Yards per Play is only half the story
by TuckNole on Dec 12, 2010 5:43 PM EST
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PrintWe talk a lot about yards per play here at TN, but I wanted to chime in to explain why that measure of an offense is only half complete. Just as importantly as expected/average yards per play is the standard deviation of the expected/average yards per play. None of these ideas are original; the guys at Smart Football, Sabremetric Research, and Advanced NFL Stats have covered this quite a bit. To start, let’s conduct a simple thought experiment:
Imagine a team that only had one play- a 50 yard bomb. This play was successful about 1/5 of the time. That means this offense averages 10 yards per play, which is a huge amount but the standard deviation is a whopping 22.3 yards per play. Because of the huge standard deviation, there is very little chance this team ever reaches the end zone unless give a short field position (the likelihood of stringing two plays together to get you in is 4%). Imagine another team that only has 1 play that averages only 3 yards per play but has a 1 yard standard deviation. This offense would almost certainly never punt. As long as your defense gave you just 1 stop per game, you would go undefeated. Looking at these two offenses through the limited lens of only yards per play, it looks as though one is far superior to the other 10 ypp vs 3 ypp. But missing is the standard deviation comparisons of ~22 to 1.Now imagine this scenario:
Offensive Plays:
Series - 1
Play 1: 0 yards
Play 2: 0 yards
Play 3: 0 yards
Punt
Series – 2
Play 1: 99 yard bomb for a TD
Series – 3
Play 1: 0 yards
Play 2: 0 yards
Play 3: 0 yards
Punt
Series – 4
Play 1: 0 yards
Play 2: 0 yards
Play 3: 0 yards
Punt
This is not a very good offense, yet it is averaging 9.9 yards per play. What that average hides is the standard deviation of 31.3 yards per play.
Standard deviation is the risk that the play will not achieve its expected/average yards. So what is the best way to tell if your offense is better at getting the most yards for the risk it is taking? Here we turn to a Finance concept: the Sharpe ratio. Sharpe ratio tells you how much reward you are getting for each unit of risk you are taking. Let’s consider another (more realistic) sample set for these two teams plays:
Team A play results in yards: 20, -1, 0, 10, 15, -10, 4, 2, 18, 12.
Team B play results in yards: 7, 3, 9, 2, 2, 5, 6, 6, 4, 3.
Team A has an average of 6.3 yards per play and a standard deviation of 10.5. That makes their Sharpe Ratio 0.6. Team B has an average of 4.2 yards per play and a standard deviation of 3.6. This makes team B’s Sharpe ratio 1.2. Team B’s offense is achieving much more for the level of risk that it is taking than Team A is despite the higher yards per play average of Team A.
I just point this out as I've never seen anyone mention the standard deviation when talking about yards per play of either FSU or its opponents, yet it should, as it is an important measure in telling whether an offense is underachieving or not.
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BTW
At some point I plan on cutting the data on FSU to show how their YPP compared to their standard deviations.
good point here Tuck.
Another thing that bugs me is when people report an average for a non-normal data set. Mean and standard deviation are parameters of the normal distribution and are very misleading when the data is non-normal. I prefer a box-plot to show the median and quartiles.
I've been working on that off and on for a week.
Got it all finished, but can’t figure out how to get graphs onto the fanpost editor.
"You should always swing as hard as you can...Just in case you hit the ball." - Dale Murphy
by Dr.KennethNoisewater on Dec 12, 2010 7:23 PM EST up reply actions
save it as a PDF
then:
Open it in Photoshop and save as a JPEG then upload to imageshack or any hosting site and use the link provided to post.
OR
use this or this to convert to a JPEG and upload it to whichever hosting site of your choice
"History I believe furnishes no example of a priest-ridden people maintaining a free civil government." — Thomas Jefferson to Baron von Humboldt, 1813
"MacGyver is the Jesus Christ of Science" — me
Great, thanks.
"You should always swing as hard as you can...Just in case you hit the ball." - Dale Murphy
by Dr.KennethNoisewater on Dec 12, 2010 10:40 PM EST up reply actions
Not a stats guy myself,
but I think this is basically why I was pissed at the NC State game…
FSU Football, making bad teams look bad since 2010.
by onebarrelrum on Dec 16, 2010 10:18 PM EST up reply actions
Tuck,
Are you planning to analyze every play? I just did analysis on yards/play/game as a means of showing which offenses/defenses were most/least consistent and to show how the Noles did against the ACC.
