math

For context on the below, see Part I for an extensive discussion of what exactly is going on here (warning: math) and Part II for some examples of why I think this is a useful exercise. Note those posts are from last year. Which is 2005.

(Performance note: generating these graphs is a dynamic process, so they can take several seconds if no one else has looked at the requested data recently. Cached ones should come up immediately.)

First: Third down efficiency. The thick line in the center is the NCAA average (e.g., approximately 68% of third and ones were converted last year). There is a second line that represents an individual team's third down efficiency. Where there is a gap between the lines that gap is filled in with either red or green depending on whether it is "good" or "bad". Being above the line is good for offenses--you convert more often. Being above the line is bad for defenses--you are converted upon more often. You want to see a lot of green in these graphs.

Second: Third down distance distribution. Again, the line in the center is the NCAA average and the thinner line is the individual team's. Green is just "above"; red just "below," since there's no clear distinction on good or bad based solely on what side of the line you're on.

Third: the raw numbers. The following graph shows the underlying data used to construct the first two. Each bar represents one yard line. Blue segments are failed conversions. Red segments resulted in first downs.

(A note on reproducing these graphs: feel free. Right click and "Save As" to get a static copy that won't break if I decide to change the URL... which I might. Please drop a link. Also: if the idea of maize and blue on your site is revolting, you can give me two other colors (specified in hex--ie, #A30924--, please) and get pretty team-color-appropriate ones.)

TUC? COP? In English, please.

Last weekend we crushed NMU. MSU is next at the Joe and then either Notre Dame or Lake Superior, depending on the outcome of the early game.

Winning Comparisons

Tossups

None.

Solid

• Michigan State. We have to go 0-2 at the Joe and State has to go 2-0 for the Spartans to pass us. Otherwise we'll win a tied comparison by virtue of our higher RPI.
• Dartmouth & St. Lawrence. Both are in the same boat as MSU: must win their conference tourney and hope we go 0-2 to flip the comparison. We cannot lose comparisons to both these schools because one has to lose.
• UMass. [was: lock we won.] I underestimated the ability of UMass to fly up the RPI with games against high-quality opposition. We can lose this comparison if -- say it with me -- UMass wins their conference tourney and we go 0-2 at the Joe.

Locks: LSSU, UNO, MSU-Mankato, Cornell, Vermont, Wisconsin, Michigan Tech, Maine [was: tossup... Maine got swept *again* by UMass], Miami [was: tossup... swept by Lake State], Denver [was: tossup... also swept.], Colorado College [was: solid win. They lost in three to MTU.]

Losing Comparisons

Tossup

None.

Solid

• BC & BU. The two archrivals play in the Hockey East semis. If we win the CCHA, we will pass the loser of that game. If the winner of that game loses in the HE final, we will also pass them. A split at the Joe does nothing for us; we'll lose both comparisons.
• North Dakota. [was: tossup we lost.] NoDak did indeed sweep Minnesota State right out of TUC status, opening the door for us. Here's a weird math thing for you: since we have fewer games against TUCs, if we win the CCHA we will flip NoDak no matter what they do. We're currently winning COP but are behind on RPI and TUC, but our 8-7-1 becomes a 10-7-1 with a CCHA tourney win and NoDak's 12-10-2 can't win that race even if it becomes 14-10-2.
• Clarkson. We have to win the CCHA and have Clarkson go 0-2 this weekend to pass them.

Locks: SCSU, Minnesota, Notre Dame, UNH.

