Eloquent Elo Examples

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Example 1) An MMA fighter’s worth

Not talking about “Fabulous life of MMA fighters” or “celebrity cribs” here. What I’m talking about is the basic case of how much a win over a certain fighter earns another fighter. This is a basic part of the system, but one that is often misunderstood.

See, Fighter A doesn’t have a set value. Beating Fighter A isn’t worth 10 points or 74 points. That’s because the ratings of *BOTH* fighters determines how much a win is worth.

Theoretical Example

Let’s assume we have three fighters:

Fighter A – 1700 rated
Fighter B – 1600 rated
Fighter C – 1500 rated

In a case like this, Fighter B doesn’t have a set value they are worth. If Fighter A were to beat Fighter B they’d get 36 points.

However, if Fighter C were to beat Fighter B they would earn 64 points.

Actual Example

GSP – 2243
Mike Swick – 1932
Chris Lytle – 1887

In this case GSP would get only 14 points for beating Mike Swick. Chris Lytle, on the other hand, could gain 56 points for a win over Mike Swick.

The reason for this is the fighters’ ratings and where they currently stand. Although Mike Swick is a solid fighter, they are definitely below GSP. At the same time, Mike Swick is a bit higher than Chris Lytle is. This leads to one fighter gaining significantly more for beating them.

As you browse the site (and finish reading this rant), always keep in mind that a certain fighter doesn’t have a set value. No one fighter is worth 10 or 20 or 80 points. The ratings of *BOTH* fighters are what determines how many points are won and lost.

Before moving onto the next example, anyone else really want to see Chris Lytle Vs Mike Swick?

Example 2) The Elo giveth and the Elo Taketh away

The other side of victory…is defeat. Let’s take a quick second to look at how points are lost in the system. Much like how the rating of both fighters determines how many points are won, it also determines how many points are lost.

Theoretical example

Again, three fighters:

Fighter A – 1800
Fighter B – 1900
Fighter C – 2000

If Fighter B were to lose to fighter A they would lose 64 points.

A loss to Fighter C would only cost Fighter B 36 points.

Actual Example

Andrei Arlovski had a rating of 2051 when he faced Fedor. Fedor had a rating of 2268. The loss to Fedor cost Andrei 22 points.

Following that loss Andrei had a rating of 2029 and he faced Brett Rogers (who had a rating of 1828 at the time). The loss to Rogers cost Andrei 76 points.

That is over three times as many points lost. Why? Because the first loss was against a *MUCH* higher rated fighter. Some people (and sites!) actually moved Andrei *UP* in their rankings despite the loss.

Rogers though was a much lower ranked fighter. Despite being an up and comer he hadn’t really beat many high ranked opponents and Andrei was clearly the favorite in the fight. Since Andrei loss to a lower rated opponent, he lost even more points.

Example 3) Risk Vs Reward

Anyone who frequents this site (thank you!) has undoubtedly seen me discuss risk vs reward. I mention it here as example three because Risk Vs Reward is really Example 1 + Example 2 (that’s a math joke, it’s OK to laugh).

Theoretical Example

Three fighters walk into an arena…

Fighter A – 1800
Fighter B – 2200
Fighter C – 1800

If we look at the possible matchups and incorporate Examples 1 and 2 we see:

Fighter A Vs Fighter B
Fighter can *WIN* 91 points or *LOSE* 9 points
That means Fighter B can *LOSE* 91 points or *WIN* 9 points

That is just terrible. Basically Fighter B is risking *TEN TIMES* as many points as they can possible gain.

If we instead consider Fighter A Vs Fighter C…
Fighter A can *WIN* 50 points or *LOSE* 50 points
Fighter C can *WIN* 50 points or *LOSE* 50 points

That seems pretty balanced in terms of risk vs reward, right?

Now, obviously not every fighter can be matched up against fighters with identical ratings, but even a 40/60 split would be more reasonable than the 10/90 we saw in the case of Fighter A vs Fighter B.

Actual Example

Let’s look at Mike Swick again.

Two fights again Mike took on Dan Hardy. At the time their ratings were:

Swick – 2035
Hardy – 2048

That means Mike could win 52 points for a win, or (as wound up happening) lose 48 points. This was a number one contender type of fight and as you can see both fighters had very high ratings. This to me is an excellent example of a fight that makes “ranking sense” and has reasonable Risk Vs Reward for both fighters.

