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*ELO Rating - season 1 - JuOSu - 08-25-2017
For those unfamiliar with the ELO system, I will briefly give an introduction. Used at first in Chess, but later picked up by popular statistical website fivethirtyeight.com - the ELO system can represent the strength of two opponents and make predictions possible as well as give an overview who is good or not.
The website uses ELO for all kinds of sports, from soccer to baseball to football to describe teams and how good they are. While the system is far from perfect, in my opinion is one of the best rating systems out there right now and as a mathematic nerd - I love that website.
I wanted to re-create the ELO rating here, though I knew it would result in a few problems. First off, the limited history. There have only been two seasons of 6 and 8 teams, not a huge history like the entire history of the NFL to get back to.
Furthermore, I had to learn how to calculate the formula first, a process that took me several days to figure out. Additionally, doing it from scratch also meant at first it was pretty meaningless, but as you will be able to see later, even towards the later part of the first season, there are already easy trends to spot.
Another issue is the insane home field advantage here, far bigger than the one in the NFL. For comparison, in the NFL around 58% of all home games are won, here it has been 67% and 70% in the first two seasons. Adjusting for that, I might have gone too far to correct for it, but in the end I am happy with the adjustment I made, since home field advantage clearly is a huge thing as of now.
Another challenge will be expansion in season 2, typically expansion teams in the nfl started at 1300 but I may use 1400 instead since the league is still early on and 1300 seems like too much of an over-correction for expansion teams.
I should probably explain ELO first. Basically, the average team has a 1500 rating, which is where all teams started. Every team that wins, gains points based on how impressive the win was (depending on strength of opponent and margin of victory).
In the NFL, home field advantage gives you about a 60 point bonus, whereas here I chose 120 points for home field advantage, as 67% win probability equals around 120 points of ELO difference. So if your team had 1500 and your opponent had 1500, home field advantage actually puts you at 1620 and therefore gives you a 67% chance to win. Similarly if you had 1500 and your opponent had 1620 and you were at home, that would mean it is a 50-50 chance of winning.
How is ELO calculated? It is quite complicated. First you need the odds of winning. which uses the formula:
1 / 10 ^ (-ELODIFF / 400) +1)
Now, that looks more complicated than it is. Basically first you calculate the difference in ELO between the two teams (adjusting for home field advantage), that number than gets divided by 400. Then take 10^ the negative of whatever result you just had. Add 1 to the result and then do 1 divided by whatever result you got.
Again, it sounds quite complicated but I did all of this manually in less than a day, so you will just have to trust my results.
Once the game is played, you have the following formula to calculate the new ELO:
OLDELO = ((natural logarithm of the margin of victory +1) x 20) x (result - expected result)
Again, very complicated looking but in reality it is much easier.
The natural logarithm is used because the margin of victory becomes less impressive after a while. The fourth or fifth touchdown difference doesn't change the result much anymore, whereas the first 10 points mean quite a lot. As far as results go, 1 is used for a win and 0 for a loss and the expected result is the odds we calculated before (i.e. a team with 67% win chance wins the game - therefore the formula there would be times (1-0.67).
What this means is that every team that wins will always gain points in ELO and teams that lose will always lose points. However, a bigger margin or a more impressive win will give you more points.
I considered putting this in statistical analysis because of those formulas but I don't think it is accurate to say it is statistical analysis. I am not analysing anything, I am just presenting facts. Also, all the formulas and information was carefully searched together from the fivethirtyeight.com website. They don't specifically state anywhere the exact process but with different quotes from different places I pieced it together. As I said, this should not be taken as the gold standard it is on that website, because our league does not have the history the NFL does.
I did the complete ELO calculations for season 1 first, as it is important to establish a history. It probably would have been easier to write a program doing it for me somehow but I did it all by hand. I will do season 2 shortly and then we will be caught up and I can do it every week in the next season. It will also be nice to have odds of winning for every game then.
Week 1:
Week 1 was fairly boring, since every team started with 1500 ELO and therefore every home team had a 67% chance of winning.
San Jose Sabercats - Yellowknife Wraiths 14-27
Arizona Outlaws - Orange County Otters - 27-12
Baltimore Hawks - Colorado Yeti 20-23
As we can see, two out of three home teams ended up winning and Arizona gets the most impressive win, with the largest margin of victory and winning on the road on top of that.
