When I took a look at Princeton through seven games the Tigers sported a 3-4 record.

In the next seven contests - getting us to the season's halfway point - Princeton went 4-3.

On paper you'll see little more than one additional victory and one less loss but the second quarter of the 2012-13 has been far more intriguing than that.

After the jump you can find lengthy analysis and projections as conversation starters, plus updates on some numbers to track throughout the season.

Please add your thoughts in the comments. Hey! Ho! Let's go!

The offense has gotten better, while the defense has dropped off slightly.

Princeton was ranked 42nd nationally on defense through seven games - which helped compensate for a middle-of-the-pack 151st ranking for the offense.

Now the Tigers are 80th defensively, but up to 116th offensively.

By comparison, last year Princeton was 79th / 121st.

The good news is that this current offensive number remains eons better than 09-10's 214th overall.

One thing the Tigers still do well on defense is forcing turnovers on 22.6% of their opponents' possessions.

Defensive two point shooting percentage has increased however from 41.4% to 45.2%.

On offense the overall field goal percentage has increased from 42.4% to 45.2%. The Tigers' Effective Field Goal Percentage is 51.7% (60th) with a 36.4% mark from behind the arc (66th) and 50.1% inside the arc (78th).

Tiger turnovers have dropped dramatically from 24.2 of all possessions (293rd) to 20.9 of all possessions (195th).

I've tried to find some correlation between the addition of Hans Brase to the starting lineup and Ian Hummer's increased efficiency but the numbers don't back me up. Instead I'll say that with Brase on the floor the offense seems to move faster from point to point. There's less thinking and more split second decision making. I think that's the primary cause of the turnover numbers decreasing on a team with decreasing minutes from traditional guards.

Coming off a horrible 24-17-17-17 turnover stretch Princeton has averaged 10.6 turnovers/contest the past seven games.

Finally, kudos to this year's schedule-maker. The 2012-13 non-conference slate turned out to be a stacked one from top to bottom, not to mention there's a formula here that should be replicable in future seasons. Princeton's overall Strength of Schedule is 53rd nationally, compared to 130th last season, 170th the year before and potentially the most difficult slate of the prior 11 campaigns.

Ian Hummer has continued to be terrific, which should shock no one.

He and Bucknell's Mike Muscala are the only two players in Division I who are leading their respective teams in scoring, rebounding, assists and blocks.

In the last seven games Hummer has started to receive more consistent support from a modified rotation that formed in the second half of what would ultimately be a very frustrating loss to Fordham, but was not fully realized until an injury necessitated additional changes.

Hummer was on pace for 136 dimes this season, which would have been third-most by a Tiger in a campaign, behind only Billy Ryan in 1983-84 and Kit Mueller in 1989-90. That pace has dipped a tad to 128 if his numbers hold, good for fourth-most in a season.

The senior forward is still being used at a high rate but that number has dropped slightly. Through seven games, 32.8% of all Princeton possessions involved the senior captain.

Hummer is still 13th nationally but he's using 31.8% of all possessions and taking 30.0% of his team's shots when he's on the floor (102nd nationally, down from 89th).

He went from eighth in Division I on Assist Rate to 31st. Last year he was 273rd overall in this category.

I neglected to acknowledge that Hummer's layup-denying block of Tony Hicks in the first half of last Saturday's game versus Penn was the 100th swat of his career.

Turnovers are still an issue (though he has dropped from 4.0/game to 3.4/game) as well as free throw shooting (up from 60.0% but still just 62.1% for the season).

He's 23-36 at the line (63.9%) these past seven games.

Returning to turnovers for a second, Hummer has 21 more giveaways than his closest teammate (Denton Koon with 27). Subtracting Hummer, Princeton averages a superb 9.5 turnovers/game.

As Hummer rises Princeton's list of all-time scorers, he's on pace for 448 points as a senior if he continues to average 16.0 ppg, which would put him at 1,618 for his career - good for second place behind Bill Bradley and 68 points clear of Doug Davis '12.

Next up is Brian Earl in sixth place, 34 points away.

It is still quite possible Hummer will pass Davis when Princeton hosts Harvard on March 1st.

Princeton is +59 with Ian Hummer on the floor with the team +39 for the season (859 points for, 820 points against).

One final Ian Hummer fact: He's in the Top 500 nationally in all of the following categories - Percentage of Available Minutes Played, Percentage of Possessions Used, Percentage of Shots Taken, Effective Field Goal %, Defensive Rebound %, Assist Rate, Block %, Steal % and Fouls Drawn/40 Minutes.

After 18 steals in his first seven games, T.J. Bray had seven steals in his next seven games. He's no longer on pace for a season total of 72, which would have left him one off of Armond Hill's program record set in 1975-76. That's completely OK.

Bray's also dipped in his pace for 120 assists which would give him 253 for his career and leave second all-time at Princeton in assists a possibility. Bray had 119 dishes as a sophomore (32 games that season), fifth-most in a season by a Princeton player. Bray has 49 assists through seven games, which would give him 98 by year's end (28 regular season games).

It is still reasonable to imagine Bray and Hummer each exceeding 100 assists. The Tigers last had two players with 100+ assists in the same season in 1997-98 (100 for Steve Goodrich and 131 for Mitch Henderson).

What I really like is Bray's 13:3 assist-to-turnover ratio in the past five games.

Bray started the year 1-19 from three point range but is 18-43 (41.9%) since and 12-25 from behind the arc the past five games (48.0%).

The Tigers are 5-0 when Bray reaches double figures and Princeton is +57 with Bray on the floor.

In the past seven games Will Barrett has committed just four turnovers while distributing 11 assists.

