Re-Introducting Z-Score and the NFL

What is Z-Score?

Z-Score is a common statistical way of standardizing data on one scale so a comparison can take place. In Layman’s terms, it is a number value assigned to something that shows how far above or below average something is within a group.  It normally operates on a scale of -4.0 to +4.0 where 0.0 is average. 0.0001 to 0.9999 is above average. 1.0 to 1.4999 is good. 1.5 to 1.9999 is great. Above 2.0 is elite, and above 3.0 is extremely rare. The same goes for the negative end of the spectrum. Typically, below -1.96 is considered in the bottom 5% of the set, and above +1.96 is in the top 5%. Anyone sporting a season Z-Score above +1.96 should be considered for league MVP.

(Discuss this on the BSL Board here.)

How do you find a Z-Score?

Z-Score = (Sample value – Sample mean) / Standard deviation

Sample Value:  The statistic in question
Sample Mean: The average value of all statistics measured in the group
Standard Deviation: This site spells it out better than I could 
 

This seems like a lot of math, no?

Yes, of course. However, the information was plugged into Microsoft Excel for the all of the difficult math, and to ensure accuracy. When has a computer ever screwed up?

Why are you introducing us to this?

I learned about Z-Score in a college level statistics course. In class we would go through problems figuring out Z-Scores pertaining to heights of trees in a park, weights of elephants in the circus, speed of turtles in a race. As enticing as all those fictional scenarios sounded, I thought to myself, why don’t I figure out Z-Scores for things I love, like sports? I started tinkering with the numbers, playing around with different statistics, and voilà! With the help of friend and former BSL contributor, Daniel Bryden, we have come up with this new way of measuring players.

Nearly 7,200 NFL player’s individual seasons measured later… We bring you NFL Z-Score.

How does this pertain to the NFL?

Instead of heights of trees in a park, I used samples of quarterbacks, running backs and receivers (including tight ends) in a season. For example, for quarterbacks, like heights of trees in a park, one of the samples was completion percentage in a season. In a season where the sample average completion percentage is 60.78%, a QB who posted that number would earn a Z-Score of 0.0 for this stat. If his CMP% was above the sample average, his Z-Score will be higher, and vice versa for lower than 60.78%.

Is this just a seasonal statistic?

No. However, measuring the best seasons is how it all began. Since myself (Michael Randall) and the real brains behind the operation (Daniel Bryden) joined forces to try to perfect this model, It will be known here as the Randall-Bryden Z-Score, or RBZ for short. We have done this for each season, which will be known as sRBZ. The hope is to also do this on a per game basis (gRBZ) career basis (cRBZ) and past five season basis (5RBZ).

Which samples were used for each position?

To find sRBZ, four of the more important, most telling statistics were accounted for. They are:

QBs: CMP%, Y/A, TDs per game. TD/turnover ratio
RBs: Scrimmage yards per touch, scrimmage yards per game, TDs per game, fumbles per touch
WRs-TEs: Rec/game, Y/Rec, Y/G, TDs per game
 (These were also the easiest to pull in bulk from Pro-Football-Reference.com).

Four Z-Scores were assigned to each player in each season. A correlation was made between all four to find one overall Z-Score assigned to the player for the season. When dealing with a large sample, like an entire season, we felt it was important to use all stats that were divided by something. (This will change for gRBZ where the individual game stats are much smaller in comparison).

Which seasons were measured?

Every season since 1950 was analyzed. I chose 1950 because it seemed like around then that QBs became a little more conventional. Before then, halfbacks took quite a few snaps, QBs didn’t throw a lot, and it would have made for some small samples. 1950 is a nice round number as well. However, you would like to have at least 30 samples to measure in an exercise like this, and for QBs, 30 of them didn’t qualify for measurement until around the merger.

Why were only offensive players measured?

No disrespect to defensive players, but the statistics gathered on the defensive side of the ball is very limited and vague. Different record books list tackles differently. Just because a CB leads the league in INTs, does it make him better? Some CBs do such a good job in coverage they rarely get thrown to. Until the advanced stats have come along, those things can’t be accounted for. The advanced stats only go back about seven years as well.

Where was the information gathered?

Information was gathered from Pro-Football-Reference.com. Qualifying players for this exercise were determined by PFRef standards. (QBs – 14 attempts per team game played, RBs – 6.25 rushes per team game played, WRs-TEs – 1.875 receptions per team game played) However, when this exercise was completed, WRs had a large advantage over the competition, because the qualifying number for players in a 16 game season was 30 catches. Since some seasons had well over 100 players notching 30 catches, and Z-Score is a measure of distance from average, the average was brought way down by the large number of mediocre WRs who “qualified”, meaning the good were made out to look much greater than they might actually have been. So I used double the number of teams in the league for the number of qualifying receivers. In a perfect world, it would be each team’s top two receivers, not including RBs. In most early years, not enough receivers even qualified so this wasn’t an issue.