We end up with this total after week 1:
Arizona Outlaws: 1537 (+37)
Yellowknife Wraiths: 1517 (+17)
Colorado Yeti: 1509 (+9)
Baltimore Hawks: 1491 (-9)
San Jose Sabercats: 1483 (-17)
Orange County Otters: 1463 (-37)
Week 2:
(1463) Orange County Otters - (1491) Baltimore Hawks 13-10
(1537) Arizona Outlaws - (1483) San Jose Sabercats 10-24
(1517) Yellowknife Wraiths - (1509) Colorado Yeti 10-13
At this point Baltimore had a 70% win chance, Sabercats 59% and Colorado 65%.
As I said in the first few weeks this will still look silly and not really mean much, as the 120 home field advantage is far greater than any difference between teams at this point. I promise that will change. Above you see good examples of how home field is meaningful. San Jose has 50 less points than Arizona but gets 120 points for home field, meaning they were a favorite by 70 points.
We end week 2 with these new totals:
Colorado Yeti: 1519 (+10)
Arizona Outlaws: 1515 (-22)
Yellowknife Wraiths: 1507 (-10)
San Jose Sabercats: 1505 (+22)
Orange County Otters: 1482 (+19)
Baltimore Hawks: 1472 (-19)
Week 3:
(1515) Arizona Outlaws - (1472) Baltimore Hawks 21-13
(1505) San Jose Sabercats - (1482) Orange County Otters 10-23
(1519) Colorado Yeti - (1507) Yellowknife Wraiths 20-16
We will later see that Arizona probably would have been predicted to win despite the home field advantage, there just wasn't enough data yet to show who the good teams were. Baltimore was favoured 61%, Orange County 64% and Yellowknife 66%, still early on and still heavily influenced by just home field advantage.
New totals after week 3:
Arizona Outlaws: 1542 (+27)
Colorado Yeti: 1540 (+21)
Orange County Otters: 1501 (+19)
San Jose Sabercats: 1486 (-19)
Yellowknife Wraiths: 1486 (-21)
Baltimore Hawks: 1445 (-27)
Week 4:
(1445) Baltimore Hawks - (1540) Colorado Yeti 39-24
(1501) Orange County Otters - (1486) San Jose Sabercats 17-6
(1486) Yellowknife Wraiths - (1542) Arizona Outlaws 13-14
This is already one of the biggest upsets. With home field advantage, Baltimore overcame a 215 point deficit to beat Colorado on the road, who were favoured 77%. San Jose was a favourite with 64% and Arizona with 71%
New totals after week 4:
Arizona Outlaws: 1546 (+4)
Orange County Otters: 1533 (+32)
Colorado Yeti: 1498 (-42)
Baltimore Hawks: 1487 (+42)
Yellowknife Wraiths: 1482 (-4)
San Jose Sabercats: 1454 (-32)
Week 5:
(1454) San Jose Sabercats - (1487) Baltimore Hawks 17-30
(1533) Orange County Otters - (1498) Colorado Yeti 16-30
(1546) Arizona Outlaws - (1482) Yellowknife Wraiths 21-27
Three home-teams winning is finally showing the strength of home-field advantage, as all three favored teams win; Baltimore at 71%, Colorado at 62% and Yellowknife at 60%.
New totals after week 5:
Arizona Outlaws: 1531 (-15)
Colorado Yeti: 1518 (+20)
Orange County Otters: 1513 (-20)
Baltimore Hawks: 1502 (+15)
Yellowknife Wraiths: 1497 (+15)
San Jose Sabercats: 1439 (-15)
Week 6:
(1518) Colorado Yeti - (1502) Baltimore Hawks 27-21
(1439) San Jose Sabercats - (1531) Arizona Hawks 3-23
(1513) Orange County Otters - (1497) Yellowknife Wraiths 13-16
Colorado managed the upset here, against a 64% favorite team with Baltimore. Arizona at 77% and Yellowknife at 66% both won.
New totals after week 6:
Arizona Outlaws: 1545 (+14)
Colorado Yeti: 1543 (+25)
Yellowknife Wraiths: 1506 (+9)
Orange County Otters: 1504 (-9)
Baltimore Hawks: 1477 (-25)
San Jose Sabercats: 1425 (-14)
Week 7:
(1543) Colorado Yeti - (1477) Baltimore Hawks 31-7
(1506) Yellowknife Wraiths - (1504) Orange County Otters 0-24
(1425) San Jose Sabercats - (1545) Arziona Hawks 12-20
The Hawks were heavily favored at 80%, the biggest so far I think. Colorado with an upset and a very decisive win, against 57% Baltimore winning, though as we see Colorado was the better team. Orange County and Yellowknife with basically the same strength, means Orange County was actually a 65% favorite because of home field advantage.
