For all your fancy-pants statistical needs.

Praise for The Basketball Distribution:

"...confusing." - CBS
"...quite the pun master." - ESPN

Dirk for MVP!

The boys over at the APBR metrics board are asking who should be MVP. I think that if we use the ridge-adjusted plus minus ratings, we can get a good answer.

I converted each player's worth into a total efficiency differential (Offensive RAPM times Minutes% for Offense, etc), then looked at how much worse we would expect their team to be without the player. I converted efficiency ratings into "pWins" or "pythagorean wins" by doing Offensive Rating^14/(ORTG^14 + DRTG^14).


My Lazy Lazy Lazy Lazy RPI

EDIT/UPDATE: I'm not very happy with the math here.

I have constructed a very lazy RPI, that is more theoretically sound than the RPI.

Considering the linear version of the Log5 win-percentage formula, we could (lazily) assume the following:

Season Win%= 0.5 + Real Win% - Opponent's Real Win%

1) Real Win% = Season Win% + Opponent's Real Win% - 0.5


2) Opponent's Real Win% = Opponent's Season Win% + Opponent's Opponent's Real Win% - 0.5

If we assume (lazily) that "opponent's opponents" play average (.500) teams, we can then also assume that their Season Win% equals their Season Win%, like so:

3) OOSeasonWin% = 0.5 + OORealWin% - .5
4) OOSeasonWin%=OORealWin%

So we can replace "Opponent's Opponent's Real Win%" in #2 with "Opponent's Opponent's Season Win%"

When we replace Opponent's Real Win% with #2, we get

5) Real Win% = Season Win% + (Opponent's Season Win% + Opponent's Opponent's Season Win% - 0.5 )-0.5
6) Real Win% = Season Win% + Opponent's Season Win% + Opponent's Opponent's Season Win% - 1

or as the RPI would have it,
RPI = WP + OWP + OOWP - 1

So in theory, Win%, Opponent Win%, and Opponent's Opponent Win% should all be weighted 'equally.'

Here We Go!!! (Into overtime!)

The (real) NCAA tournament starts in about one hour. To kick it off, I present my Overtime% for the first round.

Each game is ranked by the probability that is going into overtime*:

Here are the results

*The theoretical odds of going into overtime are lower than that of actually going into overtime**; there are a few specific things that have to happen to make the game sum to zero - the rankings are still valid though.

**End-of-40-minutes Game-scores fall under the normal distribution, but there is a significant dip around zero.

Updated Bracket Picks (Expected Wins)

I've updated the LRMC simulation to only include Clemson, and weaken BYU & Belmont (by the equivalent of 1 point per 100 possessions).

Here's the results.

For a bit of math - this method is pretty arbitrary in terms of assigning values - I just assumed this year's distribution of teams. I weakened BYU to better account for Davies' recent dismissal, and weakened Belmont, just doesn't fit for them to be #4.

Top Final Fours

The majority of huge-pool winners accurately predict the Final is a sampling of the top (seven) possible final fours that my LRMC simulation predicts.

E W SW SE Probability
Ohio St. Duke Kansas Pittsburgh 4.04%
Ohio St. Duke Kansas BYU 3.42%
Ohio St. Duke Kansas Belmont 2.10%
Ohio St. SDSU Kansas Pittsburgh 1.81%
Ohio St. Duke Notre Dame Pittsburgh 1.51%
Washington Duke Kansas Pittsburgh 0.97%
Ohio St. Duke Purdue Pittsburgh 0.88%

If you're doing a multiple-bracket pool, this might be useful...updated simulation results coming soon.

Official Tournament Picks, CONTINUED....

Here are some more numbers to help you make your picks:

"EW" means expected wins ('opening' round not included).
-Overall odds in the original efficiency simulation

-Overall odds in the LRMC simulation

-Consistency values (for each tournament team) - higher means more inconsistent

I am currently running a new efficiency simulation that uses a different formula than before to predict Percent Chance of Win.

Also, here is a quick rundown by Dean Oliver on why slow-paced teams like Wisconsin increase their likelihood of losing to less efficient teams.


This post is dedicated to my Mother, who wants my tournament picks :-D.

