Had Texas’ Luck Run Out? (a study in Pythagorean Luck)

This article is by no means intended to give a full picture of Rick Barnes’ tenure at Texas, but rather point out why he may have needed to go. I am a Rick Barnes fan and appreciate everything he did for Longhorn basketball, but I also recognize that, in the immortal words of Dr. Seuss’ ‘Marvin K. Mooney’, it was time for Rick to, “Go, Go, Go.”

The concept of Pythagorean Luck is derived from the difference between a team’s Pythagorean Winning Percentage (invented for baseball by the legendary Bill James) and their actual winning percentage. In layman’s terms, this is a difference between their expected winning percentage (based on actual offensive and defensive production) and their actual winning percentage.

Pythagorean Luck may also indicate whether a team is under or over performing. Teams tend to, “regress to the mean” or average out over a lifetime. Some years you have good luck and sometimes you have bad luck.

To find Pythagorean Luck you must first calculate Pythagorean Winning Percentage. This can be done many ways and I have decided to show two of the ways in this example. (All of the mathematical calculations are at the end, so be sure to read the whole article if you are interested in that.)


Since 2002, Texas has been a predominantly ‘unlucky’ team. Using Luck, as determined by actual points scored, Texas had been ‘lucky’ (positive luck or performing above expectations) in only four of 14 seasons (2002, 2003, 2008 and 2014). Even in years where Texas seemed to have extremely good seasons, such as 2006 and 2007, they underperformed, based on scoring.

Pythagorean Luck since 2002

Pythagorean Luck since 2002

(NOTE: this evaluation is based solely on pre-tournament data)

Using Offensive and Defensive Efficiency, Texas hasn’t fared any better. Again, four of 14 seasons show positive luck for the Longhorns. This time 2008 and 2014 still rate positively, along with 2004 and 2006.

If we look specifically at results since 2009, only in the 2014 season did the Longhorns seem to perform above what would be expected, based on scoring and defense.

I am sure this is where we could have a more detailed discussion on the lackluster offensive performances of Barnes’ teams at Texas, but the point is this – Texas still should have won more games, even with the offense they were producing.

No team should continually be on the losing side of luck, let alone so far on the other side. As a comparison, Kansas is evenly split with seven years on both sides of the luck spectrum.


2002 19 11 2360 2232 113.6185 99.4373 0.6333 0.6147 0.7032 0.0186 -0.0699
2003 22 6 2208 1923 118.7559 96.4505 0.7857 0.7609 0.7935 0.0248 -0.0078
2004 23 7 2314 1992 110.4368 93.177 0.7667 0.7782 0.7502 -0.0115 0.0165
2005 19 10 2243 2001 110.8698 96.7025 0.6552 0.7224 0.7078 -0.0672 -0.0526
2006 27 6 2512 1983 117.1721 94.3678 0.8182 0.8788 0.8023 -0.0606 0.0159
2007 24 9 2713 2374 118.9737 99.5146 0.7273 0.7537 0.7605 -0.0264 -0.0333
2008 27 6 2470 2142 118.6783 95.1518 0.8182 0.7674 0.8068 0.0508 0.0113
2009 22 11 2387 2160 109.2162 93.5709 0.6667 0.6979 0.7311 -0.0312 -0.0645
2010 24 9 2681 2300 111.595 94.5267 0.7273 0.7831 0.7454 -0.0559 -0.0181
2011 27 7 2547 2087 114.2741 89.9466 0.7941 0.8414 0.8248 -0.0473 -0.0306
2012 20 13 2411 2205 111.3908 96.3472 0.6061 0.6788 0.7188 -0.0727 -0.1128
2013 16 16 2084 2073 101.4622 95.2782 0.5000 0.5111 0.6003 -0.0111 -0.1003
2014 23 10 2446 2311 109.4989 96.3269 0.6970 0.6167 0.6962 0.0803 0.0008
2015 20 13 2242 1993 110.29 93.308 0.6061 0.7283 0.7468 -0.1223 -0.1408

This team has been underperforming for years and this year it was in record style.

It boils down to coaching. Luck happens. Luck changes. Poor situation coaching and poor player execution at critical times has haunted this program for a number of years and it was not getting better.

Rick Barnes’ luck had simply run out.