"You should always swing as hard as you can...Just in case you hit the ball." - Dale Murphy
by Dr.KennethNoisewater on Dec 12, 2010 10:42 PM EST reply actions
Every play
I have to either find the data set somewhere or create it over the holidays if I have time. My suspicion is that it will shed some light on why some games had high average per play yards, but just didn’t feel completely right from an offensive stand point.
Didn't want to steal your thunder is all
that’s a bit different from what I’ve done and would probably be a great follow up. I just used ypp/game without trying to find stats for every play. I wasn’t planning to throw a wrench in the ypp is king perception (not that you’re doing that either). I just used variance/game to show whose more consistent than who.
"You should always swing as hard as you can...Just in case you hit the ball." - Dale Murphy
by Dr.KennethNoisewater on Dec 12, 2010 11:19 PM EST up reply actions
Got your e-mail
I don’t have it but I have some ideas how it might happen
This team will improve in '10... on its 16-16 conference record over the last 4 years.... after losing 20 games in the last 4 years... after having the 7th worst major-conference defense... after not even winning its own division in the ACC in the last 4.
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Do you think
the guys at S&P or FEI would lease their data set to me?
I’d give them the money I waste on WC each month just for access to it. And I’d only be posting the stuff here.
Tuck are you just looking for a long list of yards gained on each FSU offensive play broken down by game and down?
Because if you cannot get it from S&P or something I may end up creating that in about a week for something I am working on if I get bored enough.
Yea
It seems there are several people on this site who would like to cut the data for posts they want to do. Plus others like reading this stuff. I wonder what the what the most efficient way to crowd-source this. Like each person does it for a specific game or group of games and we maintain it over the course of the season each year. We get the other ACC blog networks to do their teams. And we keep it all in a central wiki or user database that you have to be registered to the SBN to access.
Bud, you ever thought about this? Would definitely be super duper double awesome.
I will definitely chip in.
Every game was televised this year…would’ve been easy enough to go back and gather the data/put in a spreadsheet. Maybe use google docs or email to a central person or whatever. Would be cool.
"You should always swing as hard as you can...Just in case you hit the ball." - Dale Murphy
by Dr.KennethNoisewater on Dec 19, 2010 8:48 AM EST up reply actions
The only problem is
that people are familiar with mean yards per play but now with a reference to a standard error. That is, if FSU averages 7 YPP against somebody this board is going to be pretty happy. But if you said something like “Our standard error was a full yard less in magnitude over Clemson than UF” people are going to go Tom Lemming on you.
FSU Defense 2010: Taking back 1st down.
I've run some numbers
and planning to post soon. Nothing crazy and I think it won’t upset anybody. Actually shows our defense was pretty good up to and including NCSt when compared to opponent ypp/game and opponent variance.
"You should always swing as hard as you can...Just in case you hit the ball." - Dale Murphy
by Dr.KennethNoisewater on Dec 13, 2010 2:38 PM EST up reply actions
Some people may whine
but some of us want the gory statistical details. Bud does an amazing job in his post game analysis, but I think some of us would want to know if out gaining an opponent ypp misses part of the story if we have a much bigger standard deviation. Or vice versa. BC’s ypp looked respectable until you look at their st dev and realize they really had an awful offensive performance against us and got a huge amount of yards on 2 plays.
by TuckNole on Dec 13, 2010 4:35 PM EST via mobile up reply actions
This was the point I made on UNC and Clemson.
YPP is useless if, for example, you make a big throw on the first play and then crap out until halftime like we did against Clemson (I believe we averaged less than 2 YPP after that first throw). And people — including Jimbo — blamed the defense for being on the field too long when the offense couldn’t do anything.
"Words ought to be a little wild for they are the assault of thought on the unthinking."
- John Maynard Keynes
"We'll be here 'til midnight. We ain't not gonna practice."
- Jimbo Fisher
by Drew J Jones on Dec 13, 2010 5:36 PM EST up reply actions
Niiice.
MiNDSET? SWAG-ER-ISM!!!
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"Trick is right."
"Wherever you are, Trick, you are wise, indeed."
"Correct, Sir Trick."
I agree with your premise
And I think there’s a nice article on TN somewhere about this applies very well to the type of running game fsu is trying to produce (ie. no negative plays).
However, the truth is that using the extremes of situations like in your post can’t tell us what really is important. The reason I say this is because I recently read an article on footballoutsiders.com that showed how (at least this year) explosive drives or some other measure that analyzes the time it takes for teams to score is actually more indicative of a successful offense and ultimately winning.
