Serieses?
Easiest battle is Chicago over Atlanta in 5.
Closest series is the Los Angeles over Dallas in 6.
Updated Playoff Odds, 4/29
All first-round series except San Antonio/Memphis have been decided.
Serieses?
Easiest battle is Chicago over Atlanta in 5.
Closest series is the Los Angeles over Dallas in 6.
Serieses?
Easiest battle is Chicago over Atlanta in 5.
Closest series is the Los Angeles over Dallas in 6.
Not Exactly On Hiatus
Hello all!
I am currently finishing up my 8th semester at Appalachian State, and graduating in a couple of weeks.
I've been busy with non-basketball...or at least I've been attempting to be busy with non-basketball.
I'll be writing a bit for The Coolest Basketball Site (TM) this summer, which I am extremely excited about.
Anyways, here are my silly opinions on basketball as the playoffs begin:
-Nathan
I am currently finishing up my 8th semester at Appalachian State, and graduating in a couple of weeks.
I've been busy with non-basketball...or at least I've been attempting to be busy with non-basketball.
I'll be writing a bit for The Coolest Basketball Site (TM) this summer, which I am extremely excited about.
Anyways, here are my silly opinions on basketball as the playoffs begin:
- Kevin Love is NOT the MIP. He's not even in the 100 best players in the league. (Individual rebounds and Rebound% are not all that telling). And he is most DEFINITELY not the MVP *shudder*.
- Derrick Rose is not the MVP. Even if you're supposed to choose "Best player on the Best team," he does not appear to be that. He is a close overall candidate by some agreeable measures, however.
- Oh, and, with Harrison Barnes staying in Chapel Hill, the pre-season rankings will look something like this:
- #1: North Carolina
- #2: Ohio St.
- ...
- ...
- #1,000: Eventual National Champion
-Nathan
Playoff Odds as of April 8th
I simulated the NBA playoffs, under a few assumptions.
1) Memphis makes the playoffs
2) There are no tie-breakers and teams are seeded according to conference standings
2) The regularized +/- 2011 numbers are accurate
(5:38p EST) - NEW RESULTS, updated with estimated playoff minutes
EDIT: A bit on the method.
I took all players who aren't out for the season, and converted their minutes into estimated playoff minutes (per DSMok1's suggestion), which I then had to adjust to force each team's game minutes to sum to 240 total minutes.
I then looked at each player's regularized +/- numbers, and gave them a contribution of Projected Minutes% * (Offense+Defense).
I then set the league average to zero, and each team was given their own "RAPM" rating. This was used to simulate the playoffs via a spreadsheet made by DSMok1 which I modified.
1) Memphis makes the playoffs
2) There are no tie-breakers and teams are seeded according to conference standings
2) The regularized +/- 2011 numbers are accurate
(5:38p EST) - NEW RESULTS, updated with estimated playoff minutes
EDIT: A bit on the method.
I took all players who aren't out for the season, and converted their minutes into estimated playoff minutes (per DSMok1's suggestion), which I then had to adjust to force each team's game minutes to sum to 240 total minutes.
I then looked at each player's regularized +/- numbers, and gave them a contribution of Projected Minutes% * (Offense+Defense).
I then set the league average to zero, and each team was given their own "RAPM" rating. This was used to simulate the playoffs via a spreadsheet made by DSMok1 which I modified.
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).
HERE ARE THE RESULTS
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).
HERE ARE THE RESULTS
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%
Therefore:
1) Real Win% = Season Win% + Opponent's Real Win% - 0.5
and
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.'
I have constructed a very lazy RPI, that is more theoretically sound than the RPI.
4) OOSeasonWin%=OORealWin%
When we replace Opponent's Real Win% with #2, we get
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.
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, because....well....it just doesn't fit for them to be #4.
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, because....well....it just doesn't fit for them to be #4.
Top Final Fours
The majority of huge-pool winners accurately predict the Final Four...here is a sampling of the top (seven) possible final fours that my LRMC simulation predicts.
If you're doing a multiple-bracket pool, this might be useful...updated simulation results coming soon.
| 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.
"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.
OFFICIAL Tournament Picks, VERSION ONE
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 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.
-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.
-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
"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!
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.
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.
Offensive Decision% version 2
I've updated my Offensive Decision% formula to include Offensive Rebounds. A field goal attempt is now only considered one 'decision' if the player does not rebound the attempt. So the denominator now subtracts Offensive Rebounds x Shot% in an estimation of how many offensive rebounds a player makes on their own missed field goals. Here's the entire formula:
Here are the current results for the NBA, with those playing 500 minutes or more.
Here are the current results for the NBA, with those playing 500 minutes or more.
NCAA team offensive efficiency impacts
I have previously done work on estimating how much statistics (specifically, the Four Factors + 2 more) impact efficiency. My prior method was lazy and inaccurate at adjusting for Strength of Schedule. The new method adjusts each factor rating differently. For the math, scroll to the bottom* EDIT: Yes, the total numbers do not EXACTLY equal (Adjusted Offensive Rating - League Average Offensive Rating), but they are close (R^2 of .99, to be concise).
