Neural networks roughly mimic how neurons in our own brains work. Neurons act as connected nodes, passing information across layers of nodes until it converges to answer a question -- usually some kind of prediction. The neural network is taught past examples, and it learns from each case by adjusting the weights of the connections between neurons until the difference between its predictions and the actual outcomes is minimized. Much of the software behind applications such as self-driving cars and facial recognition is powered by neural networks.

Neural networks can also accurately predict the chances of Pro Football Hall of Fame induction by interpreting which combinations of criteria voters actually rely on. Using that logic, should we expect Kurt Warner, LaDainian Tomlinson or Terrell Davis to be voted in this week?

Let's take a look:

How it works

Kurt Warner was revered as one of the top QBs of his era, but is he Hall of Fame-worthy? STEVE SCHAEFER/AFP/Getty Images

This kind of analytic model is especially good at handling complex relationships and logic among multiple factors. Suppose things worked like this: A running back wouldn't make the Hall without at least two All-Pro selections no matter how many total yards or Pro Bowl selections he has, except if his TDs also exceed some value. Neural networks can recognize those types of patterns in the data. Other kinds of prediction models are typically additive, and would errantly predict a Pro Bowl regular to be inducted without the other requisite qualifications. Neural networks capture a lot of the intuitive "you know it when you see it" aspects to a question.

Our Hall of Fame neural network accounts for the career attributes of past inducted players, as well as those who did not make the Hall. The model learns from the attributes of a career that voters consider most Hall-worthy, such as statistics, longevity, career awards and postseason performance (all data courtesy of Pro-Football-Reference.com). Yardage stats and touchdowns are adjusted each season for league averages and season length. At the end of the process, we essentially have a virtual, collective mind of the Hall voters.

Its accuracy and ability to generalize to new cases is tested by excluding each player one at a time from the set of learning cases, and then asking it to make a prediction about that player. If we didn't leave out a player's inputs before testing his prediction, it would be cheating. For example, we would need to leave Jets great Curtis Martin out of the RB learning cases before asking, "Would a guy like Martin make the Hall?" Otherwise it would already know the answer. The predictions are scored based on their accuracy, and this model's accuracy is uncanny -- it has missed on just one of the 139 QBs with five or more starting seasons since 1948 (George Blanda), and on just two of the 310 RBs (Floyd Little, John Henry Johnson) with four or more starting seasons since 1948.

How voters measure QBs and RBs

Terrell Davis won Super Bowls and rushing titles, but a short career hurts his chances. Focus on Sport/Getty Images

For QBs like Warner, what voters appear to weigh most heavily are total passing yards along with total wins and longevity -- which go hand in hand. Super Bowl appearances, wins and MVPs also factor into the minds of the voters, but All-Pro and Pro Bowl selections have historically been even more important.

For running backs like Tomlinson and Davis, what voters appear to weigh most heavily are total rushing yards, total touchdowns and longevity. Unlike with QBs, voters don't hold RBs responsible for wins and losses, and don't hold them responsible for postseason success either. Immortality as a running back is gained through racking up large totals and awards like All-Pro and Pro Bowl selections.

If you asked a voter if he or she simply counted up Pro Bowls and voted based on it, the voter would certainly say no. We know how flawed the selection process can be -- and the alteration of the Pro Bowl schedule/format and its relationship to the quality of players selected could cause the value of this data point to erode in the future. But collectively, it appears the voters do value Pro Bowls -- or at least they vote based on what those Pro Bowls represent. Multiple selections represent sustained excellence relative to one's peers, which I suspect is part of the core criteria for a Hall of Famer. And although Pro Bowl selections can sometimes be based on popularity or reputation, that's OK for our purposes. Remember it's called the Hall of Fame and not the Hall of Efficiency, nor any other particular metric.

Throughout this exercise, one thing has become clear: The voters have, as a whole, been very consistent with their standards. If a single model using the same standard can accurately predict who's in and out of the Hall since 1948, then that standard must have held firm over time. This pattern would be something we would expect if the selection process were largely based on precedent and on comparisons with current inductees.

That's not to say voters are robots who simply tally totals and all-star awards. Individually, voters each have their own criteria, but as a group, there are a limited number of factors that make the difference. If there are other factors, the neural network doesn't need them to get almost everyone right.

The Class of 2017

LaDainian Tomlinson is a surefire Hall of Famer -- if not this year, then soon. Steve Mitchell/US Presswire

This year, one QB finalist will be voted on in Houston. Kurt Warner appeared in three Super Bowls, won one and was its MVP. The undrafted journeyman's career was shortened by a late start, but it still spanned 12 seasons. He was a two-time All-Pro with enough era-adjusted yards and wins to make him a near lock to be inducted ... eventually, at least. It might not be this year, but his record is consistent with others in the Hall. Keep in mind, the neural network isn't making a judgment on whether he should be in the Hall; it's only making a prediction based on how consistent his career was with those already in, compared to the careers of those left out. It might be best to put it this way: It would be remarkably inconsistent of the voters to ultimately exclude him.

Tomlinson, meanwhile, is a shoo-in. He earned three All-Pro citations and was selected to four Pro Bowls to go along with eye-watering total yards and TD numbers. He led the league in yards three times and in rushing TDs twice. His total (era-adjusted) yardage ranks sixth all-time, and his TDs rank second to Emmitt Smith. It would be shockingly inconsistent of the voters to not elect him.

Terrell Davis is the other RB finalist this year, and unfortunately for hopeful Broncos fans, the model puts his chances of being enshrined at less than 3 percent. His career burned brightly and he had great postseason success, but Davis' totals aren't there due to an injury-shortened career. Again, this is not to say he should or should not make the Hall, but his election would mark a significant break in precedent.

Next week, we'll be taking a deeper look at the neural networks for QBs and RBs in the Hall of Fame, and what they say about future induction of both current and recently retired players.

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