On Monday I discussed the Raw Strength of Record statistic. The aim of this stat was to combine a fighter's rate of success with the length of his record (all-time or within a certain time frame).
Here's the RSR formula again. On the left is a given fighter's Win Percentage; on the right, the square root of his combined wins and losses. Essentially, success multiplied by experience. The most influential missing factor, if this statistic is to evaluate a fighter's overall "greatness", is now the quality of his past opponents.
Strength of Schedule, an American football statistic, generates its value from the Win% of a team's opponents, as well as the combined Win% of those opponents' opponents. These figures have true depth and consequence, but they do not account for the success and experience factors (nor are they intended to) that RSR handles. The way in which SOS is calculated can not be effectively applied to RSR, but it can be incorporated in spirit.
This is my proposed formula for Adjusted Strength of Record (ASR). Win% remains on the left, while the right-hand variable has been altered. Instead of using combined wins and losses as the final modifier, the formula processes the sum of a fighter's opponents' RSR values (the fighter's own RSR value is not included). Unfortunately, formulaic notation (or at least my weak grasp of it) oversimplifies the meaning of this factor. To be more specific: for every win or loss on a fighter's record, calculate the RSR of his opponent as it was before their fight took place. This applies to multiple fights against the same opponent: each time they face eachother, a different RSR will be generated. The sum of these "at-the-time" RSR values will be used to produce ASR.
You'll notice that the ASR formula, like the RSR formula, takes the square root of its right-hand variable. This serves the same purpose in both formulas. In calculating RSR, the flat sum of wins and losses was far too influential and provided wildly inaccurate values. Taking the square root softened the impact of the experience factor, and tapered the effect of each win or loss past the first. In calculating ASR, we are essentially isolating each win or loss, adjusting its value based on the quality of the opponent, and then recombining them all. The square root curve remains essential to the balance of the equation.
The Sliding Time Frame
As previously mentioned, both RSR and ASR statistics can be collected based on a fighter's entire career, or a specific time frame. For active fighters, applying a time frame should provide more accurate comparative values. On Monday, I provided career RSR values for several active UFC welterweights. Although it's common knowledge who the better fighter is present day, Matt Hughes' RSR trounced Georges St. Pierre's. But this is to be expected: Hughes' career-length achievements have been mountainous, and he's much closer to pasture than is GSP. Applying a three-year time frame from which to gather data painted a more accurate picture because, in the past three years, GSP has fought more often and won more often. Here again are the three-year RSR values of the welterweights I selected:
2.4495 (6-0) GSP
2.2678 (6-1) Jon Fitch
2.2136 (7-3) Dan Hardy
2.1213 (6-2) Josh Koscheck
1.6330 (4-2) Thiago Alves
1.5119 (4-3) BJ Penn
1.3416 (3-2) Matt Hughes
0.5000 (1-3) Matt Serra
These values do not reflect strength of competition. The next step is to introduce that factor using the ASR formula. Since we're using a time frame for increased accuracy (or at least relevance), we have to remember to slide it around to accommodate for the varying dates of a fighter's bouts against different opponents. We'll calculate RSR values using data from three years before each match, in order to measure how "hot" an opponent was coming into the fight. Here are the ASR values, using a sliding three-year window.
3.6093 (6-0) GSP
3.5467 (6-1) Jon Fitch
3.4586 (7-3) Dan Hardy
3.3440 (6-2) Josh Koscheck
2.3647 (4-2) Thiago Alves
2.1637 (4-3) BJ Penn
1.6705 (3-2) Matt Hughes
0.6685 (1-3) Matt Serra
Immediately you can see that, relative to eachother, the fighters' positions remain the same. I really wish this hadn't happened, but analyzing the data provides some explanations.
1.) When calculating ASR values, my number one assumption was that Dan Hardy would drop two or three spots. His higher-than-expected spot in the RSR rankings was a result of two things: a.) he had a decent win rate and b.) he fought more frequently (ten times) in the past three years than any of the other welterweights in question. Hardy was awarded a bonus for the opposite of ring rust (ring polish?). I'm comfortable with that advantage because in real life, that likely translates to a healthy, non-injured fighter who's constantly in the gym and very composed come fight time. If that's not the case, win-loss record will naturally reflect it as that fighter will probably receive quite a few ass kickings. As I glanced through the names on his resume, I expected the RSR values of his opponents to counteract the aforementioned advantages, producing a relatively lower ASR value. What actually happened is that I realized Hardy faced off against a lot of currently uninspiring names at times when they were quite dangerous. I was most surprised by Marcus Davis: when he fought Hardy, Davis was 11-1 in three years. That's both a great win percentage and a very busy fight schedule. If the Davis fight never happened, Hardy's ASR and record would fall to 3.0722 (6-3) and he would drop one spot in the rankings. This made me worry that the experience factor was too strong an influence, until I examined the data for...
2.) BJ Penn. In the past three years, Penn has faced numerically strong competition, but the bottom line is that he hasn't beat as many as we expected him to. Push his three-year window back 10 months and he goes from 4-3 to 5-1. Sobering. In this case, while Penn has consistently faced high-threat opponents, his win rate kills his ASR value. This might lead one to suspect that win rate is too influential, but in Hardy's case the experience factor appeared to be at fault, and they can't both be overvalued. So the reality is probably just that in the past three years, based on win percentage, level of activity, and quality of opponents, Dan Hardy has been a more successful fighter than BJ Penn.
3.) As for the lack of change between RSR and ASR rankings, I believe that I simply chose a poor set of fighters from which to expect that sort of movement. First of all, I just chose GSP and his last seven opponents. This was done purely out of convenience, and in hindsight was not a good idea. GSP has been consistently active and successful in nearly any three-year portion of his career. His RSR is a large and steady part of the other fighters' ASR values (except Koscheck's, as their bout occurred more than three years ago). Additionally, all of the eight welterweights except Dan Hardy have also fought another man in their set other than GSP. Overall, I suspect that the fighters did not change positions between RSR and ASR rankings because their levels of competition were really that similar.
Hyper-Adjusted Strength of Record
As I mentioned earlier, football's Strength of Schedule (SOS) statistic digs three levels deep into a team's record, going so far as to include that team's opponents' opponents' win percentage. I am not going to apply this depth to RSR/ASR anytime soon, but it's completely possible to do.
This would take a ridiculous amount of time to calculate for each fighter, although I'm sure the increase in accuracy would be significant. Personally, I'm comfortable with the less-considerable depth of the ASR statistic, not least of all because it is already intended to represent three independent factors, versus the single type of data calculated by SOS.
My next post will be a walkthrough of an experiment to see what ASR values are produced under completely controlled and more easily decipherable circumstances. It should be ready in a few days; let me know what you think until then.