Taking stock: introducing quarterback win expectancy (QWE)

By
Updated: July 9, 2013

By calculating a quarterback’s win expectancy — his statistical contribution to his team’s win/loss record — we can calculate how many wins a quarterback should have over a specific period.

Recently we explored the interesting question of how well an NFL quarterback must perform in a game in order for us to say that he “did enough to win.” After looking at several hundred games over the past five years, we came to the conclusion that if a quarterback posts a passer rating of at least 71.6 or a CQBR of at least 61.9 in order to give his team a probability of winning that’s better than chance (i.e., “50-50″).

Neither of these ratings is very high; indeed, as we noted, the passer rating required was actually below the average rating posted by quarterbacks in our sample. As long as a quarterback puts up an average to slightly above-average day, he should put the team in a position to win.

In a conversation we had after publishing those articles, my esteemed colleague, Johnathan Wood, suggested that we could use the same equations we derived in those articles to calculate a team’s probability of winning in any game based on their quarterback’s performance in that game — and that, moreover, we could in so doing assign the quarterback’s personal contribution to the win or loss.

And so the concept of the quarterback win expectancy (QWE) was born.

Doling out shares

See, it’s easy to jump to the erroneous conclusion that teams should always win whenever their quarterbacks exceed the minimum threshold. Nothing could be farther from the truth.

The source of this confusion is that, ignoring ties, which are an extreme rarity in the NFL, the outcome of a football game is a binary state — you either win or you lose. There’s nothing in between. Win probabilities, on the other hand, aren’t nearly so neat, because they occur on a spectrum. They only really have meaning over the course of many games.

For example, when a quarterback produces a CQBR of 61.9 in any one game, he gives his team roughly a 51 percent chance to win that game. But that doesn’t mean they will win every time he does so; it means that if he were perform at that level for 100 games, they would win roughly 51 of them. They would still lose a gut-wrenching 49 times out of that 100.

Similarly, if he turned out a CQBR of 74.73 a hundred times, his team should win about 63 of them — but they’re still going to lose about 37 times.

What this means is that we can’t simply look at a quarterback’s games and say, “Well, he put up a CQBR better than 61.9 in 21 of 35 games, so the fact that he only won 18 of them proves the rest of the team let him down.” Instead, we need to add the win probabilities from game to game together to get a better picture of how many games the quarterback “should” have won.

Adding the probabilities

As an illustration, let’s imagine the following stretch of five games:

CQBR Win Probability
74.73 0.63
-22.32 -0.11
-10.31 -0.02
69.39 0.59
90.85 0.75
Total 1.84

Looking at those numbers, we might say, “The quarterback exceeded the 61.9 CQBR baseline three out of those five games, so his team should have won at least three of them.” This assumption results from a fundamental misunderstanding of probability and in most cases, would produce a wildly wrong prediction.

Instead, what we should do is add together the win probabilities from all those games, which, as we can see, total 1.8. This tells us that theoretically, the quarterback did well enough to win just under two of those five games. In fact, history shows that his team did actually , which matches well with our prediction and shows that the team as a whole slightly outperformed the quarterback himself.

What this tells us is that quarterback win expectancy can help us determine how many games out of a given sample that a quarterback should have won assuming the rest of his team had been up the task.

To be more specific, a positive QWE represents a good-enough-to-win effort on the part of the quarterback, while a negative QWE represents a failing performance.

In the example above, the quarterback gave his team a respectable chance to win in three of the games (although never enough to guarantee” a win) and didn’t do enough to win in two of the games. Not surprisingly, his team lost both of the games in which his win expectancy was negative. They won two of the three games in which his win expectancy was positive, but ironically enough, lost the game in which his win expectancy was the highest (0.75, representing a 75 percent probability of winning). Even at the very high level of performance represented by a QWE of 0.75, the team would have been expected to lose one out of every four games.

Putting win expectancy to the test

All of this sounds great in theory, but how does QWE hold up in the real world? How well does it actually tally with wins and losses over the course of a season and across the years? Surprisingly well, actually. Tomorrow we’ll look at all the quarterbacks of the NFC North and NFC South to see how much they personally have contributed to the wins of their teams over the past several seasons.

About the author(s)

Rourke Douglas Decker covers the Green Bay Packers beat for Water Cooler Sports. He resides with his family in the Twin Cities. He can be reached for questions or comments at . Connect with .

1252 comments
Preparation_A
Preparation_A

I'd like to nominate BSL for some award or another for being, I believe, the first person in the history of WCSN to use the phrase "hoisted him on his own petard".

Lovely.

MIBearFan
MIBearFan moderator

FUCK PHYSICS???????

FUCK YOUR STATISTICS!!!!!

Preparation_A
Preparation_A

  

You can't, because they don't want their average customer to have to spend an additional $12 per year.

falconsriseup19
falconsriseup19

  i cant get any page on the site to laod either...

MIBearFan
MIBearFan moderator

   

Sounds hard on the dick.

vanderheap19
vanderheap19

  I still get a kick out of my old ShopKo store manager thinking he was the shit because he was the manager of a WalMart-like store. 

BearsSaveLives
BearsSaveLives moderator

  Starting is like 11-12, I think, but they treat their people right and give them raises. 

Preparation_A
Preparation_A

   

Does that include profit sharing returns?

falconsriseup19
falconsriseup19

   both our workplaces internet isnt working. what a cowinkydink

50CaliberFalconoles
50CaliberFalconoles

    

the new post will come up but the comment section wont load

falconsriseup19
falconsriseup19

   no, now i cant go to google, must be network problem at work. although i can refresh other pages. just can open any new ones. weird.

falconsriseup19
falconsriseup19

  other sites working fine for me. just not this one.

BearsSaveLives
BearsSaveLives moderator

  Physically hard, or statistically hard?

vanderheap19
vanderheap19

   Sure seems to. IT manager and my direct supervisor are cool, but they seem few and far between even within the same company, much less what I hear from others.

Tearloch
Tearloch

  I get about 11-12% of my annual salary in stock every year, plus performance bonuses.  Pretty sweet deal.

Preparation_A
Preparation_A

My wife's company isn't employee owned, per se, but they do profit sharing and I support it fully!

Tearloch
Tearloch

   I work for an employee owned company.  They are great!

Preparation_A
Preparation_A

The employees also own shares in the store and get substantial profit sharing if I understand it correctly.

Tearloch
Tearloch

   Its not really optics.  Light is electromagnetic energy.  Optics is about manipulating light.  Wavelength, et all, are factors in that, but not the core of optics.

Preparation_A
Preparation_A

That's aiiight. Wait til I start talking about football and you'll see what dumb sounds like.

falconsriseup19
falconsriseup19

   yeah, i didnt really think about what optics branched from lol. i sounded dumbbbbbbbbb

BearsSaveLives
BearsSaveLives moderator

   It's optics, a branch of physics.

Preparation_A
Preparation_A

You don't think wavelengths of light is physics?

50CaliberFalconoles
50CaliberFalconoles

    

Crazy aint it? you would think black would be all the colors cause when use all the color crayons on a sheet it turns black

BearsSaveLives
BearsSaveLives moderator

  White is all the colors of the spectrum.

BearsSaveLives
BearsSaveLives moderator

   You hoisted him by his own petard.

Preparation_A
Preparation_A


White is also the absence of color...WHO WORKS THERE???

50CaliberFalconoles
50CaliberFalconoles

   SO only Blacks can work on the floor? being black is the absence of color

Extend Capers thru 2020
Extend Capers thru 2020

  yep. Along with health benefits. Approximately 90 percent of employees are apart of their health care system