But here's what you really want.
NCAA adjusted offensive four factors
*The original method took (Deductive Efficiency - Deduced efficiency with league average stat) and multiplied this by (Adjusted Efficiency / Raw Efficiency). The new method is a little more complex. I found out that each stat didn't impact efficiency as much as I thought, since each factor interacts with one another. I found the following:
While predicting change in efficiency (minus average), the following weights occur: eFG&FG+=1.065833, TO%+=1.088916, OR%+=0.935664, FTR&FT+=0.38507
Each individual output would have to be multiplied by these coefficients. However, I still needed to adjust for strength of schedule. To do this, I subtracted Adjusted - Raw Offense for each team to get their Schedule Adjustment Factor. I then weighed each of the four factors so that they would sum to one (fg=0.306672, to=0.313314, or=0.269218,ft= 0.110796). Here's an example of how eFG%&FG% look:
eFG&FG+=1.065833 * [(Deduced Efficiency - Deduced efficiency with average eFG% and FG%) + .306672*Schedule Adjustment ]
But here's what you really want.
NCAA adjusted offensive four factors
*The original method took (Deductive Efficiency - Deduced efficiency with league average stat) and multiplied this by (Adjusted Efficiency / Raw Efficiency). The new method is a little more complex. I found out that each stat didn't impact efficiency as much as I thought, since each factor interacts with one another. I found the following:
While predicting change in efficiency (minus average), the following weights occur: eFG&FG+=1.065833, TO%+=1.088916, OR%+=0.935664, FTR&FT+=0.38507
Each individual output would have to be multiplied by these coefficients. However, I still needed to adjust for strength of schedule. To do this, I subtracted Adjusted - Raw Offense for each team to get their Schedule Adjustment Factor. I then weighed each of the four factors so that they would sum to one (fg=0.306672, to=0.313314, or=0.269218,ft= 0.110796). Here's an example of how eFG%&FG% look:
eFG&FG+=1.065833 * [(Deduced Efficiency - Deduced efficiency with average eFG% and FG%) + .306672*Schedule Adjustment ]
NCAA player offensive ratings
Just put together another round of player offensive ratings - data via KenPom.com. It adjusts for quality of defense and usage% - the final number is an estimate of how efficient an average team's offense would be with the player on the court.
Here's the results
Here's the results
2010 Tourney "All-or-nothing" Ratings
This is using my pre-tournament LRMC simulation from last year. See my last blog post for the method,. I still haven't come up with a good name for it.
How does "effective likelihood of doing better than statistically expected" sound?
The first-round component gives us the most meaningful information (as the later rounds heavily favor better teams). Let's take a look at the results:
1) Xavier: as a 6-seed, beat 11-seed Minnesota and 3-seed Pittsburgh
2) Washington: as an 11-seed, beat 6-seed Marquette and 3-seed New Mexico
3) Marquette: lost to the (more-volatile) Washington
4) Utah St: lost to Texas A&M (who was just 0.07 lower in volatility)
5) Minnesota: lost to (highest-volatility) Xavier
other notables: the official Cinderella of 2010, Butler, was #7 (volatility of 0.48). Also, Cornell (who beat the 5 & 4 east seeds as a 12-seed), was ranked 19, with 0.4.
On to the second round:
1) West Virginia: made it to the Final-Four as a two-seed.
2) BYU: fell to Kansas St, who was 5th in volatility
3) Duke: Won the tournament...
4) Kentucky: Didn't make it past West Virginia, but succeeded as a (statistically) overrated team
5) Kansas St: Fell to Butler in the Elite 8 - pulled through in a pretty tough bracket though (statistically)
other notables: Butler is the highest-ranked 5-seed in 2nd-round volatility.
The third round doesn't tell us much new information, although Duke is the highest-ranked team here (in a bracket that statistically favored Kansas).
Anyways, the information here is hard to quantify, but I think some important things can be learned, especially from the first-round component!
How does "effective likelihood of doing better than statistically expected" sound?
here's the first, second and third (r1, r2, and r3)
The first-round component gives us the most meaningful information (as the later rounds heavily favor better teams). Let's take a look at the results:
1) Xavier: as a 6-seed, beat 11-seed Minnesota and 3-seed Pittsburgh
2) Washington: as an 11-seed, beat 6-seed Marquette and 3-seed New Mexico
3) Marquette: lost to the (more-volatile) Washington
4) Utah St: lost to Texas A&M (who was just 0.07 lower in volatility)
5) Minnesota: lost to (highest-volatility) Xavier
other notables: the official Cinderella of 2010, Butler, was #7 (volatility of 0.48). Also, Cornell (who beat the 5 & 4 east seeds as a 12-seed), was ranked 19, with 0.4.
On to the second round:
1) West Virginia: made it to the Final-Four as a two-seed.
2) BYU: fell to Kansas St, who was 5th in volatility
3) Duke: Won the tournament...
4) Kentucky: Didn't make it past West Virginia, but succeeded as a (statistically) overrated team
5) Kansas St: Fell to Butler in the Elite 8 - pulled through in a pretty tough bracket though (statistically)
other notables: Butler is the highest-ranked 5-seed in 2nd-round volatility.
