No team has improved its playoff odds more over the past month than the New Orleans Saints, who the Football Power Index estimated to hold a 5.1 percent shot of hitting the postseason after an 0-2 start. After rolling off a pair of impressive victories before their bye and winning a rollicking encounter against the Lions in Week 6, the 3-2 Saints are now favorites to make their way back into the postseason, with a 62.9 percent chance of playing past Week 17.

Naturally, the player at the heart of the Saints is quarterback Drew Brees. In writing about the league's potential MVP candidates after Week 4, it felt as if we were almost taking Brees for granted, given that he had arguably the best numbers in football.

Over the past three games, though, a defense that had served as a punchline has shown signs of life. The Saints have jumped from 31st in defensive DVOA after Week 2 to 15th, lofty heights for a unit that has ranked either last or second-to-last in the league in 2014, 2015 and 2016. Dennis Allen's unit has produced shocking numbers over its past three games, but even if the defense can't keep it up, the Saints might only need to be competent to challenge for the NFC South crown. Few quarterbacks have needed -- and gotten -- less from their defenses to succeed than the 38-year-old the Saints have under center.

Help out Brees -- just a little bit

No quarterback of this generation has gotten less help from his defense than Brees. It's backed up by the numbers. I looked at every quarterback to begin their career since the 1970 AFL-NFL merger and found each season in which they were the primary starter for their team. I took the points allowed by each team and standardized them against the averages for each year in question, making it possible to compare quarterback defenses across eras. (More on that methodology here.)

There have been 38 quarterbacks to start 10 or more seasons since the merger. Brees has the sixth-worst average defense over that period, and the worst of any active quarterback. Here are the quarterbacks with the 10 worst defenses, their average standardized score, and what that would translate to in terms of a 2016 defense:

Player Avg Def 2016 PPG Archie Manning 0.80 25.5 Jim Everett 0.74 25.3 Dan Fouts 0.70 25.1 Boomer Esiason 0.65 25.0 Steve DeBerg 0.50 24.5 Drew Brees 0.47 24.4 Jim Plunkett 0.40 24.1 Vinny Testaverde 0.28 23.7 Jake Plummer 0.25 23.6 Warren Moon 0.21 23.5

It has to be sad for Saints fans that the guy at the top of the list also happens to be a New Orleans franchise icon. Manning never once had a defense that finished in the upper half of the league rankings in scoring defense, but after he gave way to Ken Stabler in 1982, the Saints finished in the top half nine out of the ensuing 11 seasons, including seven top-10 appearances and two league-leading defenses in 1991 and 1992.

Brees' defenses in New Orleans Year Defensive

DVOA Rank Record Playoffs? '06 22 10-6 Yes '07 30 7-9 No '08 26 8-8 No '09 17 13-3 Yes '10 10 11-5 Yes '11 28 13-3 Yes '12 32 7-9 No '13 10 11-5 Yes '14 31 7-9 No '15 32 7-9 No '16 31 7-9 No

During his time with New Orleans, Brees hasn't needed a great defense. He hasn't even needed a decent one. When Sean Payton gives Brees a remotely competent defense, Brees delivers him to the postseason. I've mentioned this before, but the numbers are staggering. Check out the chart on the right.

The Saints have ranked in the top 25 of the league's 32 defenses four times in 11 seasons with Brees. They've made the playoffs each time and won an average of 11.3 games along the way. Again, the Saints' defense doesn't even have to be good. As long as it's not awful, Brees seems to be able to drag the team into the playoffs. He even delivered a 13-3 record with a dismal defense in 2011, only to be taken out in the postseason by an offensive outburst from Alex Smith and the 49ers in one of the most dramatic playoff games in recent NFL history.

Brees and the Saints' offense are holding up their end of the bargain through five games. They went four games without turning the ball over, only giving way against the Lions in a wild game last weekend. New Orleans ranks third in offensive DVOA, while Brees is fourth in passer rating and adjusted net yards per attempt. The Saints are great on offense, which should be no surprise.

What we're taking for granted, though, is just how little the Saints have around Brees. This isn't a team with Jimmy Graham and a boatload of high draft picks at the skill positions. The Saints traded away Brandin Cooks and replaced him in their receiving corps with Ted Ginn Jr. Their top wideout is Michael Thomas, a second-round pick in 2016 who was the sixth wide receiver chosen. Joining him is undrafted free agent Willie Snead, who just returned to the lineup in Week 5. Brees has been down both of his starting offensive tackles for most of the year, with Terron Armstead debuting last week and Zach Strief hitting injured reserve after 78 snaps. First-round pick Ryan Ramczyk has filled in, playing every offensive snap this season at either left or right tackle.

