostly as an innocent bystander. The topic was why the Chicago Bears suck. That the Bears currently suck was not in dispute. However, the question was, do the Bears suck in general, and if so, why.

The main interlocutors, Robert and Mike, agreed that the Bears suck both currently and in general (btw, both are Bears fans, I think). But they disagreed on why they suck. Robert’s theory is that the Bears management suffers from 1) craptacular judgment and 2) a case of the cheaps. Not only do they mismanage the team but they are unwilling to shell out the dough to get good players. Mike concurred with 1) but not with 2). Presumably, that the Bears are craptacular managers is not in question. Rather, are they both cheap and craptacular?

That brought to my mind a different but related set of issues. Can you buy wins in the NFL? That is, is there a statistically significant relationship between money spent on player salaries and number of wins in a year? Furthermore, assuming that there is a statistically significant relationship, who manages their money the best? Which teams are best (or worst) at converting money spent into wins, and how good (or bad) are the Bears at that conversion?

The best way to figure all this out is to build a regression model relating salaries to wins and then use that model to create a benchmarking framework. Sounds fancy, huh? It’s actually simple and can be done in 3 (more or less) easy steps: 1) gather data; 2) get Excel to regress wins against salaries; 3) see what the results are and then see how many wins the Bears should have given the amount of money that they spend.

What the data says (NFL seasons 2000-2008)

A quick Google search brought me to the USAToday website which, fortunately, had salary data for all NFL teams from 2000-2008 (actually all the way back to 1910)/ Unfortunately, it was in html table format (rather than Excel). And also, unfortunately, the salary tables didn’t have corresponding data on wins, which meant I had to input by hand (oh the things I do for science!). Several hours, ermmm, I mean, a bit later, I had the dataset ready (o.k., yes, I’m a nerd). Here are a few highlights:

A) Total money spent on NFL player salaries from 2000-2008: $23.8 B (yes that’s B as in billion; for perspective, that’s the amount required to bailout Dubai)

B) Maximum any one team spent: $785.7M by Washington Redskins

C) Minimum any one team spent: $687.7M by Green Bay Packers (excluding Houston Texans who entered the league in 2002)

D) Bears total salary in period: $770.2M, which ranks them 7^th in spending among all 32 teams

On the surface, maybe Mike was right. 7^th place puts the Bears in the top quartile (top 8 teams) who are willing to spend on players. Maybe they are not so cheap after all.

But there are a couple of problems with relying on total salary. Total salaries are in nominal values, meaning, it doesn’t take into consideration the rate of inflation (i.e., a dollar in 2000 was worth more than a dollar in 2008). Compounding this is the fact that while the annual rate of inflation from 2000-2008 was 2.83%, the annual growth rate of NFL salaries was 10.15% -- a whopping >3.5X more.

This growth in NFL salaries would have the effect of inflating the nominal value of any moves made by a team in the later portion of the 9 year period. Lets say you’re comparing the Bears and the Rams. Suppose the Rams made their big move (i.e., paid for lots of good players) from 2000-2004, while the Bears made their big move from 2005-2008. Suppose also that the Rams and Bear got the same types of players (i.e., equal number of equally high-skilled players) only at two different periods of time. Because of the NFL’s salary inflation, the Bears would have had to pay a higher nominal amount for the same types of players.

When comparing nominal values across time, you’re actually comparing apples to oranges. To compare apples to apples, we need a way to convert nominal values across the different years into a single comparable measure.

Enter standard deviation

Standard deviation (st. dev.) takes the average of a set of numbers and measures the distance between a particular number and that average and then converts it onto a normalized scale or score. In terms of NFL salaries, it allows us to measure the distance between any particular team’s salary on any given year and the average NFL team salary for that year. It will also allow us to compare salaries across years since, for example, a score of 2.6 st. dev on year 2000 is comparable to a score of 2.6 st. dev on year 2008.

Any positive st. dev. score indicates that a team is spending more than the league average. Any negative st. dev. score indicates that a team is spending less than the league average. If there is a relationship between the amount a team spends and its ability to win, then we should expect that the higher a team’s st. dev score is, the higher will be its winning percentage.

The equation for this is: winning% = constant + spendcoeffficent*st. dev. score.

Winning% is just the expected percentage of wins for a team given the amount of money that team spent. The constant is the percentage win that a team should expect if they are spending the exact league average (i.e., st. dev. = 0). In fact, we can guess in advance that the constant will be 50%. Why? Winning in the NFL is a zero-sum game, which means that if someone wins, someone else has to lose. Because it is a zero-sum game, the average NFL winning percent should be 50%.

The key is the “spendcoefficient,” which indicates the percentage point increase of winning per additional unit of st. dev. If a team spends 1 st. dev above the league average, it should expect to gain an additional spendcoefficient winning percentage points above 50%. If a team spends 1 st. dev. less than the league average, it should expect to be that spendcoefficeint winning percentage points below 50%.