I have looked at every pick and noted its overall value in ESPN's tournament challenge.
Ohio St. winning the championship is the highest value not because they have a great chance of winning the championship, but putting them there

Here's the Spreadsheet (version 1, efficiency ratings)

For the mathematically inclined:

I used DSMok1's adjusted ratings and ran ~10,000 simulations of the bracket to find each team's odds of getting to each round.

Each round value = Sum of all Previous (Round Value * Odds of Winning That Round) + Round Value * Odds of Winning That Round.

Of note: these values did NOT include the probable home-court advantage (for example, UNC plays in Charlotte). I will add this soon if I feel its warranted.

S-Curve Madness: The Good, The Bad, and The Ugly

Wow, what a bracket. I'll be very quick here (forgive me if I miss something important), as I've got to get moving on my official predictions.

The good:

-Notre Dame didn't get a 1-seed (they didn't deserve one).
-St. Johns was a 6-seed (still a bit too over-seeded, but I'll take it).

The bad:
-Utah St, Clemson, Missouri, Gonzaga, Marquette are significantly better than their seeds suggest.
-Obviously, Virginia Tech not making the tournament is pretty ridiculous.
-Duke has the easiest path in the world until they will likely meet (#4 Pomeroy) Texas in the Sweet 16.

The ugly:

-As I disdainfully remarked on twitter, Belmont is seeded worse than ~THIRTY FOUR teams that have played worse than them, according to Ken Pomeroy's very reliable ratings. By adjusted efficiency, Belmont is #18 and Wisconsin #9. By adjusted margin of victory, they are #20 and #11. By genius-math-hyper-accurate-point-margin, they are #4 and #12. Ugh.

-Carolina vs. Washington is a very similar matchup, if they both go to the round of 32. Pomeroy has UNC at #14, Washington at #15. LRMC has UNC at #15 and Washington at #8. And Raymond has UNC at #14, Wash. at #7.

Alright, I'll keep everyone posted. Let's go Georgia!

The Humans are a Little Too Impressed...

As it gets down to crunch time for the teams who are on the bubble, and as the 68-team-field will be together in under 100 hours, I present to you a quick summary of the teams that impress pollsters, but not computer ratings.

"The Computers Aren't As Impressed"

Notre Dame: #4 AP, #4 Coaches, #15 Pomeroy
Now statistically, we can't really be sure of where a team's true value lies any better than +/- ten places or so, but currently Notre Dame's good record comes from winning close games (13th in 'Luck'). I would be relatively surprised if Notre Dame made it to the final four, although they have a decent chance of getting a #1 seed.

Arizona: #16 AP, #15 Coaches, #28 Pomeroy
Again, Arizona is good, but they're not that good. Many of their wins include single-digit-victory home games.

St. Johns: #17 AP, #18 Coaches, #34 Pomeroy
Inconsistency is the key here. Pollsters (and everyone) is impressed with wins against West Virginia, Georgetown, Notre Dame, Duke, Connecticut, Cincinnati, Marquette, Pittsburgh, and Villanova. While many of those wins came closely at home, this still is a huge sample of good performance against good teams. This St. John's squad has also lost to St. Bonaventure at home, Fordham on the road, Seton Hall on the road (by 14!). Their six Big East losses have come at an average of 14.7 points. Ouch.

Xavier: #18 AP, #20 Coaches, #35 Pomeroy
Xavier has definitely improved. After only beating Western Michigan by 3 at home, going into overtime with IUPUI Ft. Wayne at home, and losing to Miami OH on the road by eleven, they have won 16 of their last 17. The computers are not impressed, however, by the mediocre schedule those 16 wins came against. The one loss in that stretch? To #207-Pomeroy Charlotte.

Temple: #24 AP, #25 Coaches, #38 Pomeroy
Again, the pollsters just felt like boosting up a mid-major with lots of wins. While Temple beat Maryland and Georgetown, they don't have anything particularly great on their resume (the Georgetown win came at home, and was only by 3). Temple has mostly been feeding off their weak conference to get here.

That's all for now. Selection Sunday and bracket simulations coming soon!

Unranked Lurkers

There are several teams who simultaneously impress statistical rankings, but do not impress poll-rankings.