Brees does this or something like this every season, so we've grown accustomed to how consistently excellent he is. He has never been the best quarterback in football, so there's no peak season for us to point to. Even during 2009, when Brees led the league in passer rating and quarterbacked a 13-3 Saints team to the top of the NFC and then the Super Bowl, he mustered only 7.5 MVP votes to the 39.5 of Peyton Manning. Brees has racked up only six other MVP votes over the rest of his career combined, so while he consistently has been a top-eight quarterback, we're collectively sleeping on just how impactful he has been for so long.

Drew Brees has only missed three games since 2004, when he was on the Chargers. Stephen Lew/Icon Sportswire

An improvement, and what has changed in 2017

After two games, it looked as if the Saints were going to offer Brees more of the same league-worst defense, which has dragged New Orleans down to 7-9 each of the past three years. The Saints were carved up by Sam Bradford on Monday Night Football in the opener and then toyed with by Tom Brady at the Superdome in Week 2. The Patriots and Vikings combined for 65 points through two games, and that was with the Pats mostly taking off the fourth quarter on offense. Same old, same old.

And then, suddenly, things were different. The Saints dominated the Panthers in Week 3, picking off Cam Newton three times and holding Carolina to 13 points. Next, they shut out the Dolphins in London. Last week, while the Lions scored 38 points, those numbers included two return touchdowns that shouldn't be counted against the New Orleans defense, which forced five turnovers and scored three defensive touchdowns themselves. This from a defense that had recorded one defensive touchdown in the past four years combined? Yeah, things are different.

A few games doesn't sound like a lot, but let's put that in context for what New Orleans has been like over the past few years. The Saints gave up 13 points to Carolina; over the rest of their games, the Panthers have averaged 23 points. The Saints held Newton & Co. 10 points below their season average. Miami hasn't been great, but it fell 15.3 points below expectation when the Saints shut it out in Week 4. (The Lions exceeded their season average, but even that's only a trick of defensive scoring.)

The Saints had held a team 10 or more points below its season average only twice in 48 tries from 2014 through 2016. The last time they managed to even hold two consecutive teams below their average -- even by a tenth of a point -- was in October 2014, and even that required Aaron Rodgers to limp through most of a 44-23 Saints win over the Packers because of a hamstring injury.

The numbers are, honestly, downright remarkable. The New Orleans run defense hasn't been anything to write home about; it ranks 31st in rushing average, giving up 5.8 yards per carry, although that mostly comes down to two 30-plus yard runs by Curtis Samuel and Ameer Abdullah, The Saints are giving up a first down on 15.4 percent of the rush attempts they face, which is a far more respectable 22nd.

Cameron Jordan, a first-round pick in 2011, has 51.5 career sacks. Derick E. Hingle/USA TODAY Sports

The New Orleans pass defense, though? It's like Pat Swilling and Rickey Jackson are out there all over again. Over the past three games, the Saints have the league's best opposing Total QBR at just 11.7, with no other team within 15 points. They're second in the NFL in passer rating allowed (56.7) and sack rate (10.1 percent). They're giving up 4.4 yards per play on first-and-10, the third-best rate in the league. The defense has forced more takeaways in three games (nine) than it did over the entire second half of 2016 (eight).

What has inspired the sudden improvement?

The play of Cameron Jordan. Jordan has always been seen as the brightest bulb in an especially dim Saints defense, but he has looked like a Defensive Player of the Year candidate over the past three games. In his past 12 quarters, Jordan has four sacks, five quarterback knockdowns, three passes defensed, a forced fumble, a pass breakup that led to an interception, and a pick-six. He produced one of the most physically dominant plays you'll see all season last Sunday, when he bull-rushed reserve Lions tackle Brian Mihalik backward into Matthew Stafford, sacking the Lions quarterback without Jordan ever laying a hand on the former first overall pick.

Improvements from Kenny Vaccaro. New Orleans' first-round pick in the 2013 draft, Vaccaro has had an up-and-down career. This season has been no different, as Payton threatened to bench the inconsistent Vaccaro after the opener and then did so against the Patriots in Week 2, with Vaccaro playing just 64 percent of the defensive snaps. Vaccaro was put back in the starting lineup against Carolina, and he has played superbly since, racking up five pass deflections, three tackles for loss against the run and two interceptions. It's difficult to trust Vaccaro after years of vacillating between superstar and scrub, but if he can be anything close to this impactful the rest of the way, he's going to have a big contract year.

Changes to the defensive personnel. While the Saints are already down a pair of starters after losing Nick Fairley in the offseason to a heart condition and Delvin Breaux to a fractured fibula, they've been able to make changes and find better personnel on their bench. While their defensive line rotation has mostly stayed identical throughout the season, the Saints have made moves elsewhere.