Barrett holds a team-best Effective Field Goal Percentage of 60.8, boosted by 23-45 three point shooting (51.1%). The EFG% number is 68th nationally and his True Shooting Percentage is 96th nationally. All this despite being 16-38 inside the arc (42.1%).

Barrett has dropped his fouls called/40 minutes from 6.9 as a sophomore and 5.8 as a junior to 2.9 as a re-junior.

After starting the year 11-14 on free throws (78.6%) he's gone 6-11 (54.5%) at the line.

The nicest number might be Barrett's career high 10 rebounds against Penn.

Clay Wilson is 0-6 from three point range and 0-7 overall his last three games. The contests versus Elon and Penn were the first times Wilson has not played double figure minutes this season.

When Wilson has entered games recently, plays have been run specifically for him to get free around screens for wing three point looks. I wonder if not doing that right upon insertion to the lineup would change these figures at all.

Chris Clement is 0-5 from the floor the past seven games and did not attempt a field goal in the prior 19 minutes of court time against Akron, Elon and Penn.

Clement actually has not scored since the Tigers visited Lafayette despite being on the floor for 68 minutes of action! He has no assists and one turnover during that same stretch.

Princeton with Denton Koon coming off the bench (four games):

77-195 (.395)

Princeton with Denton Koon in the starting lineup (10 games):

237-500 (.474)

Princeton's opponents with Denton Koon coming off the bench:

92-191 (.482)

Princeton's opponents with Denton Koon in the starting lineup:

198-489 (.405)

Koon has played 34 minutes or more in each of the Tigers' last five games.

Thinking about Koon, I keep coming back to a comment from Coach Henderson about how Koon is the fastest Princeton player. That thought never crossed my mind previously, but it could explain how Koon is able to stealthily get behind defenses and meet the ball in time for layups and dunks.

Koon's biggest detriment is a team-worst 25.1 turnover percentage.

Seven games ago I wondered: "Is the fabled 'two-headed monster' Henderson has mentioned emerging?"

Hans Brase changed the question and the answer. Having never played more than 18 minutes in a game and four times seeing single digit action, the freshman earned 18 minutes in the second half versus Fordham and was a huge part of why the Tigers were able to build a (regrettably surmountable) 12 point lead.

In the next game Brase replaced Brendan Connolly as the starting center and has been on the floor for between 18-28 minutes each game, with the Tigers going 4-1 when Brase starts.

Even as he has struggled to score the last two contests versus Elon (1-9 from the field) and Penn (1-4 from the field) he's had 15 combined rebounds and six combined assists.

Brase's 7.1 fouls/40 minutes have dipped slightly to 6.4 fouls/40 minutes.

Using Brase as center has meant Connolly is established as his backup, which slid Mack Darrow to the forward spot. More on that in a bit.

Princeton with Hans Brase coming off the bench (nine games):

188-439 (42.8%)

Princeton with Hans Brase in the starting lineup (five games):

126-256 (49.2%)

Princeton's opponents with Hans Brase coming off the bench:

179-433 (41.3%)

Princeton's opponents with Hans Brase in the starting lineup:

111-247 (44.9%)

Connolly is averaging 11.2 minutes/game off the bench since Brase replaced him. Connolly deserves commendation for a team low turnover rate of 13.7.

The return of Mack Darrow is a welcome sight.

I won't pretend to be inside the senior's head, but Darrow was a mess at the start of his final year. He wouldn't shoot (four games with either no FG attempts or one FG attempt), he couldn't score (two points total his first five games) and he added very little support for his teammates off the bench.

While Darrow had a solid game to counteract the ridicule of Kent State's broadcasters out in Ohio, the nadir was soon to follow - a scoreless two game stretch versus Fordham (four minutes) and Rider (six minutes) that did little to indicate a forthcoming consistent change.

Then Will Barrett got hurt.

Barrett's thigh bruise versus Rider combined with the replacement of Connolly with Brase meant Darrow was going to play forward - at least for a single game. Darrow responded with 10 points in his lone start of 2012-13, which was also Princeton's best win of the season - a 79-67 decision over Bucknell.

I don't know what happened but from that juncture forward over these last four games Darrow has been Mack Darrow. He's shaken his funk and returned to what he did well as a junior.

For starters, he's doing what his coach and teammates have begged him to do - shoot the basketball! Darrow is 7-15 from three the last four games (46.7%) and 11-21 from the field overall (52.4%). He's rebounded well (15 total boards) during this stretch, also contributing 11 assists versus one single turnover.

I loved how Darrow was able to run the offense in the second half against Penn, giving Princeton an extra option to break pressure up the floor and a "point forward" to go with Bray as the point guard.

Darrow's offensive rating as a senior has risen to a team-best 110.6. He was at 86.6 through seven games, down from 120.3 as a junior and 115.2 as a sophomore.

Heading into their two week exam break, Princeton is 7-7, but 4-1 in their last five games.

Most importantly, they're 1-0 in conference before exams. The Tigers never completely recovered from a 1-1 start to the 2011-12 Ivy campaign, especially with the first Penn game falling the day classes resumed.

It feels like a similar position to one year ago in a numerical regard - Princeton's defense is tops in the Ivy League with Columbia (152nd) second and Harvard (161st) third. The Tigers' offense is second among the Ancient Eight with Harvard (40th) first and Columbia third (163rd).

The remaining five Ivy programs have offenses ranging from 226-308 and defenses ranging from 188 (Penn) to 232 (Dartmouth).

Pomeroy projects both the Tigers and Crimson going 11-3 in Ivy action. With each school already 1-0, this year's title may be determined by who is blinks first in their other 11 matchups.

At the halfway point of the season, Mitch Henderson's team certainly feels a lot closer to sanity than they did just seven games ago.