The model

Phew, that’s a lot of info. Now here’s the regression result.

Winning% = 49.9% + st. dev. score*3.01% [at 0.9165% significance level]

Seems so anticlimactic, and yet, oh so satisfying a result! What this tells us that for each st. dev. unit above (or below) the league salary average, a team should expect to gain (or lose) 3 winning percentage points per year, which translates to ~1/2 a game (or 16 games*3%). If your team is 2 st. dev. above (or below), then you should gain an extra win per year. In short, spending 2 st. dev. should be the difference between going 9-7 and going 8-8, which can be the difference between getting into the playoffs or not (will test that out in another model).

Further, with a significance value of 0.9165%, the model confirms that salary spending is a statistically significant variable (in general, anything below 5% is considered statistically significant).

Benchmarking: where do the Bears stand compared to other teams?

Now that we know spending is a statistically significant variable, we can use it to show how much the Bears should be winning (i.e., make a prediction) based on how much money they have spent. In fact, we can do that for the whole league.

The chart above plots each NFL team’s winning percentage against their average st. dev. score for the 2000-2008 seasons. I’ve divided the chart into 4 quadrants with labels that I hope are self-explanatory. Accordingly, the Bears are located in the “Moderately good” category, which means that they are willing to spend a greater than average amount of money and are achieving a greater than average winning percentage. But are they winning at a rate they should be given how much they are spending?

The dashed diagonal line indicates the level of winning team should be given the amount its willing to spend. Being above that line means a team is overperforming, while being below means that it is underperforming. The further toward the right you go on the chart, the more willing a team is to spend, while the further left you go the less willing a team is to spend. The team most willing to spend has been the Redskins; the team least willing to spend has been the 49ers.

The Bears rank 6^th on willingness to spend. So, in fact, as Mike thought, they haven’t been cheap at all. On the other hand, the Bears are well below their expected winning level. How far below? By ~6.5%. Translated into games, that means that the Bears are winning on average a full game (~1.04) less each season than they should given how much they have been willing to spend. Their actually average wins per season is 8.22, while their expected wins per season is 9.22.

We can do this for every team and show how well they over- (or under-) performing relative to how willing they are to spend by calculating the difference between their actual winning percentage and their expected winning percentage (a positive winning percentage means they are overperforming, a negative that they are underperforming). Here a list of the top (and bottom) over (and under) performers as well as where the Bears fit in:

Top 5:

1. Patriots

2. Packers

3. Titans

4. Colts

5. Broncos

…

22. Bears

…

Bottom 5

28. Raiders

29. Redskins

30. Cardinals

31. Lions

32. Texans

Ranking in this way shows us which teams are getting the most bang for their bucks, that is, the best at converting the money they do spend to actual wins, as well as which are the worst. The rankings are probably not very surprising, but they do show the Bears at 22 – that is, they are the 22^nd best at converting dollars into wins, which is approach suckiness.

But the chart does show a few other interesting things. For my money, the best place to be in is the upper left quadrant, i.e., the “Very good” who don’t spend a lot but win anyway. Here are located several mid-market teams, i.e., Packers, Titans, Broncos, and Buccaneers, which is not surprising since they are likely to be salary constrained. However, there are also two big market teams in the “Very good,” namely, the Patriots and Giants. Moreover, there are at least two mid-market teams, i.e., Colts and Steelers, who are in the "May suck" quadrant, and who seem willing to pay big market salaries. However, since both these teams have won Super Bowls in the last 5 years, its hard to say they really do suck.

In terms of Super Bowl championships, 56% of the Super Bowl winners spend more than the league average while 44% spent less. Draw your own conclusions.

The suckitude of the Bears

So we come back to the original question, do the Bears suck because they don’t spend money or do they suck despite spending money? The simple answer is they aren’t cheap (well that’s a relief), but they are underperforming (doah!!!). In fact, they don’t really suck, if your measure for performance is staying above 500. However, they do suck if your measure of performance is winning percentage relative to how much they are spending. In other words, they may suck, but they aren’t cheap (sorry Robert).

The Bears just are not getting the same bang for the buck as, say, the Packers, who are winning 21.8% more than they should given their payroll (btw, that translates into winning 3.5 more games than their expected win per season, which is ~6 wins). Meanwhile, the Giants and Patriots are successfully getting away with not having to pay the big market salaries of other big market teams, e.g., Bears and Eagles.

All about the Benjamins?

Obviously, winning in the NFL is not all about money, otherwise, all teams would be right on the dash line. Baked into the difference between actual and expected win percentage are the intangibles, things like quality of management, leadership, and coaching, as well as luck with injuries (btw, if someone can find injury stats by team by year, I can work that into the model). However, according to this model (granted, it’s a very simple model), we conclude that the Bears are 22^nd best in those intangible qualities.