As I stated above, to calculate Luck, you need to first calculate Pythagorean Winning Percentage. The first way is by using actual points scored and allowed and is similar to the way baseball calculates it, using points scored and points allowed:

Pythagorean Winning Percentage = (points scored ^ x)/(points scored ^ x + points allowed ^ x), where x is a value such anywhere between 1 and 18. This formula is credited to Bill James, who applied it to baseball. Houston Rockets GM Daryl Morey is credited with creating the first use of it for basketball.

Here’s a second way to calculate PWP, using Adjusted Offensive and Defensive Efficiencies:

Pythagorean Winning Percentage = (Adjusted Offensive Efficiency ^ x)/(Adjusted Offensive Efficiency ^ x + Adjusted Defensive Efficiency ^ x).

I have elected to use these two popular methods. I have also decided to use only from 2002 to the present. The reason for this was primarily a lack of consistent data for Offensive and Defensive Efficiency. Ken Pomeroy provides this data back to 2002 on his website, so I am electing to use it.

I used approximately 8.4 and 6.5, respectively for the two equations. I arrived at this by completing a least-squares (and least square-root) analysis using all regular season games between 2002 and 2015, minimizing the error between actual and expected values.

To then calculate Pythagorean Luck, you must calculate the difference between these values and the team’s actual winning percentage. Sometimes this is calculated as a straight difference and sometimes as a deviation, using something like the Correlated Gaussian Method, popularized by ESPN and former Denver Nuggets statistician, Dean Oliver.

For my purposes, I simply used the difference (subtraction).

A Little Data For Picking Your March Madness Pool

I have been combing through lots and lots of data, as I prepare my own entry to the Kaggle Machine Learning March Mania Contest again this year. I won’t go into how I am managing my entry right now, as the competition is obviously still open, but I thought I would share some of the insights I have accumulated along the way.

First off, you need to have a strategy. You can be the guy with the chalk bracket or the batshit-crazy-upset-dude, but we all know somewhere in the middle is probably where you need to go… just enough chalk, just enough upsets.

To get a good feel for how the tournament has played out over the past 20 years, I have put together a few graphics. The first one shows the winning percentage for each seed against every other seed since 1985. (The winning % is for the seed down the left side)

Seed v. Seed Winning Percentage

Seed v. Seed Winning Percentage

It’s kind of crazy. If look look at it, #1 seeds are only 40% versus #11 seeds since 1985. WTH? This obviously needs context, so here’s the same chart showing how many times each seed has played in that time frame.

Seed v. Seed Matchup Counts

Seed v. Seed Matchup Counts

Now we can calculate that #11 seeds have actually won 3-of-5 times against #1 seeds. Great, but what does this mean?

Hopefully this can help you solidify your strategy once the draw comes out. Maybe you like a certain 11-seed. How far should you maybe consider riding them? It should also be a guide to help you LIMIT your upsets from being just too wacky.

Another thing to consider is just how volatile the tournament will be. I have analyzed each year individually since 1985 and here are a few of my thoughts.

In the past 30 years, 19 of those seasons have been below “average” when it comes to upsets. I have defined these as the Chalk years. They tend to have fewer upsets and fewer large-scale upsets. The list includes: 1987, 1988, 1989, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 2000, 2003, 2004, 2005, 2007, 2008, 2009 and 2012.

Since ’85, there have been an average 17.7 “Upsets” (by seed) and 7.9 “Big Upsets” per season. I define Big Upsets as those where the seed differential was greater than 4 (at least a 6 over a 1). I also used Mean Upset  — the sum of all upset differentials over the number of tournament games.

QUIRKY STAT MOMENT: Two years with the most upsets since 1985? 1999 (23) and 2014 (22). Guess who won both years? UCONN. Strange, huh?

When figuring out the “upset” and “chalk” years, the upset years stood out. Those would be 1985, 1986, 1990, 1999, 2001, 2002, 2006, 2010, 2011, 2013 and 2014. As you can see, four of the last five season fall into this category. Why? That’s a story for another day.

I am sure there are plenty of ways to argue the way I divided up the years, but the concept is solid: there are upset years and there are chalk years… and we seem to be in a time of upsets.

Remember, even though a season is defined as chalk, there are still plenty of upsets. In 2012, the most recent chalk year, two 15-seeds, Lehigh and Norfolk State, both won games over 2-seeds. Also, 10, 11, 12 and 13 seeds all had first round wins. However, the tournament was dominated by lower-seeded players throughout.

I hope some of this helps. Remember get a little crazy, but not too crazy… and it also help to be really lucky.