Purdue, one of last year's biggest surprise improvements, sits a 0-3 after a loss to Missouri. How did we get here?

Jeff Brohm got to West Lafayette and engineered a big turnaround right away.

After going 3-9 and ranking 105th in S&P+ in Darrell Hazel's final year, the Boilermakers ranked 41st and finished 7-6 in Jeff Brohm's first season at the helm. It was a shocking turnaround, even for someone has well-regarded as Brohm.

At Western Kentucky, Brohm built a fearsome offense that rose all the way to No. 5 in S&P+ in 2015. But defense was behind Purdue's immediate improvement in the Big Ten West. Coordinator Nick Holt masterfully coached up a unit that was 99th in Def. S&P+ into one that finished 2017 at No. 35 in that very same area. Offensive improvement was part of Purdue's turnaround too, with that side of the ball moving from 94th to 60th in S&P+, but that kind of bump could be somewhat expected given Brohm's history. The defensive leap was not.

This was likely going to be a season of regression for Jeff Brohm and the Boilermakers no matter what.

The defense, which was the team's driving success in 2017, was almost certainly due for a setback. From Bill's 2018 Purdue preview:

Brohm made the most of last year's personnel and will undoubtedly do so again, but the defense, the driving force of last year's surge (it went from 99th to 35th in Def. S&P+), is starting over in the front seven and at cornerback. The offense should be ready to carry more weight, but with a schedule that features six projected top-40 opponents (including three 12th or better), plus trips to Minnesota, Nebraska, and Indiana, it might take another magic act to top about 6-6.

The Boilermakers' defense ranked 125th(!!!) in Bill's returning production rankings. Among the losses to Purdue's defense: linebacker/defensive captain Ja'Whaun Bentley, defensive linemen Gelen Robinson, Antoine Miles, Austin Larkin and Eddy Wilson, cornerbacks Josh Okonye, Da'Wan Hunte and Kamal Hardy, linebackers or edge rushers Garrett Hudson, T.J. McCollum and Danny Ezechukwu.

Dear lord.

Purdue's regression so far has looked bad on the scoreboard. But stats say they've been a bit better than the final scores indicate.

The Boilermakers are 54th in S&P+ entering Week 4. Last year, they finished 41st. Not the kind of tremendous drop you might think of a team that's 0-3. Let's explore:

So far, Purdue's offense surged from No. 60 in 2017 to No. 24 so far in 2018, but the defense has fallen off a cliff, going from No. 35 to No. 92.

Rushing defense was a cornerstone of Purdue's success in 2017. Their Def. Rushing success rate ranked fourth in FBS, with their Def. IsoPPP ranking 68th. After three games, their 2018 def. rushing marginal efficiency ranking is 57th and their marginal explosiveness ranking is 107th. Their efficiency and explosiveness rankings on pass defense have also slid from bad in 2017 to worse in 2018.

But while Purdue has lost three games, the Boilermakers have held postgame win expectancy metrics that indicate performances that were better than the final scores would have you believe.

FWIW, Bill has previously defined postgame win expectancy like this:

It basically looks at the key stats from that game and says "You would have won this game X percent of the time."

Purdue's three postgame win expectancies:

Week 1 vs. Northwestern: 65.1

Week 2 vs. Eastern Michigan: 56.5

Week 3 vs. Missouri: 60.8

And the adjusted scoring margins, which try to project what the score would be based on the key stats:

Week 1: Purdue by 4.1 points

Week 2: Purdue by 1.7

Week 3: Purdue by 2.9

That's right, Bill's numbers say Purdue looks more like a 3-0 team than an 0-3 team.

game_date offense points postgame_win_prob drives plays yards yards_per_play success_rate scoring_opps points_per_opp average_fp yardage_margin success_rate_margin pts_per_opp_margin fp_margin turnover_margin exp_turnover_margin turnovers_luck 8/30/18 Northwestern 31 34.90% 14 79 401 5.08 44.30% 7 4.43 31.6 -71 3.50% -0.07 5.1 3 -0.27 3.27 8/30/18 Purdue 27 65.10% 14 71 472 6.65 40.90% 6 4.5 26.5 71 -3.50% 0.07 -5.1 -3 0.27 -3.27 game_date offense points postgame_win_prob drives plays yards yards_per_play success_rate scoring_opps points_per_opp average_fp yardage_margin success_rate_margin pts_per_opp_margin fp_margin turnover_margin exp_turnover_margin turnovers_luck 9/8/18 Eastern Michigan 20 43.50% 13 65 416 6.4 33.90% 3 6.67 29 -60 -13.10% 3.33 3.8 1 2.18 -1.18 9/8/18 Purdue 19 56.50% 12 66 476 7.21 47.00% 6 3.33 25.3 60 13.10% -3.33 -3.8 -1 -2.18 1.18 game_date offense points postgame_win_prob drives plays yards yards_per_play success_rate scoring_opps points_per_opp average_fp yds_per_play_margin yardage_margin success_rate_margin pts_per_opp_margin fp_margin turnover_margin exp_turnover_margin turnovers_luck 9/15/18 Missouri 40 39.20% 13 89 608 6.83 50.60% 10 4 25.8 -1.82 -6 5.50% -0.63 0.4 0 0.66 -0.66 9/15/18 Purdue 37 60.80% 12 71 614 8.65 45.10% 8 4.6 25.4 1.82 6 -5.50% 0.63 -0.4 0 -0.66 0.66

Under scrutiny, these win expectancies hold up. Purdue outgained Northwestern but turned the ball over three times. Purdue outgained Eastern Michigan, and ran for 341 yards on the ground, but turned it over twice to EMU's zero times.

Against Missouri, Purdue held a 614-608 advantage in total yards and a 8.7 to 6.8 edge in yards per play, and each team had one turnover. Brohm's team has lost three games by a combined eight points. That's notable, but still not something you'd call entirely positive. Northwestern just lost to Akron, and Eastern Michigan isn't anything special. Beating those teams by a few points each would have made Purdue's record look a whole lot nicer, but it would have still indicated underlying problems.

Missouri, however, might be actually good. The Tigers are No. 29 in S&P+ compared to Northwestern's No. 66 and EMU's No. 74. Purdue only lost to them by three and had more yards per play, more points per scoring opp., a slightly worse success rate and and advantage in turnovers luck.

How much should we be worried?

The Boilermakers have a biiiig test coming up in Boston College (No. 17 in S&P+). They do get this game at home, but an 0-4 start is more likely than not. S&P+ projects a 10.8-point margin in favor of the Eagles, who are good.

And after that, Purdue's schedule, even though the Boilermakers reside in the Big Ten West, ain't easy going forward. Illinois is the only team left ranked lower than the Boilers:

at Nebraska (No. 46)

at Illinois (No. 99)

vs. Ohio State (No. 2)

at Michigan State (No. 20)

vs. Iowa (No. 34)

at Minnesota (No. 48)

vs. Wisconsin (No. 13)

at Indiana (No. 23)

Nebraska and Minnesota seem like toss-ups at this point, while Ohio State, Michigan State, Iowa, Wisconsin and Indiana all seem like losses. This all points to Brohm's team looking worse to most fans than it actually is. Maybe that ends up benefitting the Boilermakers, who'd get to keep a hot coaching commodity in West Lafayette a little longer.