What is Z-Score?

How do you rank the best players in any sport? With so many variables involved, players who excel in different areas of the game, players at different positions, it’s hard to tell. In baseball, do you value hitters over pitchers? Maybe pitchers more than hitters. Do you base your rankings on getting on base, or hitting for power? What about football? Who was the better player in 2012? Adrian Peterson or Peyton Manning? Two different positions. How can you compare quarterbacks to running backs? How do you compare players of different eras such as Tom Brady to Johnny Unitas? Apples and oranges, right? People in Baltimore will take Johnny U every day of the week and twice on Sunday. Folks in Boston would tell you Brady is the better of the two. But how can you really tell?

You can only value how great a player is against the competition they played with and the era they played in… Until now…

It’s called Z-Score. A formula taught in many college level statistics courses. “A common statistical way of standardizing data on one scale so a comparison can take place,” according to the textbook. Z-Score is a measurement on a scale of -4.0 to +4.0 of how far above or below average something is. Zero being average. Over two is very good, hall of fame like. So because you assign this value to the players existing stats, you can apply it to any sport.

So for example, Drew Brees broke Dan Marino’s record for passing yards in a season in 2011 with 5,476 yards, to Marino’s 5,084. Does that make Brees the superior QB? Variables include the era they played in. It’s a passing era these days as 3 QB’s tossed for over 5,000 yards in 2011 and 10 tossed for 4,000 yards or more. In 1984 when Marino set the bar only three men tossed for over 4,000 yards. (Phil Simms and Neil Lomax). Also consider that Marino did it in 93 fewer passing attempts. It’s like Brees had an extra two or three games worth of passes to set his mark. Brees threw slightly less INT’s (17 to 14) but Marino threw slightly more TDs (48 to 46). So what do you go by to rank these two performances?

First, you have to examine to total package of a player. Efficiency is what makes the best quarterbacks. Guys who complete the highest percentage of their throws which moves the chains. Guys who get the most yards out of each attempt which also moves the chains.  Guys who keep the ball out of the other teams hands and end drives with TDs. Agreed? What good is a QB who throws for 5,000 yards if he throws 20 INTs, and doesn’t even complete 50% of his passes?

So I found the Z-Score (how far above or below average) for each player using four of the most important categories pertaining to QBs. Completion percentage, TD/INT ratio, yards per attempt, and passer rating.

1984 League averages

Comp %	Yds per Att	TD/INT	QB Rating
57.246%	7.296	1.265	78.854

2011 League averages

Comp %	Yds per Att	TD/INT	QB Rating
59.697 %	7.224	1.773	84.241

So if you are a QB who had a 59.697 completion percentage in 2011, your Z-Score for that statistic is Zero. Above that your Z-score would be in the positive, below that it would be in the negative. Good so far?

Using an Excel spreadsheet to do the complicated math, you subtract the mean (average) from each player’s statistic in question giving you their deviation. Square each player’s deviation. Add all of the squared deviations up, take the sum and divide by the number of players minus 1. Take the square root of that number and divide each player’s original deviation by it, and you get their Z-Score

1984 – Dan Marino

1984	Comp %	Yds per Att	TD/INT Ratio	QB Rating
League Average	57.246%	7.296	1.265	78.854
Dan Marino	64.2%	9.0	2.824	108.9
Z-Scores	1.496067	2.36148	2.363285	2.541354

Average the four Z-Scores, Dan Marino’s overall Z-Score in 1984 was 2.191796. Best in the league. Second best was Joe Montana at 1.869571. Who met in the Super Bowl in 1984 again? Marino and Montana. Funny how that works out.

2011 – Drew Brees

2011	Comp %	Yds per Att	TD/INT Ratio	QB Rating
League Average	59.697 %	7.224	1.773	84.241
Drew Brees	71.2 %	8.34	3.286	110.6
Z-Scores	2.402954	1.245076	1.182203	2.040788

Average the four Z-Scores, Drew Brees’ overall Z-Score in his “record setting” year of 2011 was 1.717755. Not a knock on Drew Brees, 1.71775 is very good. But it isn’t higher than Dan Marino’s 1984 Z-Score, and not even the highest Z-Score of 2011! That would go to Aaron Rodgers at 2.873904. So given the each era and quality of QB’s in the league, Aaron Rodgers was better in 2011 than Dan Marino was in 1984.

What made Rodgers Z-Score so high? His 9.25 Yds/Att, 45 TDs against only 6 INTs and a 122.5 passer rating are all off the charts ridiculous good.

But who went to the Super Bowl in 2011? Eli Manning and Tom Brady. Brady posted the 3^rd best Z-Score at 1.385714. Eli Manning came in 7^th at 0.565798. That tells you that Manning had the better team around him. Teams win games. Teams win Super Bowls. In 1984, the best quarterbacks led their teams to Super Bowls.

Where am I going with all of this, and how does it pertain to Baltimore? Well, we know that Joe Flacco had a pretty good postseason. Good enough to be mentioned in the same breath as Joe Montana with 11 TDs and 0 INTs. So according to Z-Score, where does his post season performance rank all-time?

Joe Flacco posted a 1.434683 Z-Score in the 2012 postseason.

Eli Maning, 1.081681 in 2011.

Aaron Rodgers, 1.054213 in 2010.

All three the best Z-Scores of their respective postseasons, all three Super Bowl Champions.

Small sample size, but I haven’t done the other years yet. Stay tuned for that to see where Joe Flacco ranks in all-time postseason performances.