To contrast that fight, look at Mike Swick’s previous fight…

Swick – 2009
Saunders – 1829

Now I have nothing against Ben (except maybe his nickname), but it’s very obvious who had more to gain and who had more to lose in this fight. At the time of the fight Swick was becoming a consensus top 10 fighter and Saunders was a prospect with just a couple wins in the UFC after some time on the ultimate fighter.

For winning the fight Swick earned 26 points. That’s a fair number of points, but considering the situation and the 74 points he was risking I think this fight was on the other side of reasonable. Mike clearly had a *LOT* more to lose and very little to gain. Even the announcers mentioned that Saunders really had nothing to lose in the fight.

Some like to talk about “year of the upset” and how “volatile” MMA is, but that’s only because the matches get made in the first place. Just because Swick won doesn’t mean it was OK to make such a fight. MMA is a sport and the fighters are athletes. As such, both fighters should have reasonably balanced “risk” and reasonably balanced “reward”.

Example 4)Bottom Feeding

One of the false claims people often make about the system used on the site is along the lines of,

“It doesn’t matter who you beat, just beating 10 cans is better than beating 9 title holders”.

I’m going to piggyback a bit on Example 1 (I reference so you can scroll back up if needed) and show you how the system prevents such bottom feeding.

Theoretical Example

I’m going to give the fighter the benefit of the doubt here and say that they just started out and had a 1500 rating. I’m then going to play horrible match maker and continue to match them up against 1500 rated opponents.

Fight 1 – 1500 rating to start
Win earns +50 rating

Fight 2 – 1550 rating to start
Win earns +43 rating

Fight 3 – 1593 rating to start
Win earns +37 rating

Notice what is happening? When our theoretical fighter had a 1500 rating, then facing a 1500 rated opponent was reasonable and earned them good points (+50). As they win though their rating goes up, that means the rating of their opponent has to also go up in order for them to continue to accrue similar rating gains.

In this case our fighter is continuing to be matched up against 1500 rated fighters. As they beat them, their rating will increase by less and less.

*Skip ahead*

Fight 10 – 1776 rating to start
Win earns +17

See how the points have dwindled? Our fighter is now getting about 1/3 of the points they previously got. This situation will only get worse.

Since I’m not going to provide an actual example here, I’m going to say a bit more (lucky you).

When we consider this situation using Example 1 we see that the fighter is getting less and less for a victory. Now let’s also consider how devastating a loss would be.

If in fight 10 our fight instead *LOST* instead of winning they’d have:

Fight 10 – 1776 rating to start
Loss costs them -83 rating

That means with a single loss our fighter is now back down at 1693. That single loss offset almost all of the points from this fighter’s previous *FOUR* wins combined.

By continuing to face weaker competition (potentially through no fault of their own) our fighter is earning less and less and risking more and more. Even without losing the system creates a relative ceiling that they simply can’t surpass unless better matchmaking happens.

In theory you would hope a fighter that is 9-0 against 1500 rated opponents gets a bump in competition (I’d hope for it long before 9-0), but even if it doesn’t this is one way the system can pseudo correct for poor match making.

Example 5) Strength of Schedule

Strength of Schedule is a reasonably hot topic and though I’m glad to see it discussed, I can’t help but feel some don’t “quite” get it. When we talk about a fighter’s strength of schedule we are talking about the level of opposition they have faced.

I think strength of schedule is an intriguing stat, but many miss how big a factor it already plays in calculating a fighters base “rating”.

Theoretical Example

In example 4 we saw what happens when a fighter goes 10-0 against 10 1500 rated opponents. Now let’s contrast that against a fighter going 10-0 against 1800 rated opponents.

Fighter A – 10 wins against 1500 rated opponents
SoS – 1500
Rating – 1793

Fighter B – 10 wins against 1800 rated opponents
SoS – 1800
Rating – 2012

That means Fighter B has a 219 rating point advantage. That is a *TON*. Not to mention, Fighter B actually got so high that taking on 1800 rated opponents was a bit weak for them.

How big an advantage is it? Well, if Fighter B (instead of winning all 10) won their first 8 and then *LOST* their next two, they would have a rating of…1825.

That’s right, by taking on stronger fighters Fighter B is able to offset the losses and still come out ahead of Fighter A.

Example 6) What have you done for me lately?

Another common misconception about the site is that old fights matter the same (if not more) than more recent fights. This is quite false and I’d like to provide a few examples to illustrate this.

Theoretical Example

In this example I want to re-use Fighter B from above. Remember this fighter had 10 fights and always fought 1800 rated opponents.