The Upshot

We are in. I have fiddled with every nightmare scenario available at TBRW -- 0-2 at the Joe, UMass and St Lawrence doing well, UNO's TUC status evaporating in a puff of smoke -- and the worst case appears to be #12. On the other side of the coin: believe it or not, with the right set of results Michigan can vault all the way to #5. Only four comparisons are completely gone, mostly thanks to UNO hanging on to TUC status by .0008 over RIT, Minnesota State, and a bunch of other teams. You might expect UNO is safely in the barn since all the teams near the TUC cliff are done for the season, but you would be wrong. Since RPI is 75% opponents' and opponents-opponents' schedule there will be some jitter down there and it's possible we could lose those two TUC wins. The above projections assume that this does not happen. If it does we cannot win the BU, BC, or Clarkson comparisons; North Dakota requires us to pass them in RPI; the rest of the comparisons still in play are unaffected.

Assuming UNO remains a TUC, Michigan controls its own destiny and can play themselves into 5-6-7 by winning the CCHA tourney. Michigan will hold all of the comparisons it currently does and will take at least two comparisons from NoDak, BC, and BU, escaping the dread Minnesota zone.

If Michigan splits they are locked into the 8-9 game and a bracket with the #1 overall seed unless they get swapped out because of an intra-conference conflict.

If Michigan gets swept at the Joe things will depend on how the other games go. Figure State is slightly less than 50-50 to win the CCHA tourney in that situation and that Dartmouth and SLU are collectively about 50-50 to win the ECAC tourney. UMass may be 10-20% to win HE, so we figure to lose slightly more than one comparison on average. That would put us either #10 or #11.

So the good news is that you can show up at the Joe and root for the Wolverines without any nagging concerns about Michigan getting boned by winning. A CCHA title probably means a two-seed in Grand Rapids, possibly with a Notre Dame team we (hypothetically) just beat.

Others of Note

Michigan State is on shakier ground than we are but is in with a split and is probably in even if swept. Miami is currently hanging onto its bid by the skin of its teeth at #14. They must root against LSSU, Wisconsin, MTU, Dartmouth, and Quinnipiac in their respective conference tourneys. Any autobid handed out to a team currently behind them dumps them from the tourney. The Redhawks dodged an enormous bullet last night when Minnesota and St. Cloud got late goals -- in St. Cloud's case, really really late: the third OT -- to boot UAA and UMD from the WCHA tournament.

Since the last time we took a detailed look at the Pairwise, Michigan split a pair at OSU and a bunch of other teams played a lot of games. Western fell out of TUCland; UNO and Lake State entered. Michigan's TUC record is now a mediocre 8-7-1 with a 1-1 record versus LSSU and a 2-0 record versus UNO hovering around the cliff. Northern, Michigan's opponent this weekend, is not a TUC.

Winning Comparisons

Tossups

• Denver. We're in a worse spot now that DU has drawn UW in the WCHA playoffs. If they sweep that series they'll win COP and probably move past us in RPI.
• Maine. [Last time: a solid comparison we lost.] Maine did cough it up against UMass, getting swept, and that was enough to flip the comparison... but only by a tiny amount. RPI is virtually tied. They win COP and we have a fair edge in TUC. Maine's first round playoff series is against the same UMass team that just swept them; if they win the series they'll probably take the comparison at year's end. If they lose it's ours.
• Miami. [Last time: a tossup we lost.] Margins are razor-thin everywhere. Whoever finishes better in the CCHA tournament will win the comparison. If one team wins the consolation game while the other loses the championship game, Miami probably takes the comparison.

Solid

• Colorado College. Status quo: decent RPI edge and unassailable in COP. We'd have to lose our series versus Northern for them to flip the comparison with a long WCHA playoff run.
• Michigan State. [was: tossup we won.] We now have a big COP edge and a medium RPI one. If we beat Northern, State will have a hard time passing us even with a H2H win.
• Dartmouth. Don't think there's any way for them to flip the comparison unless they win the ECAC and we lose to Northern.
• St. Lawrence. TUC is now very tight, but we win COP and have a 0.1 RPI edge.

Locks: LSSU, UNO, MSU-Mankato, Cornell, [was: solid win]. Wisconsin, Michigan Tech, Vermont. [was: solid win], UMass.

