A Statistical Look at the Health of the Light Heavyweight Division
MMAFighting.com's Fan Post of the Day:
Quote:
 Bloody Elbow (the source of my rankings data) did not, I believe, produce metarankings for April 2008, May 2008, and December 2008; also, until July 2008, less than 25 fighters were ranked. These two facts account for the differentsized gaps in the data sets.
 I got the fighter information from Wikipedia.
 Please vet or improve my work. You can download the Excel 2007 database at http://www.mediafire.com/view/?69971q68ym8o8gp
 In this post, I use the term "division" in a panorganizational sense.
 I'm going to try and keep the analysis to a minimum.
Chart 1 comprises three graphs: the average age of the top 25 fighters, the average age of the top 10 fighters, and the average age of the top 1125 fighters. As this and other charts show, the light heavyweight division is "upside down" during the first half of 2009: the Top 10 contains wellworn fighters who are about to be heaved into the lower ranks. From March 2009 (the nadir of Top 1125 graph) to July 2009, the Top 10 losesand the Top 1125 absorbsChuck Liddell, Wanderlei Silva, and Renato Sobral. The overall aging of the Top 25 is evidenced by the blue trend line; the fighters in the Top 1125 are primarily responsible for this shift.
Chart 2 comprises three graphs: the average number of bouts fought by a top 25 fighter, the average number of bouts fought by a top 10 fighter, and the average number of bouts fought by a top 1125 fighter. As they fluctuate around the blue line, one can easily see the inverse correlation between the Top 10 and Top 1125 data sets (i.e., the mirrorimage effect). This is due to the fact that, when rankings change, fighters swap places with members of the other set. From mid2009 onwards, the top ten fighters do not appear to have significantly more career bouts (on average) than the top 1125 fighters; the subsequent chart, however, shows that top 10 competitors spend more time in the cage.
Chart 3 comprises three graphs: the average total cage time of a top 25 fighter, the average total cage time of a top 10 fighter, and the average total cage time of a top 1115 fighter. The most obvious explanation for the higher values in the Top 10 data set is that top 10 fighters are more likely to engage in 5round bouts.
Chart 4 comprises three graphs: the average number of losses for a top 25 fighter, the average number of losses for a top 10 fighter, and the average number of losses for a top 1125 fighter. The rise in the Top 10 graph from March 2011 onwards is no doubt partly the result of Jon Jones, who won the title in March. In late 2011, the average number of losses for a top 10 fighter actually outstrips the average number of losses for a top 1125 fighter, a circumstance which indicates low turnover in the Top 10.
Chart 5 comprises three graphs: the average number of KO and TKO losses for a top 25 fighter, the average number of KO and TKO losses for a top 10 fighter, and the average number of KO and TKO losses for a top 1125 fighter. Again, note the upsidedown state of the division during the first half of 2009. The graphs cross in June 2009, when Rich Franklin (3 KO/TKO losses) displaces Wanderlei Silva (5 KO/TKO losses) in the Top Ten. An interesting feature of this chart is the lack of inverse correlation between the Top 10 and Top 1125 data sets from approximately 2010 onwards. The large dips in the Top 1125 graphdips that are "ignored" by the Top 10 graphare a product of the old guard being swept out of the rankings. In June 2010, the apex of the Top 1125 graph, Chuck Liddell and Wanderlei Silva are ranked in the top 1125; both are gone by January 2011. The appearances and disappearances of Randy Couture and Keith Jardine in the top 1125 also contribute to the swings in the data.
Chart 6 comprises three graphs: the average Inertia of a top 25 fighter, the average Inertia of a top 10 fighter, and the average Inertia of a top 1125 fighter. Inertia (IN) is an ad hoc metric given by the sum of the chronological ranks of a fighter's nonDQ losses divided by the fighter's total number of bouts. For example, a fighter with ten fights who lost his second and fourth bouts would have an IN of (2 + 4)/10 = 0.6. An unbeaten fighter always has an IN of 0; a fighter who loses for the first time always has an IN of 1. IN gaugesin theory, at leasta competitor's ability to move up the ranks. Prospects, dominant champions, and fighters on long winning streaks tend to have low IN scores; battered veterans and fighters on losing streaks tend to have high IN scores. [Below] is a small table of some fighters and their IN scores as of July 2012. As of August 16, 2012, Machida's IN is 2.62 (after a win over Bader) and Shogun's IN is 4.07 (after a win over Vera).
In Chart 6, as in Chart 4, the Jon Jones era stands out: from March 2011 onwards, the red graph is driven upward by top 10 fighters losing to the champ and to each other without being demoted into the Top 1125. In the first half of 2009, the Top 1125 is crowded with lowinertia fighters; these fighters help to "flip" the division in the second half of 2009. In early 2012, on the other hand, the Top 1125 is not crowded with lowinertia fighters.
Chart 7 comprises three graphs: the average Damage Index of a top 25 fighter, the average Damage Index of a top 10 fighter, and the average Damage Index of a top 1125 fighter. Damage Index (DI) is an ad hoc metric given by the sum of the weighted zscores (i.e., [value  mean]/[standard deviation]) associated with a top 25 fighter's age, number of bouts, total cage time, number of losses, number of KO/TKO losses, and Inertia, multiplied by 100 and minus an offset. Total cage time (which I considered removing entirely) is given onefourth the weight of the other categories. The offset is included to prevent the graphs on Charts 7 and 8 from falling into negative territory. As a result of the offset, someone incurring a perfectly average amount of damage (for a top 25 fighter) would have a DI of 293.93. [Below] is a small table of some fighters and their DI scores as of July 2012.
Chart 8 comprises two graphs: Volatility and the ratio of the average Damage Index of a top 10 fighter to the average Damage Index of a top 1125 fighter. Volatility is given by the sum of the positive differences between every top 25 fighter's last rank and current rank. Fighters who were unranked or ranked worse than 26th the previous month are, for the purposes of the Volatility calculation, assigned a Last Rank of 26. [Below] is the Volatility calculation for March 2011.
As the Top 10 incurs damage or the Top 1125 sheds damage (via turnover), the ratio described by the black graph on the above chart increases. Conversely, if the Top 10 sheds damage or the Top 1125 incurs damage, the ratio described by the black graph decreases. If the Top 10 is damaged relative to the Top 1125, one would expect the Volatility of the division to increase (and vice versa). From June 2009 to September 2011, the two data sets behave as expected; that is, they are positively correlated. Roughly six months into the Jones era, however, the correlation is turned on its head: Volatility drops while the upper ranks become comparatively "weak." Finally, notice (a) the high Volatility during the divisional tumult in 2009 and (b) the general trend in decreasing Volatility.