What about quarterbacks who run and running backs that catch a lot of balls? Won’t their numbers not measure up to the traditional guys?

That is why stats like cumulative passing yards and rushing yards alone were omitted for sRBZ. Using Y/A for QBs takes scheme out of the equation, while still evaluating what QBs are asked to do. Throw the ball. Running QBs can still have a high Y/A number.  For RBs, scrimmage yards were measured rather than rushing yards alone. Also, players were only measured among their positional counterparts. So if a running QB qualified for rushing stats by amassing enough carries, he wouldn’t be measured with the RBs as well in this exercise. The same holds true with RBs who catch enough balls to qualify with the receivers.

That sounds great. But what does it all mean?

Since Z-Scores are a measure of above or below average, you could say I have found who had the best and worst overall seasons. When we reveal single game Z-Scores (gRBZ) We will find each players best and worst games in their career by assigning a game score of sorts to each game. This would take a lot of effort, so for now, we’ll just do it for Ravens players. This is a Baltimore centric site.  

What about the different eras of the game?

Z-Score standardizes the data, it does take into account the era players played in as well, for example:

Minnesota  Vikings QB Randall Cunningham in 1998 ran one of the most prolific offenses of all time. He was a first team All-Pro and led the league with a 106.0 passer rating that year. Cunningham was 2nd in the league with 34 passing TDs (35 total). 60.9 Completion %, committed just 12 turnovers, and 8.7 Y/A.

Turn back the clock to 1955 when passing wasn’t as big a part of the game. Browns QBs Otto Graham posted a 53% CMP%, 9.3 Y/A, 21 Total TDs, 15 turnovers. He threw for 1721 Yards in a 12 game season.

Cunningham passed for nearly 2,000 more yards than Graham in just four more games. On the surface, Cunningham’s numbers are far and away better with 14 more TDs, three less turnovers, only Y/A favors Graham.

Otto Graham’s 1955 season Z-Score: 2.5895
Randall Cunningham’s 1998 season Z-Score: 1.8685

98’ Cunningham finished seven spots behind 55’ Graham on the overall list. This is because of the era. Yeah, the Vikings offense was one of the best and he was the general of it. But a lot of teams were scoring points by this time in NFL history. Passing had become more prolific, and the game is easier for receivers by then. Players are turning the ball over less, so possessing it more, and racking up more stats.  Check out these QB sample averages:

1955: CMP% – 48.71%, Y/A – 6.858, Total TDs – 13.83, TD/Turnover – .675
1998: CMP% – 56.69%, Y/A – 6.848, Total TDs – 18.07, TD/Turnover – 1.035
2013: CMP% – 61.34%, Y/A – 7.15, Total TDs – 21.54, TD/Turnover – 1.362

The same applies for comparing different positions. I feel like you can’t really compare a player with 4,000 passing yards to one with 1,500 rushing yards. But when you assign a simple number value to each player’s important collective stats, sure you can. 1.9 is in fact better than 1.8, no matter what you are measuring.

Ok, so where do we go from here?

We’ll unveil the notable players and their seasons here one decade at a time, starting with the 1950s. In each unveiling we’ll take a look at the best and worst seasons according to Z-Score. We’ll see if there is any alignment with the MVP winners, the Champions from that decade. Who played poorly for great teams and who played great for awful teams? This is a Baltimore driven site, so we’ll be sure to point out the notable Baltimore Colts and Ravens when necessary.

Also, this is something that we’ll be able to keep track of throughout the season in 2014. Everything is a trial, so who knows if weekly will work, or monthly, but periodically throughout the 2014 season we’ll figure out the current Z-Scores and we’ll be able to see who stock is rising and falling, and who is on pace for an all-time great, or not so great season. 

Has anyone else done this?

Scouring the internet, I found some examples of folks who did maybe one stat for one position for one year. I’ve seen articles where folks have done this with career numbers, but those are cumulative and thus not telling you anything, and a bit flawed. (See the Cunnigham/Graham comparison as to why cumulative yards don’t work). But no one that I have found has gone nearly as in depth and as committed as this compilation is. Again, 7,180 players’ seasons spanning 63 years and counting!

I hope everyone enjoys it, and keep one thing mind. No stat is perfect. Not even this one. It is just one more tool for the tool box. One more number to throw out there during your bar stool debates.

Its sports, numbers, and fun; nothing more and nothing less. Enjoy!

 

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About the author


Mike Randall   

Ravens Analyst

Mike was born on the Eastern Shore, raised in Finksburg, and currently residing in Parkville. In 2009, Mike graduated from the Broadcasting Institute of Maryland. Shortly after he started up a Baltimore area sports blog called The BOHpen. Mike became a Baltimore City Fire Fighter in late 2010.


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