Losing Comparisons

Tossup

• North Dakota. NoDak's in a weird situation: their first round opponent, MSU-Mankato, currently sits #23 in RPI. If they sweep Mankato it's likely they'll no longer be a TUC; the Sioux are 3-0-1 against Mankato this year. Even if they lose the Screamin' Eagles, they'll still be ahead of us in TUC, but we win COP and RPI is pretty tight.

Solid

• Boston College. [last time: tossup we lost]. They made up a lot of ground by sweeping UNH.
• Boston University. If they lose their series against Vermont we can pass them. Otherwise they'll be ahead of us.
• Clarkson. [last time: lock we lost... guess not.] We own COP, they have a sizable edge in RPI. TUC could get interesting. If LSSU drops out and Clarkson loses to a TUC in the ECAC tournament, we could pass them with a CCHA championship. It's a longshot but just possible enough.

Locks: SCSU, [was solid loss]. Minnesota, Notre Dame, UNH.

The Upshot

Our position has improved. A couple teams have moved into the Lock Win category, Maine is now in a dead heat with us, and Michigan State is now significantly behind us. Only the BC sweep of UNH damaged any of our comparisons.

With our OSU split things are basically the status quo: we are locked into the 7-12 range. Denver gacked it up against CC last weekend and fell to 10th, which significantly reduces the chances we'll get paired with them in Denver, but we're now 9th and staring down a bracket featuring Minnesota. There's a tremendous amount of jitter in the PWR and things will change enough between now and the tourney selection that it's not worth getting exercised about yet, though. One thing that does seem likely: a bid in Grand Rapids. Most brackets I see from educated prognosticators give GR attendance the benefit of the doubt and put Michigan there whenever possible. Since Notre Dame is within driving distance of GR, there's also some sentiment to put the Irish there. No offense to ND, but as a relatively untested #1 seed who caught us when Billy Sauer was at his nadir and minus Cogs and Jack, I'd rather see them than any other potential #1.

(Named after the (apparently) famous Price Is Right game. Ask Orson.)

Hello! More exploration of the sketchy ethics of college football recruiting. Orson Swindle and I gathered the last six years of classes for every BCS team and found average-sized recruiting classes for each team. For comparison's sake, a team with 100% retention that never redshirts or recruits JUCOs or transfers should average 21.25 scholarships a year. A team with a 100% retention rate that redshirts everyone but still avoids JUCOs and transfers should average 17. If you figure about half of all freshmen redshirt (figure pulled directly from rear), then 100% retention means a class of slightly over 19 kids.

Disclaimers go here: Numbers are from Rivals. Scout has different numbers that are on average a little bit smaller. 100% retention is impossible and there are many completely kosher reasons for kids to leave a college football program before their eligibility expires. JUCOs and transfers were not accounted for in these numbers and obviously have a distorting effect (though transfers don't even show up in the rivals DB, so the net effect of a transfer to your school is to make your school look less like an Indonesian ferryman shoving people off the boat into alligator-infested waters.)

I've got the Big Ten, Pac-10, and Big 12. Check EDSBS around noonish for the ACC, Big East, and (drumroll...) SEC.

Our Indonesian Ferryman for the Big 12: Iowa State. An unsurprising second and third are Kansas State, Texas Tech, and their insatiable lust for JUCO blood.

And the Big 12 Mr. Chips Award For Academic Integrity goes to big, bad Texas -- though their number would be but middling in the Big Ten.

Yea, verily the Pac-10 is a conference of extremes.

Our Indonesian Ferryman for the Pac 10 is Oregon State with a staggering 29 scholarships handed out per class and a whopping 134 recruits over the past four years. Oregon State is the national Indonesian Ferryman and the sketchiest program in all the land.

Meanwhile, Stanford is puttering along at 18 scholarships per year. They win the Mr. Chips Award For Academic Integrity for the Pac-10 and the nation.

