Let's say you have a friend moving to the United States from China. This guy likes living in a city, so he's thinking about moving to Washington, DC. You advise against it, and instead point him to Alaska, because more people live in Alaska than DC, so clearly has the better city environment.
Now let's say you have a friend from Japan in the same situation, except they want to live in a warmer climate, Florida to be specific. They also love the city life, and want to live in the biggest city possible. Again you do research, and this time you advice him to move to Jacksonville, since it's the largest city in the state, having over twice as many people as the second-place Miami.
The two examples above are clearly absurd. DC and Alaska may be similar in population, but their size differences make the actual living experience quite different. In this case, it's the population density that matters. It's the reason Rhode Island isn't considered the middle of nowhere while Montana is, even though they have almost the same number of people living there.
The second example shows a similar fallacy, but in the other direction. People would be surprised to find that Jacksonville is the largest city in Florida (not Miami), Kansas City is the largest city in Missouri (not St. Louis), and Columbus the largest in Ohio (not Cleveland or Cincinnati). That's because the true size of a city isn't the people just in the city, but the metropolitan area. In terms of metro area, Miami is far larger than Jacksonville.
This should be obvious, but people make the same kinds of mistakes when trying to analyze football players. Without really thinking about it, people cite touchdown numbers to back who they think is a better runningback. But what they miss is that touchdowns usually aren't created in a single play, but are instead formed after a succession of plays that allow a team to be close enough to the end zone to score.
Take for example our game against the Rams in 2010. In the 4th quarter Jamaal Charles had an 80 yard run that took our offense from our own 18 to the Rams' 2. The next play Thomas Jones ran for 2 yards and got the touchdown. In that situation, Charles was clearly the player who created that touchdown, but Jones got the touchdown to put on his statistics.
Just like the population of a state can be misleading in describing the city life, so too can touchdown stats mislead you into believe good players are bad and vise versa, because who scored the touchdown tells you very little about how much that player contributed to actually creating it. Sure, good players tend to have lots of touchdowns, just like big states tend to have big cities, but because it doesn't directly measure the player's skill, it is not a very good stat to use in determining who the best players are.
The same goes for total yards. Sure, good quarterbacks and runningbacks tend to have lots of yards, but it is not always the case that a player with more yards is the better player. Total passing yards correlates well with total passing attempts (obviously the more you pass, the more yards you have), but having a lot of passing attempts doesn't mean you're a good quarterback.
Teams tend to pass more when they're down and run more when they're winning. That's how you can have Matt Cassel throw for 469 yards in a single game, a feat Tom Brady has only done once in his long, Hall of Fame career. In that game we were down by a huge margin very early in the game, so Cassel got plenty of pass attempts. It's also why he was 3-3 in games where he passed for more than 200 yards, and 7-2 in games where he passed for less than 200 yards. (You can find a similar trend with almost any other QB in any given season.)
The solution is to see how many yards the player gets on a per play basis. This stat eliminates some of the external noise like game situation. In the 2010 Cassel example, he was 5-1 when above 7 Y/A and 5-4 when below 7 Y/A. He was also 3-0 when above 9 Y/A and 2-2 when below 6 Y/A. There are still problems with using this statistic, mainly that big plays can skew it, but it is still clearly superior to total yards.
The biggest problem when analyzing football statistics is that we're trying to measure how good an individual player is, but how well a player performs depends heavily on how good the talent and coaching around them are. There's a reason Priest Holmes wasn't any good until he came to Kansas City, and then became a star behind our amazing offensive line. Then, when that line started to retire, Larry Johnson went from super star to worthless.
That is a problem that is difficult, if not impossible, to solve using just statistics, and is the biggest thing stopping a team from being the NFL Moneyball. So when you have noise that is impossible to remove from the data, why would you want to use stats, like total yards and touchdowns, that introduce even more noise?