The third round doesn't tell us much new information, although Duke is the highest-ranked team here (in a bracket that statistically favored Kansas).
Anyways, the information here is hard to quantify, but I think some important things can be learned, especially from the first-round component!
Team Volatility
This is going to be a shortish post considering the amount of new analysis I'm introducing, but I would like to start offering some tools to help predict even the strangest of occurrences. For example, it would have been statistical folly to predict Northern Iowa or Cornell to win as many games as they did in 2010; I want to predict the next Cornell!
So let's go in order of depth.
First, basic probabilities: teamrankings.com has some phenomenal pre-selection simulation projections for the tournament, giving individual probabilities for each team making it to round X.
From these we can find AVERAGE PROJECTED WINS: simply sum together each of the 6 probabilities to find the mean-expected wins each team will have in the tournament.
From this, we can do some theory: given that team x wins at least y games, how many wins will they THEN be projected to have; I call this "Average Projected Wins with X games secure." This would be estimated like so:
=Y games won + sum(probabilities of the rest of the tournament)/(probability of winning Y games)
So for two games secure, the math would be:
The first three rounds are the ones that tell us the most information, l
So let's go in order of depth.
First, basic probabilities: teamrankings.com has some phenomenal pre-selection simulation projections for the tournament, giving individual probabilities for each team making it to round X.
From these we can find AVERAGE PROJECTED WINS: simply sum together each of the 6 probabilities to find the mean-expected wins each team will have in the tournament.
From this, we can do some theory: given that team x wins at least y games, how many wins will they THEN be projected to have; I call this "Average Projected Wins with X games secure." This would be estimated like so:
=Y games won + sum(probabilities of the rest of the tournament)/(probability of winning Y games)
So for two games secure, the math would be:
=2 + sum(probabilities of winning the 3rd,4th,5th, and 6th games)/probability of winning in the second round)
From this, we can get a hybrid statistic, that I like to call Volatility: this is the marginal wins gained from winning any specific round of the tournament, TIMES the probability of winning that round. We do this by subtracting "X games secure" from our starting average (zero games secure).
For example, one team's volatility in the first round would be:
=[(2-win secure average wins) -( 0-wins secure average wins)] * odds of winning those first two games
From this, we can get a hybrid statistic, that I like to call Volatility: this is the marginal wins gained from winning any specific round of the tournament, TIMES the probability of winning that round. We do this by subtracting "X games secure" from our starting average (zero games secure).
For example, one team's volatility in the first round would be:
=[(2-win secure average wins) -( 0-wins secure average wins)] * odds of winning those first two games
The first three rounds are the ones that tell us the most information, later rounds are skewed by higher-quality teams having much higher odds of winning the games beforehand. On the right are the top ten teams by "first round volatility," considering the projected fielding of teams.
This tells us, roughly, which team will benefit the most if they can overcome early obstacles. A better utilization of this method would be to subtract from the ESPN National Bracket "average wins" rather than my statistical "zero wins secure average." This gives us a better picture of which team will do better than expected by most, and therefore, which team will help you destroy everyone in your office pool!
This tells us, roughly, which team will benefit the most if they can overcome early obstacles. A better utilization of this method would be to subtract from the ESPN National Bracket "average wins" rather than my statistical "zero wins secure average." This gives us a better picture of which team will do better than expected by most, and therefore, which team will help you destroy everyone in your office pool!
Offensive Decision%
Finally, some good old fashioned statistics that don't have really good theory behind them!
Often-times, when I'm watching a basketball game, I mentally determine who is making the most good decisions and the most bad decisions on offense.
So here's a basic metric of what my eyes see, and I call it Offensive Decision %. It basically measures, poorly, Good Offensive Decisions / Total Offensive Decisions.
=(FGM + Assists + .44 * FTM) / (FGA + Assists + TO + .44 * FTA)
And here's the top NBA players (as of earlier this week) with median minutes played or more.
Often-times, when I'm watching a basketball game, I mentally determine who is making the most good decisions and the most bad decisions on offense.
So here's a basic metric of what my eyes see, and I call it Offensive Decision %. It basically measures, poorly, Good Offensive Decisions / Total Offensive Decisions.
=(FGM + Assists + .44 * FTM) / (FGA + Assists + TO + .44 * FTA)
And here's the top NBA players (as of earlier this week) with median minutes played or more.
Estimated defensive rating formula, with Usage% !
EDIT/UPDATE: This formula, like Dean Oliver's is based on some good theory, but as I have examined it more, it is a very poor measure of defensive success. If you need a quick fix, the following explains player defense better than the formula described:
(Points Allowed On Court / Possessions Played) - (Points Allowed Off Court / Possession Off-Court)
Woo! This one took a lot of work, but I think I have all of the theoretical errors taken care of. It's very similar to Dean Oliver's box-scoreformula, but with a few important adjustments:
(Points Allowed On Court / Possessions Played) - (Points Allowed Off Court / Possession Off-Court)
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