Our Indonesian Ferryman for the Big Ten: Michigan State. To be fair to the Spartans, their total would be good for but fourth in the Pac-10 and a piddling sixth in the Big 12.

Raise your hand if you thought Northwestern would win the Mr. Chips Award for the Big Ten. That's all of you, good. Now raise your hand if you thought Ohio State would come in second. Anyone? Bueller? Bueller? Ohio State is increasingly irritating: first they go and win against us all the time, reducing my ability to make fun of them to critically low levels, then they go and stop getting in trouble altogether -- a third string kicker selling weed just doesn't cut it, even if his last name is a popular synonym for semen. What's a blogger to do?

And there's one relevant team floating out there not in any conference...

To its credit, Notre Dame retains like a mother. Either that or Willingham was so bad at recruiting they left large numbers of scholarships open.

EDSBS will have has the ACC, Big East, and SEC up... how do they stack up? Stay tuned! Spay or neuter your dogs and such!

Many, many thanks to Sioux Sports for their handy PWR/RPI widgets. This post would not be possible without them.

So: we've established that a Western split is probably good enough to keep them a TUC. Does it matter? A comparison-by-comparison look at the PWR.

WINNING COMPARISONS

(ie: Comparisons Michigan wins right now. Prefer all of these to be "Etched In Stone.)

Tossups

• Denver. We own COP, but RPI is really really close and TUC is ridiculously close.
• Michigan State. H2H is tied. We have a significant COP edge that could go away since we're in the same conference. TUC is very close, RPI is very close.
• North Dakota. We win COP, but TUC and RPI are very, very close. NoDak's final four games are against TUCs, so there's a lot of wiggle here.

Solid

• Colorado College. We own COP and have a medium-sized RPI edge. TUC could go either way but as long as we're ahead of them in RPI we'll take the comparison.
• Cornell. No COP, they're well behind in RPI and have an ugly TUC record.
• Dartmouth. See "Cornell".
• St. Lawrence. We win COP and have a sizable TUC advantage that could go away if we lose WMU. Michigan has a 0.1 RPI advantage.
• Vermont. Same situation as St. Lawrence, but only if they do well in two games against BU upcoming.

Etched In Stone

• Lake State (or whoever is #25). Michigan will beat either Lake State or whoever replaces them simply by virtue of being well above .500.
• UMass. Huge RPI edge and we own COP.
• Michigan Tech. See Lake State.
• Niagara. See Lake State.
• Quinnipiac. See Lake State.
• Western. See Lake State.
• Wisconsin. H2H win and major RPI/TUC advantages. They win COP at the moment.

LOSING COMPARISONS

(Prefer these to be tossups.)

Tossups

• Boston College. Michigan has an RPI advantage of about 0.1, which is probably going to stand. They've lost COP and can't get it back. BC currently wins the TUC category because they're 9-8-0 and Michigan is 9-8-1.
• Miami. We have a tiny RPI edge; they have a tiny edge in TUC and a decent-sized lead in COP. A lot of wiggle in this comparison since it's a conference team.

Solid

• Boston University. Michigan has lost COP and is far behind in TUC. If BU gets swept by Vermont and Michigan outperforms BU in their respective conference tourneys Michigan might get by, but it's doubtful.
• Maine. We've lost COP. TUC is dead even at 9-8-1; Maine has two left against TUC Vermont and a decent RPI advantage. If Maine coughs it up at the end of the season we could move past them; doubtful.
• St. Cloud. The Huskies have a brutal closing stretch against Minnesota and North Dakota and could conceivably lose their TUC advantage over us if Michigan plays well down the stretch. We own COP right now with two against Minnesota pending. It would take a hefty collapse by SCSU but it's not impossible.

Etched In Stone

• Clarkson. We've lost COP, don't have the games to make up TUC.
• Minnesota. Duh.
• UNH. Duh.
• ND. Duh.

