I recently decided to improve my graph theory based MMA ranking system which modeled fighters as vertices and wins as edges on a directed graph. Previously the system generated a single large list of fighter rankings, evaluating all fights on record to generate data. The only problem is that this does not show how these rankings have changed over time – for instance, how has the ranking of Georges St-Pierre changed over the last decade? His recent retirement had made me curious.

I decided that instead of running this analysis for a single day in the present and looking back at all fights in the past – why not run the analysis for a given arbitrary day, and limit the fights which are included in the analysis to only those fights occurring within a certain period of time before that day? This analysis could then be ran and re-ran as I iterated day by day to obtain data demonstrating how rankings changed over time for a certain lookback period.

I ran this analysis between January 1, 2004 (roughly one month before Georges St-Pierre’s first fight in the Octagon) to the most recent UFC event at the time of this post (UFC on FOX 12, July 26, 2014) for lookback periods ranging from two to sixteen years in the past. To provide context I also ran this analysis for every UFC welterweight champion during this timeframe (Matt Hughes, Matt Serra, and Johny Hendricks). A visualization and brief summary of this data can be found in the table below. The color of the graphs range from green (shortest lookback period of 2 years) to yellow (longest lookback period of sixteen years).

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Johny Hendricks: Arriving in the UFC in mid-2009, Hendricks demonstrated strong performance in the shorter lookback periods but simply hasn’t had enough time to climb up the rankings in the longer term.
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Matt Hughes: A legend of the old guard, his shorter lookback period rankings started to slip in 2007 but still ranks highly in the long term, evidence of years of dominance.
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Matt Serra: Saw big gains in 2007 with his defeat of George St-Pierre but couldn’t hold on to them. Note the dropoff in scores into negative territory when the lookback period no longer considers his Georges St-Pierre win (ie early 2009 in the 2 year lookback period, early 2011 in the four year lookback, etc).
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Georges St-Pierre: A steady gainer who got a big pop in the mid to long term rankings in late 2006 after defeating BJ Penn. Short term lookback periods show weaker performance post-2010 due to injury and slower scheduling, but long term ranking are strong.

So how are we supposed to compare performance between fighters? Thirty two time series with eight separate lookback periods is a mess to visualize effectively, so we need to find the best lookback period or periods to compare. Shorter lookback periods respond quickly to recent wins and losses, but are fickle, ignoring long term consistency. Longer lookback periods are more stable and reflect consistent performance, but take years to reflect possibly rapid changes in fighter performance. After evaluating many different approaches, I decided to average the results from the 2, 4, 8, and 16 year lookback periods. Each lookback period is sufficiently different from the other and provides new information, and the combination provides a good balance between short and long term viewpoints.

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The resulting chart makes qualitative sense and shows the early dominance and slow fade of Matt Hughes, the rise of Georges St-Pierre, Matt Serra’s spike when he captured the welterweight championship, and the new guard of Johny Hendricks quickly approaching. We can also look at the day to day changes in George St-Pierre’s ranking to capture some events that influenced the changes in his ranking most heavily.

Biggest One-Day Gains Biggest One-Day Losses
March 4, 2006 +0.232 Georges St-Pierre wins by split decision against BJ Penn in a close battle at UFC 58. April 7, 2007 -0.119 Matt Serra defeats Georges St-Pierre in an infamous upset at UFC 69.
November 18, 2006 +0.204 Georges St-Pierre defeats Matt Hughes by TKO in the second round at UFC 65 to become the new UFC Welterweight Champion. September 23, 2006 -0.096 Matt Hughes defeats BJ Penn at UFC 63. Note that this occurred shortly after GSP defeated BJ Penn for a massive gain in the rankings. BJ Penn’s drop in the rankings as a result of this loss also caused GSP’s ranking to slip as a second-order effect.
August 9, 2008 +0.203 Georges St-Pierre defeats Jon Fitch at UFC 87. September 23, 2006 -0.067 Thiago Alves defeats Matt Hughes by TKO at UFC 85. A large portion of GSP’s rankings relied on beating Matt Hughes. As Hughes’ ranking slipped due to losses, GSP’s did as well due to second order effects.

Most of George St-Pierre’s big gains occurred earlier in his career, which makes sense – it’s hard to move up when you’re already the champion. His worst days were also the predictable loss to Matt Serra, and the days when his most prominent prior wins (BJ Penn, Matt Hughes) ended up losing themselves.

And when was Georges St-Pierre’s peak? Well by the numbers, it was the week shortly after his defeat of Dan Hardy at UFC 111 when he reached a career high of ~0.727, at roughly the start of the controversy about him finishing fights. A year and a half later, he would injure his ACL which reduced the frequency of his fights to such a degree eventually his ranking slid below that of a young upstart named Johny Hendricks. The two eventually fought on November 16, 2014 – and Georges St-Pierre won, for a one-day gain of 0.120, his seventh best on record.

After all, if you’re going to retire, you might as well go out on top.

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