Last week, The Machine from ASL showed us how drafting a top-tier tight end can impact your fantasy championship hopes. Today, let's do a similar exercise with the quarterback position and with a slight dynasty-league twist.

A member of the ASL team recently traded the first pick in his dynasty draft for Indianapolis Colts quarterback Andrew Luck. Making such a move basically means he has forfeited the chance to own rookie running back sensation Ezekiel Elliott, stud wideout Odell Beckham Jr. and a handful of other stars who seem destined to have long, productive careers. But our team member made this move out of necessity foremost; his starting quarterback was Tony Romo. In case you hadn't heard, that's not good.

Our team member felt confident about the deal since Luck has already proven he can put up gigantic numbers in the league, will turn just 27 years old in September, and quarterbacks traditionally have a longer peak than running backs in the NFL. The likes of Adrian Peterson and LaDainian Tomlinson, backs who consistently produce over an eight-, nine- or 10-year span, are few and far between. Perhaps Elliott will be good enough to join that select group. Our team member is betting against it. Plus, the fact that he already owns Rams running back Todd Gurley -- another top dynasty choice -- makes the decision to grab Luck at the expense of Elliott easier to stomach.

Going from Romo to Luck is unquestionably an upgrade. But just how much of one, exactly? That's where The Machine comes in.

The method used is the same one presented last week: An empty 12-team league is placed into The Machine, and each team is given a pair of quarterbacks. The team with the best QB according to The Machine, Cam Newton, was given the the 24th-best QB as a backup. The team with the second-best QB, Russell Wilson, was given the 23rd-best as a backup, and so on. The Machine ran the numbers and here is the breakdown, ending with each pair's championship win probabilities:

(1) Cam Newton / (24) Blaine Gabbert: 9.79 percent

(2) Russell Wilson / (23) Ryan Tannehill: 9.05 percent

(3) Andrew Luck / (22) Jay Cutler: 9.22 percent

(4) Ben Roethlisberger / (21) Tony Romo: 8.57 percent

(5) Aaron Rodgers / (20) Joe Flacco: 8.63 percent

(6) Drew Brees / (19) Tyrod Taylor: 7.99 percent

(7) Blake Bortles / (18) Ryan Fitzpatrick: 7.88 percent

(8) Marcus Mariota / (17) Jameis Winston: 7.93 percent

(9) Eli Manning / (16) Matt Ryan: 7.99 percent

(10) Carson Palmer / (15) Derek Carr: 7.75 percent

(11) Matthew Stafford / (14) Philip Rivers: 7.69 percent

(12) Andy Dalton / (13) Kirk Cousins: 7.51 percent

A couple of things to point out: This was done before Romo's recent back injury, so he's no longer among The Machine's top 24 quarterbacks. And Tom Brady isn't present due to his suspension.

There are a couple of conclusions we can reach thanks to these rankings, which are for standard redraft leagues. By moving from Romo to Luck, our team member has raised his overall chances of winning his league this year by more than two percentage points. That margin could increase next year -- who knows how either player's fantasy stock will look in 2017? -- but we know for certain that the trade has increased his odds of winning in 2016 significantly.

Secondly, look at how the win percentage of each pairing falls. There are somewhat substantial gaps from the Newton pairing to the Wilson pairing, from the Luck pairing to the Roethlisberger pairing, and from the Rodgers pairing to the Brees pairing. Past that, the numbers trail off rather evenly. This data shows how advantageous it is to draft Newton, Luck or another top-notch quarterback. But it also shows that if you miss out on the top three or top five quarterbacks, don't panic. There are plenty of good options and value available after those early rounds, depending on which platform you play fantasy.

Lastly -- and we can't stress this enough --  if you want a real edge in your league, get The Machine. It’s math is far more than just adding fantasy points like the other products out there. It uses probability distributions and understands the true value of backup players, highlights injury probabilities, analyzes your matchup schedule, evaluates trades, sees the value of regular season wins versus playoff wins and much more. It makes recommendations based on how each move you make affects your probability to win your league title. There is no other fantasy sports resource like it.