(Aside: notice how we're killing WCHA teams in COP? This is largely because we only had to lose to Minnesota once. Some of these teams, good otherwise, are rocking 0-4 records versus the Gopher death machine. Another item to add to the Complaints Against The Pairwise.)

THE UPSHOT

Without highly improbable events we have limited upside but limited downside. If we take all five tossups and nothing in the solid categories flip we'll be the last two-seed. If we lose all of them we have minor trouble, as we'll be tied for 12th with State. Since they win our comparison in this hypothetical scenario, they'll get the #12 seed and we'll be a couple of conference tournament upsets from getting bounced.

The good news: I don't think Western's TUC status matters all that much in terms of getting into the tournament. It will be hard to pull many of the tossups without that 3-1 boost, but the only way we can not make the tournament is by killing our RPI with bad performances against OSU and in the first round of the playoffs. Michigan's fate is entirely within its own hands. And with the vagaries of the PWR, where you actually get seeded is virtually irrelevant. I'd rather end up #12 than #9 and have to face Minnesota. (Unless Holy Cross wins the Atlantic Hockey tournament.)

Assuming at least a split versus OSU and a Michigan victory in their first-round playoff series, we are in, Western or no. If Michigan goes out and loses four straight, we're out, but assuming a reasonable performance down the stretch Michigan's tourney streak is not in jeopardy.

The status of Western Michigan, Lake State, and Ohio State is vitally relevant to Michigan's tournament chances. At this moment, both Western and Lake State are tentatively TUCs (assuming, as most do, a "good win" bonus of .003); Ohio State is not. Michigan plays OSU this weekend; Western and Lake State play at the Soo. All four games are critical for Michigan. Obviously, losing to OSU is bad but it gets even worse if getting swept shoves the Buckeyes into the top 25 in RPI, adding an ugly 0-2 to Michigan's TUC record. Michigan is 1-1 against Lake State and would probably prefer the Lakers to not be a TUC; they are 3-1 against Western and very much want those games to count extra.

This calculation was easier a year ago when there was a set threshold instead of a top 25, but we do what we must. With two games against a decent opponent, a Western sweep will retain their TUC status. The chasing teams don't have the opponents to pass the Broncos. Threat by threat:

• RIT plays Bentley, 55th of 59 in RPI.
• Sacred Heart plays Army, 44th.
• Lake State plays... uh... Western.
• MSU-Mankato plays Colorado College.

Only Mankato has the opportunity to break past Western if they sweep, and that would require an implausible sweep of their own. OTOH, if Western takes the pipe their RPI will drop to 0.4986. Though teams are going to bounce around madly over a weekend of play, as of right now that would be good for but 32nd. There's no chance they get swept and retain TUC status.

Is a split good enough? Maybe. They're 24th now, so one team can pass them. With a split Western will see their RPI drop to .5057 from .5100 -- not good. Both RIT and Sacred Heart are better than that now, albeit barely. Since they're playing crappier opponents than Western, if either one of them splits Western would stay ahead of them. Lake State will not pass Western with a split and Mankato needs three points from CC to make the leap. Past that you're looking for fairly improbable things to happen, like Bemjidi sweeping its last four games or Northeastern taking its last three, for anyone to pass the Broncos.

In sum: Western sweep is good. If they get swept they're gone. If they split we're rooting for Army or Bentley to take one of four games and for CC to not completely blow it against Mankato. The chances of that are around 75%, just to pull a number out of thin air. One of two should be good enough for now. The playoffs will also play a major role, but projecting out past the next couple games is fruitless.

Nasty, close your eyes and shiver scenario: That is, unless Michigan gets swept this weekend. That would propel OSU past Western into the 25th spot in the 75% scenario, replacing our 3-1 record versus them with a (hypothetical) 0-2 record versus Ohio State. Our RPI would plummet to 15th, our TUC record would get eviscerated, and the chances of an at-large bid would virtually flatline.

Moral of the story: do not lose to Ohio State this weekend.