I say all that to say that obviously ypp alone is not sufficient, and while figuring out deviations in ypp will help you probably still won’t have the ‘whole story’.
I’m sure you realize all this, and I wish I had that article to link, but I’m on my phone.
Looking forward to the analysis.
by BenDNole on Dec 14, 2010 11:22 AM EST via mobile reply actions
Think you are missing something
You seem to be assuming that I am sayin that st dev is the whole story. It too is only half the story. That’s why the Sharpe Ratio exists to compare the two. It’s great to have a high average/expected ypp if you aren’t taking too much risk to get it. If you are averaging 10 ypp with a st dev of 10 yards and your Sharpe Ratio is 1, the that compares favorably to a team with a 5 ypp and a 6 st dev. It’s great to be explosive as long as it is worth the risk. It’s just like in the stock market, people don’t care about returns, they care about risk adjusted returns.
by TuckNole on Dec 14, 2010 4:42 PM EST via mobile up reply actions
The original application for this
was in analyzing the optimal rushing / passing play selection. People wanted to address the Passing Paradox – ie. the fact that passing yields more average yards per play yet NFL teams seem to run a lot, and therefore they must be idiots. It took a couple publications by finance in the Sports Quant journals to explain that coaches rush because it has a lower risk / standard deviation. When you apply a utility function to the NFL as a whole, it turns out not that they aren’t passing enough, but that they are passing too much!
http://smartfootball.blogspot.com/2008/06/runpass-balance-game-theory-and-passing.html
Something else I’d like to do in the future is figure out if Fisher ran too much or passed too much this year on a risk adjusted basis.
I think that would be an interesting piece.
My only skepticism would be based on the fact that we know certain teams sold out to slow down Ponder so we ran the ball more….. except for the game where we knew they were going to try to stop the pass, but decided to work on the passing game anyway (i.e. Wake Forest)
I think I probably didn't explain myself well enough
I realize that ypp is not the whole story, and that st dev is not the whole story. I also realize you don’t believe st dev to be the whole story…. but it does seem like you are saying that ypp + st dev is the whole story. My main point is that even with ypp and st dev you still probably don’t have the whole story (meaning it’s not 50% and 50%; more like 40 and 40, with 20% being found in other statistics or even unmeasurable aspects)
My other point is taken from an article I read somewhere on football outsiders. It said that, statistically, teams that lack the explosiveness to score quickly (i.e. >10 ypp) are not as successful as those who don’t. So while trying to reduce risk and ensure x amount of yards per play without risking getting zero or negative yards is a good idea, if an offense lacks the big play potential, they likely aren’t going to be as successful (per the gathered data, not theory)
I don't think that disagrees with this analysis...
It actually is baked into it. Being explosive is good, as it limits your chances for mistakes, but it has to be risk adjusted. If a team is successful in getting to the endzone they must have a good Sharpe Ratio, or else they wouldnt be making it in. You simply can never put a whole drive together because if you dont achieve at least 10 yards every 3 plays, you punt. High st dev increases the number of times 3 plays strung together doesn’t equal 10 yards.
by TuckNole on Dec 15, 2010 6:03 PM EST via mobile up reply actions
I also think this is why MKE Nole's comment about box plots is helpful
Box plots let you see the distribution of the data much more effectively. They demonstrate the average play (or should I say median play) while still allowing you to understand how explosive the noles were and how frequently they were losing yards. In fact, I think it would be really cool to see all of the data in a regular graph too
I also like the idea of applying the Sharpe ratio to offensive play-calling and I am very interested to see the results, but my only hesitation is the situational aspect of football. 1st and 10 is a much different down than 3rd and 1, and that’s not even adjusting for formation and all of the other variables that play into decision making. Still, I think that it will tell us a lot.
Agreed.
I brought this up amongst my stat-geek friends and a long debate ensued.
I think the final settlement was that you’ll have some 3rd and longs and some 3rd and shorts and net-net, they’ll cancel each other out. I think that is an incredible lazy assumption.
Agreed on that being lazy
I’m trying to think of a good way to separate the data to adjust for the variable downs/yardage, but I just don’t like the hard categories of something like 2nd and less than 5 vs 2nd and more than 5. I’m thinking of doing some fun visual stuff with the data though. Did you ever find a good data set to work with?
You guys are on the right track
It will be time consuming. Didn’t BUD have the plays before garbage time with the yards on each play?
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