Let’s continue our analytics tour of the various fantasy football positions this week by focusing on quarterbacks, where the objective is to find late-round value in 12-team leagues.

Here are the previous pieces that focused on zeroRB and under-the-radar, highly-skilled wide receivers.

[Join a Yahoo Fantasy Football league for free and make 2016 your season]

For quarterbacks, the idea is to measure overall efficiency (yards per pass attempts) and expect that touchdown efficiency will track that as it historically does. Think of YPA as the dog wagging the Passing TD% tail. The higher the YPA (all passes), the better the TD% (very few passes) should be. We want to avoid the quarterbacks who had a TD% far higher compared with the league average than their YPA and we want to target as draft values those passers who were efficient overall but somehow inefficient in throwing touchdowns (considering this more fluke than fact).

Since 2000, QBs with a YPA under 6.5 had a TD percentage of 3.2% (or 16 TD passes per 500 attempts). A YPA of 6.5 to 6.99 equalled a TD% of 3.9% (19.5 TD/500 attempts), 7.0-7.49 4.3% (21.5 TD passes), 7.5-7.99 5.2% (26 TD passes), 8.0+ 6.1% (30.5 TD passes). Remember, this is per 500 attempts and last year a record 15 teams threw 600+ passes.

Now let’s plug in these expected TD% rates above for each quarterback according to where their YPA last year sat. First we see that 11 of the 29 quarterbacks were within two touchdowns of their actual total and 18 were within five. This means the model is conceptually sound.

The major outliers on the negative side, meaning they threw way more touchdowns than their YPA suggested was reasonable: Cam Newton (should have thrown nine less TDs), Ryan Fitzpatrick (nine), Blake Bortles (nine), Aaron Rodgers (nine), Eli Manning (eight), Derek Carr (seven), Matthew Stafford (seven) and Andrew Luck (six, but on just 293 attempts, making him arguably the MOST lucky QB last year).

We can argue that Fitzpatrick and Bortles have great wide receivers. But then why aren’t they efficient all over the field and only in the red zone? Maybe having tall wideouts allows for more margin of error in the red zone because if you miss high, the ball goes out of bounds vs. risking an interception in the middle of the field. But the simplest solution is that they were just very lucky.

Rodgers is arguably the greatest quarterback of all time, so we’ll just ignore his YPA last year as a fluke and draft him as we always would.

I’m certain that Carr doesn’t have two great receivers and he may not even have one so I would definitely not draft him at all in a 12-team league. Ditto for Stafford. Luck outpaces his peripherals in fantasy all the time, mostly due to his running. He’s overrated but obviously productive. But I would not draft Luck over, say, Drew Brees.

Newton is going to burn the owners who are making him the exception to middle/late-round QB this year, I’m convinced. Look where he was drafted last year (15th in QB ADP).

Manning has a wide receiver in Odell Beckham Jr. on pace to be one of the best ever so I can’t say to avoid him.

Now what about the values, meaning quarterbacks who should have thrown more TDs considering their overall efficiency?

Matt Ryan tops the list, earning with his YPA about 32 TD passes last year vs. the 21 he actually threw on his 614 attempts. So there’s your late-round QB in fantasy. Heck, in many 12-team leagues you can get Ryan with your last player pick, before defenses and kickers are selected.

There are only two other values, with Ben Roethlisberger the prime middle-round target. Last year, in his limited action (just 469 attempts), Roethlisberger earned 29 touchdown passes with his scintillating 8.4YPA — or eight more than he actually threw.

Later in drafts, the model says to bet on Jameis Winston, who managed 22 touchdowns on his 535 attempts and not the 28 his 7.6 YPA said was most likely. Of course, he made up for this by scoring six rushing touchdowns. But many experts are correcting down his rushing scores (you should) but not boosting his passing TDs. Bottom line: Winston is likely a very good quarterback considering his outstanding rookie YPA. Plus, Mike Evans, who is just now turning 23, may be a top-shelf wideout.