Here are three scenarios…

All wins – Final rating 2012
Lost *LAST* fight – Final rating 1912
Lost *FIRST* fight – Final rating 1981

See that?

If we take “all wins” as a baseline (2012) we see that losing their last fight results in Fighter B being a full 100 points lower than they could be. By losing their *FIRST* fight though Fighter B winds up at 1981 rating which is only 31 points lower than they could be.

Why is that?

It’s because the value of a fight is based upon the ratings of *BOTH* fighters. By losing their first fight that means Fighter B had a lower rating going into their second fight. That means they *WON* more points for it.

When a fighter loses their last fight though, they haven’t had time to regain any points. This means the most recent fight has the biggest impact on a fight. Not an over-the-top–all-or-nothing-screw-sport level of impact, but still the strongest impact.

Actual Example

Now that we see how important recent fights are, let’s take a look at how important older fights are.

One of the most discussed fighters in MMA is Fedor. On this site Fedor currently has the highest all time rating (2300). Many feel this is because of his old fights and that fights from 10(ish) years ago are what makes his rating so high.

For my first example I want you to follow me back to May of 2000 as I give Fedor an even *HIGHER* rating. That’s right, a *HIGHER* rating. Instead of saying that Fedor had a 1500 rating in May and just started his career I want you to assume he’d been fighting for YEARS previous to that.

For this example let’s say that in May of 2000 (when Fedor really had his first fight) we’ll say that he was already 2000 rated. That is a 500 points rating jump that we are giving him. So now, with years of past wins having gotten Fedor to 2000 rating, we now step through his exact career.

The result?

On 2009-11-07
Rating – 2316

Yup, 16 points. We gave Fedor *YEARS* more wins, gave him over 500 more rating points and he still wound up almost exactly where he was. Why? Look back at the previous examples (all of them, you didn’t laugh enough yet and the jokes are there if you look for them).

I chose Fedor in part because he is so highly discussed, but also because his rating is the most extreme. If we use a fighter like Big Nog and do the same (give them an extra 500 rating to start) we see that their rating would only be 8 points different today if the “rest” of their career played out the exact same.

To take it from the other side, if we said Anderson lost a *TON* before his career started and that he had a 1000 rating instead of a 1500 rating at the time of his “first” fight, we’d see that his rating would only be about 18 points different today.

Since we now know that having a super high (or low) rating doesn’t carry over indefinitely, let’s look at some interesting (and potentially inflammatory) examples.

Staying with Fedor let’s say instead of starting his career in May of 2000 that he instead started it in January of 2005. Why that date? Because it’s *AFTER* his second Nog win. So let’s set Fedor to 1500 rating, and roll through his career from 2005 till now.

Result?

Rating – 2071

Not quite his current 2300, but he lost 5 years of fights, including not one, but TWO Nog wins.

I picked the 2005-01-01 date mostly at random, but let’s consider a more specific date in history….

Fedor starting at 1500 rating on 2007-06-02 (date ring a bell?)
Fedor’s “current” rating would be…1814

For those that get the date, they can handle the comparison themselves. Just keep in mind that if Fedor had “started” on that date, then his first win was legit (it was Brock’s intended first opponent) he then beat back to back former UFC champions, and then beat a 10-0 contender. If those are your first four fights, that’s pretty impressive. Fedor’s activity during this time range was definitely low though.

Now, Fedor’s rating during this time isn’t the highest of all fighters (GSP’s is higher and Anderson’s is insane). It does help illustrate his recent accomplishments though. I don’t want to get off on a sub-rant, but many like to bash Fedor and say all of his “good” wins are in the past. There’s no doubt that prime crocop, some wins over nog and other fights are great. However, in his last three fights Fedor has beaten two former UFC champions (both top 5ish at the time of the fight) and a 10-0 contender (top 10ish at the time).

If you don’t consider Fedor #1 due to activity, brain damage or American arrogance, that’s OK and I can logically understand it. The people that say he isn’t “top 10″ or that Carwin has done more literally cause brain bleeds and god to smite kittens though.

Pencils down…

So, we’ve looked at “wins”, we’ve looked at “losses”. We’ve looked activity (though no specifically covered it’s there if you look for it). We’ve discussed bottom feeding, strength of schedule and all kinds of other fun things.

The system on this site is very powerful, very clean and, oh yeah, fair. Perfect? No, but also not as bad as some try to claim.

If there are any cases you’d like to see covered in more detail (other readers hope not), then let me know.

Til next time,
- Evil Envoy Extraordinary

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