Here are all the teams who are in the top-25 of at least one of my three favorite systems --and not ranked in either major poll--: by Ken Pomeroy's efficiency margin, Raymond's Ratings (basically SRS, if you're familiar), and GA Tech's Bayesian Logistic Regression Markov Chain.

Top-25, The-Humans-Are-Unimpressed
(bold indicates a computer system being similarly unimpressed, italics indicate top-10 computer rating)

-Washington (P10, 19-9) - #13 Pomeroy, #8 Raymond, #6 LRMC

Washington has had a particularly tough time away from home, losing two of three on neutral courts (by single digits to Kentucky and Michigan State), and losing six of eleven on the road (only once by double-digits). At home, on the other hand, the Huskies won their first thirteen before putting up a non-characteristic eFG% of 39.7 against Washington St. on Sunday, losing by eleven. Their blowout wins prove a marked inconsistency, as they absolutely beat up on decent teams. Washington beat top-100 Pomeroy teams Oregon, Long Beach St, Arizona, UCLA, USC, Cal (twice), and Stanford, by an average of 18.4 points. I won't give up on them (as Pomeroy similarly encourages you to do) because of this, and their demolishing of Arizona and their quality road performance at UCLA.

-Maryland (ACC, 18-11) - #16 Pomeroy, #16 Raymond, #32 LRMC

Four of these losses include: An 8-point road loss at Duke, an 11-point road loss at Carolina, a 9-point neutral loss to Pittsburgh, and 8-point road loss to Villanova. Their overall strength of schedule is low since 1/3 of their season has been against sub-200 teams. This is evident in the extremely flawed RPI, who knocks Maryland down to #83. Ouch. If these guys win the ACC tourney, I would expect them to win a couple in the big dance...but the odds are not in their favor to get that first step.

-West Virginia (BE, 18-10) - #18 Pomeroy, #18 Raymond, #19 LRMC

Exactly half of WVU's ten losses have come against top-25 Pomeroy teams, and they have wins against Vanderbilt, Cincinnati, Purdue, and Notre Dame. Their Pomeroy strength of schedule, as one might expect, is 2nd in the country.

-Belmont (ASun, 27-4) - #20 Pomeroy, #24 Raymond, #8 LRMC

Belmont is an interesting case. We have a very low sample size of decent competition with these guys - they've only played three games against tougher opponents than #106-Pomeroy East Tennessee St. In fact, only eleven of their thirty-one games have been against top-200 Pomeroy teams. At any rate, their only losses have come against decent opponents (save Lipscomb), on the road, by an average of only seven points.

-Illinois (B10, 18-11) - #21 Pomeroy, #22 Raymond, #20 LRMC

The Illini have been extremely inconsistent this season. While they have lost to Illinois-Chicago on a neutral court, they beat tough opponents in Maryland, Wisconsin, Gonzaga, and North Carolina. Also, they've had to deal with the nation's 6th-highest string of opponents (by Pomeroy's metric).

-Cincinnati (BE, 22-7) - #24 Pomeroy, #28 Raymond, #34 LRMC

Cinci is at least somewhat recognized by humans, as they received the 32nd most votes in the AP poll this week. Their seven losses have come from teams with an average ranking of 19-Pomeroy.

-Marquette (BE, 18-11) - #25 Pomeroy, #26 Raymond, #27 LRMC

Marquette has had an unfortunate schedule. They've lost to neutral-court Duke by 5, road-Pittsburgh by 8, road-Lousville by 1, road-Nova by 5, road-Notre Dame by 5, and road Georgetown by 9. While the humans might not be impressed, just from those numbers alone, a statistical-minded Nathan Walker would call Marquette a top-25 team.

-St. Mary's (WCC, 23-7) - #45 Pomeroy, #32 Raymond, #23 LRMC

St. Mary's inconsistency is marked by a high-high and a very-low-low. They only lost to BYU by 1 on a Neutral court, but lost to #302 Pomeroy San Diego. In between has come a few losses to good teams and beating up every other average team they encountered.

Unfortunately, some of these squads are going to be Nationally Invited, if you know what I mean. For those that make the big dance, there's a good chance they'll beat their better-seeded opponent.


About Me

I wish my heart were as often large as my hands.