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BSL: Re-Introducing Z-Score and the NFL


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#1 BSLMikeRandall

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Posted 05 June 2014 - 12:36 PM

http://baltimorespor...ng-z-score-nfl/

 

I touch on this about a year and a half ago, got some feedback, tweaked some things, and graded over 7,200 NFL players seasons with it.

 

FAQs when it comes to this unique stat.


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#2 BSLMikeRandall

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Posted 05 June 2014 - 12:40 PM

1950's:
http://baltimorespor...ade-team-1950s/

 

A look back at the football boom of the 50s. How did the top players in each season according to Z-Score measure up to the guys on championship teams, the guys voted Player of the Year, and Rookie of the Year. 

 

Also, the top ten and bottom ten individual seasons of the decade.


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#3 BSLChrisStoner

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Posted 05 June 2014 - 12:44 PM

It's an impressive amount of time and effort that Mike has put into this.



#4 SammyBirdland

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Posted 05 June 2014 - 01:11 PM

What is Z-score?

 

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#5 DanBryden

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Posted 05 June 2014 - 02:43 PM

The Z-score is a nice tool for standardizing data.  It's use is in determining whether a score is more extreme than the population mean (in this instance, mean of a given stat for a given year).  With a low n (i.e. number of values; in this case # of players), there is only a small chance that a given person's season will ever achieve statistical significance above (or below) the mean (z-score <or> 1.96; ~2 SDs above the mean).  Still, the ability to put players on a normal distribution for a particular statistic is a good idea.

 

Mike, be sure to report the raw numbers along with the z-scores.  A z-score of 1.5 can have a wide range of meaning given its association to other players and the year/era.

 

Another idea is to increase your n by >=16 fold by treating each game as a data-point rather than a season as a data-point.  This will unfortunately skew the infrequent statistics (fumbles, INTs, etc), but it can be useful for determining statistical significance.


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#6 BSLMikeRandall

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Posted 05 June 2014 - 03:03 PM

The Z-score is a nice tool for standardizing data.  It's use is in determining whether a score is more extreme than the population mean (in this instance, mean of a given stat for a given year).  With a low n (i.e. number of values; in this case # of players), there is only a small chance that a given person's season will ever achieve statistical significance above (or below) the mean (z-score 1.96; ~2 SDs above the mean).  Still, the ability to put players on a normal distribution for a particular statistic is a good idea.
 
Mike, be sure to report the raw numbers along with the z-scores.  A z-score of 1.5 can have a wide range of meaning given its association to other players and the year/era.
 
Another idea is to increase your n by >=16 fold by treating each game as a data-point rather than a season as a data-point.  This will unfortunately skew the infrequent statistics (fumbles, INTs, etc), but it can be useful for determining statistical significance.



Thanks Dan. Maybe I could do it on a per game basis this upcoming season. Im wanting to do something in season relating to this. I thought about adding up all the Z-scores to get a total, but i figured whether it was a total, or an average of the totals, it would still be the same order or players. Just different numbers.
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#7 Dupin

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Posted 05 June 2014 - 03:49 PM

Oh man, this takes me back to stats class.  Good times.



#8 DanBryden

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Posted 06 June 2014 - 10:52 AM

Mike,

 

I'm not entirely sure what you mean by adding up z-scores.  A z-score is standardized based on its own population's variance (i.e. standard deviation [^2]).  You could certainly use running z-scores, you'd just hafto renormalize when you get new data.  That's easy though.

 

That said, you could easily create a massive population of scores from [some stat] for every game ever, for a given decade too.  This would be your population and you could ask, on a weekly basis, whether a player's performance is better or worse than the mean for a given stat.  Or, you could compare say, Flacco's yards-per-attempt in a single game to *his* historical yards/attempt.

 

Endless possibilities.


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#9 BSLMikeRandall

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Posted 07 June 2014 - 09:19 AM

Mike,

 

I'm not entirely sure what you mean by adding up z-scores.  A z-score is standardized based on its own population's variance (i.e. standard deviation [^2]).  You could certainly use running z-scores, you'd just hafto renormalize when you get new data.  That's easy though.

 

That said, you could easily create a massive population of scores from [some stat] for every game ever, for a given decade too.  This would be your population and you could ask, on a weekly basis, whether a player's performance is better or worse than the mean for a given stat.  Or, you could compare say, Flacco's yards-per-attempt in a single game to *his* historical yards/attempt.

 

Endless possibilities.

What I meant by adding them up was keeping a running total each week.

 

So in week one, for the four stats I used, if Flacco has Z-Scores of 1.5, 1.0, .5, 1.5, His total that week is 4.5, or an average of 1.125. In week two if he scores 2.5, 1.0, 2.0, 1.5, his total is 7, or an average of 1.75. So going into week three his total on the year would be 11.5, or going by cumulative weekly average of all four stats its 2.875, or going by weekly total average its 5.75 per week. 


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#10 BSLMikeRandall

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Posted 12 June 2014 - 09:46 AM

1960s:

http://baltimorespor...ade-team-1960s/

 

Taking a look back at the most innovative decade in the games history. How did the players voted MVP, Rookie of the Year, measure up to those ranked atop my metric. 

 

Also the top ten (and bottom ten) individual seasons of the decade. 