At linebacker, Alex Anzalone was targeted and exploited so badly by the Patriots that it seemed like a good idea for the rookie to cut his flowing blond hair at halftime and blend in with the rest of the roster. (Love it while you can, Alex.) Anzalone took regular reps in Week 3, but he suffered a shoulder injury against the Dolphins that ended his season. The Saints have replaced him with veteran Craig Robertson, who lines up as the de facto starter alongside every-down player A.J. Klein. Robertson took only 24.1 percent of the defensive snaps through Week 2, but that's up to 58.6 percent since.

The defensive backfield has changed more drastically. Rookie corner Marshon Lattimore has been promising and locked down one starting spot, although he missed the Panthers game because of a concussion. Ken Crawley stepped in and excelled, and when starting corner P.J. Williams was benched against the Dolphins for disciplinary reasons, Crawley kept his job alongside Lattimore in the lineup. Crawley had some iffy moments against Golden Tate last week, but he's now an every-down cornerback. When Breaux comes back, the Saints could finally have a trio of promising young cornerbacks to build around.

Crawley jumped ahead of De'Vante Harris in the lineup, and Harris hasn't taken a defensive snap in two weeks. With the Saints leading more frequently over the past three weeks, they've been able to go to their big nickel package on a regular basis, pushing 2016 second-round pick Vonn Bell into the lineup. There are seven first- and second-round picks playing meaningful roles for the Saints, so it shouldn't be talent; if Allen can turn players like Bell, Marcus Williams and Sheldon Rankins into above-average players, the Saints could get good on defense quickly.

Drew Brees has thrown 10 touchdown passes to just two interceptions this season. AP Photo/Tim Ireland

New Orleans has gotten after opposing quarterbacks. With exactly one great pass-rusher on the roster in Jordan, the Saints have blitzed heavily in recent years. In 2016, New Orleans blitzed on 40.5 percent of opposing dropbacks, the highest rate in the league. Over the past three games, the Saints have kept that up by blitzing 42.6 percent of the time. That's also tops in the league.

The Saints also have been impossibly great when blitzing during this hot stretch; they're allowing a passer rating of just 29.2, which is nearly 30 points better than anybody else in the league. If you remember the 10.1 percent sack rate figure I quoted earlier, you can probably put two and two together and figure out that opposing quarterbacks are running for their lives when the Saints bring pressure.

That's not necessarily true. Jordan & Co. are pressuring quarterbacks only 21.7 percent of the time during their winning streak, which is good for only 27th in the league. The Saints haven't had a dominant pass rush over the past three games, but when it has arrived, the pass rush has gotten home more frequently than you might expect.

As I've mentioned in the past, history suggests that both players and teams alike will generally turn about 40 to 45 percent of their quarterback knockdowns into sacks. The Saints were third in the league last season with 106 knockdowns of opposing quarterbacks, but they generated only 30 sacks. That 28.3 percent conversion rate was the lowest in the league; if they'd sacked quarterbacks at a league-average rate relative to their knockdown total, they would have racked up 41 sacks.

Over the past three weeks, the Saints have been on fire. They've turned their 16 knockdowns into 13 sacks, good for an 81.3 percent clip. Jordan, who had 7.5 sacks on 24 knockdowns a year ago, has five sacks on eight hits this season, including four sacks on five hits in his past three games. That's how you produce a great sack rate without much pass pressure.

Can the Saints keep up that sack rate? Probably not. Will they be one of the best defenses in football over the next 11 weeks? I'd be skeptical. Showing steady signs of life after three years of awful performances, though, is promising. Defenses as bad as the Saints' have often regressed to the mean by virtue of the dead cat bounce; they get rid of replacement-level talent, change their coaches, invest in new talent, or get luckier.

What's next

It has taken the Saints three years to get out of the gutter, but they might finally be bouncing back toward mediocrity.

The reality is that the Saints don't need to possess a top-three defense to make it to the postseason. If the defense can just flirt with competency, that should be enough for Brees and the offense to hit 10 wins. FPI has the Saints nearly there, with 9.6 wins and a division-best 39.4 percent chance of winning the NFC South. With New Orleans catching a break and facing a Packers team without Rodgers in Lambeau this weekend before hosting the Bears, the Saints look to be in great shape to stay in the thick of the NFC South race.

Maybe we'll even be reminded of how great their quarterback is in the process. It's not exactly typical for a player to win his first MVP award at 38, but there aren't many quarterbacks who have aged as well as Brees has. With Rodgers injured, the Patriots' defense playing a lot like the bad Saints units of the past, and Kareem Hunt playing a less valuable position, this is Brees' best shot at taking home hardware before retirement. The MVP award would probably require the Saints to win the South and claim a first-round bye, which the Saints have a 19 percent shot at accomplishing, per FPI. If the defense can hold up its end of the bargain, it seems likely Brees will hold up his.