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#11 BSLMikeRandall

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Posted 18 June 2014 - 01:11 PM

1970s

 

http://baltimorespor...ade-team-1970s/

 

Taking a look a the first decade post AFL/NFL merger. A decade where a receiver with 60 yards per game was elite, and one that brings us one of the biggest MVP snubs in the games history. How did the MVPs and ROYs measure up to our metric?

 

Also, the top and bottom ten individual seasons of the 1970s. 


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#12 BSLMikeRandall

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Posted 02 July 2014 - 11:15 AM

Putting this project on hold for a couple weeks. It's not worth doing something if your not going to do it right. After consulting with our old friend here, Dan Bryden, I'm able to do this the right way. Little bit of editing going on, and I'll continue on with the 80s and more soon. 


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#13 BSLMikeRandall

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Posted 30 August 2014 - 10:05 PM

http://baltimorespor...ade-team-1980s/

 

Finally got this project back on track, with a little help from a friend. Taking a look at who had the best seasons of the 1980s, with one glaring omission. How a certain "great" season, maybe wasn't all that after all. 


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#14 BSLMikeRandall

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Posted 27 September 2014 - 07:36 PM

http://baltimorespor...ade-team-1990s/

 

Taking a look at the best seasons from the 1990s. It's funny. When people mention the best QBs of all-time, people mention Marino, Elway, Montana, and the list goes on. One guy that seems to get passed over is Steve Young. Maybe he shouldn't be passed over any longer. 


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#15 RShack

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Posted 27 September 2014 - 08:22 PM

Well, first off, this is very interesting.  

 

Plus, it's always good to see somebody take an idea and run with it.  So, props to you.

 

I also find myself being kinda dubious about one particular thing.  It's there throughout your assessment of the '50's and '60's and summed up in your statement about the '60's: 

 

"You can also tell by the lack of quarterbacks to make our player of the year list thus far, how important they were in this era of football. There wasn't a huge gap in level of play between the best and worst QBs like there is in today’s game."

 

Trusting Bill James comment about valuing the judgment of a player's contemporaries, I can't help but wonder about this, especially regarding Unitas. Everybody at the time thought he was reinventing the position, and it wasn't just sportswriters, it was contemporary players and coaches too.  

 

It's especially true re: the combo of Unitas and Berry.  Berry was slow and mainly good at having glue for hands, and a "lot" of the passes he caught happened because he and Unitas would practice until dark after everybody else went home.  Their main trick: timing plays, where they both knew exactly where the ball was supposed to be when... so Unitas would put the ball at some invisible spot, and Berry would have his hands at the same invisible spot at the same time the ball got there.  The only way to defend it was to know/guess which invisible spot Unitas had called.  How come Berry gets credit for this but Unitas doesn't?

 

All in all, I gotta wonder (not conclude, but wonder) if there's not something very real about QB's that your methods aren't seeing.  Whatcha think?


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#16 BSLMikeRandall

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Posted 27 September 2014 - 08:51 PM

Thanks for the props RShack. Ive wondered the same thing as I have worked on this project off and on for over a year trying to get it right.

The only thing I can think of is that to get a real accurate representation you want at least 30 samples. Before the merger there were 12-16 QBs? So the small sample size might hurt those earlier QBs. Later on when the sample size is larger, guys like Montana, Young, Brady, Warner, Manning, all get their due.

Might have been better to leave the pre merger years out, maybe?

But you could go round and round with the questions like did Rice make Montana or did Montana make Rice? Same with Unitas and Berry. There is no right answer.
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#17 RShack

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Posted 27 September 2014 - 09:12 PM


Might have been better to leave the pre merger years out, maybe?

 

Nah, don't do that, those years matter.... plus, the issues they reveal can help you get it righter.... you can't make it better without something telling you what needs to be better... so, problems are your friends...

 


But you could go round and round with the questions like did Rice make Montana or did Montana make Rice? Same with Unitas and Berry. There is no right answer.

 

It's not either-or, it's both.  

 

AFAIK, "both" is the hardest thing for stats to deal with... there's an accounting mentality that wants to attribute stuff to one thing or another, but in reality "both" is often the truth...


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  You have no faith to lose, and ya know it" - Bob Dylan


#18 BSLMikeRandall

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Posted 27 September 2014 - 09:31 PM

AFAIK, "both" is the hardest thing for stats to deal with... there's an accounting mentality that wants to attribute stuff to one thing or another, but in reality "both" is often the truth...



Yup. And im far from a brainiac. I definitely had help from smarter folks refining this idea that came to me in a college statistics class.

I know that no single stat is perfect. Just another tool to use.
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#19 RShack

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Posted 27 September 2014 - 09:44 PM

I wonder if would work to handle "both" by counting it both ways, then taking the mean or something... face it, Unitas had a lot of high-z-scoring players around him... meanwhile, in actual practice, he was the O-coordinator re: deciding whose number to call when... so, if you scored QB's of that era the way you did, and then scored them again giving them credit for what their receivers and maybe-RB's did, and then took the avg, I wonder how they'd rank then...

 

Not saying you're really supposed to do all that... I'm just thinking out loud, that's all...


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  You have no faith to lose, and ya know it" - Bob Dylan


#20 BSLMikeRandall

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Posted 30 November 2014 - 11:55 AM

http://baltimorespor...ade-team-2000s/

 

Taking a look at the best seasons of the decades from the 2000s.

 

Spoiler alert: Peyton Manning and Tom Brady are pretty good. 


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