New totals after week 7:
Colorado Yeti: 1579 (+36)
Arizona Outlaws: 1553 (+8)
Orange County Otters: 1526 (+22)
Yellowknife Wraiths: 1484 (-22)
Baltimore Hawks: 1441 (-36)
San Jose Sabercats: 1417 (-8)
Week 8:
(1579) Colorado Yeti - (1484) Yellowknife Wraiths 7-29
(1417) San Jose Sabercats - (1526) Orange County Otters 7-35
(1441) Baltimore Hawks - (1553) Arizona Outlaws 34-31
We have another huge upset with Baltimore besting Arizona despite a huge deficit. And we are getting closer to the first away team being favored, with Yellowknife only having a 55% win probability as the home team.
New totals after week 8:
Colorado Yeti: 1551 (-28)
Orange County Otters: 1540 (+14)
Arizona Outlaws: 1532 (-21)
Yellowknife Wraiths: 1512 (+28)
Baltimore Hawks: 1462 (+21)
San Jose Sabercats: 1403 (-14)
Week 9:
(1512) Yellowknife Wraiths - (1462) Baltimore Hawks 12-17
(1540) Orange County Otters - (1532) Arizona Outlaws 7-19
(1403) San Jose Sabercats - (1551) Colorado Yeti 30-17
Probably the biggest upset of the entire year, the Yeti were favored to win 83% but lost. Miracles do happen. Baltimore and Arizona were both favored to win and did, with 58% and 65% chances.
New totals after week 9:
Arizona Outlaws: 1550 (+18)
Orange County Otters: 1522 (-18)
Colorado Yeti: 1508 (-43)
Yellowknife Wraiths: 1496 (-16)
Baltimore Hawks: 1478 (+16)
San Jose Sabercats: 1446 (+43)
Week 10:
(1478) Baltimore Hawks - (1496) Yellowknife Wraiths 20-40
(1550) Arizona Outlaws - (1446) San Jose Sabercats 27-14
(1508) Colorado Yeti - (1522) Orange County 6-13
We are getting so close to an away team being the favorite. The Sabercats were only a 52% favorite and lost, so we can see, winning on the road can become a viable option when teams are more dominant.
New totals after week 10:
Arizona Outlaws: 1577 (+27)
Orange County Otters: 1535 (+13)
Yellowknife Wraiths: 1514 (+18)
Colorado Yeti: 1495 (-13)
Baltimore Hawks: 1460 (-18)
San Jose Sabercats: 1419 (-27)
Week 11:
(1460) Baltimore Hawks - (1514) Yellowknife Wraiths 10-19
(1535) Orange County Otters - (1419) San Jose Sabercats 26-9
(1577) Arizona Outlaws - (1495) Colorado Yeti 10-19
And there it is, the first complete toss-up. Sabercats only had 50% win probability at home and lost.
New totals after week 11:
Orange County Otters: 1564 (+29)
Arizona Outlaws: 1562 (-15)
Yellowknife Wraiths: 1526 (+12)
Colorado Yeti: 1510 (+15)
Baltimore Hawks: 1448 (-12)
San Jose Sabercats: 1390 (-29)
Week 12:
(1526) Yellowknife Wraiths - (1448) Baltimore Hawks 17-13
(1510) Colorado Yeti - (1390) San Jose Sabercats 13-17
(1564) Orange County Otters - (1562) Arizona Outlaws 3-23
And now we officially have it, the first away team favorite. Yeti were actually 51% favored here, despite their loss. Still, we finally managed to overcome home-field advantage officially.
New totals after week 12:
Arizona Outlaws: 1583 (+21)
Yellowknife Wraiths: 1543 (+17)
Orange County Otters: 1543 (-21)
Colorado Yeti: 1494 (-16)
Baltimore Hawks: 1431 (-17)
San Jose Sabercats: 1406 (+16)
Week 13:
(1494) Colorado Yeti - (1583) Arizona Outlaws 0-15
(1543) Yellowknife Wraiths - (1406) San Jose Sabercats 20-19
(1431) Baltimore Hawks) - (1543) Orange County Otters 17-24
And yet another away team favorite, the Wraiths were even 54% favorites and won the game on the road.
New totals after week 13:
Arizona Outlaws: 1596 (+13)
Orange County Otters: 1551 (+8)
Yellowknife Wraiths: 1549 (+6)
Colorado Yeti: 1481 (-13)
Baltimore Hawks: 1423 (-8)
San Jose Sabercats: 1400 (-6)
Week 14:
(1549) Yellowknife Wraiths - (1481) Colorado Yeti 10-20
(1423) Baltimore Hawks - (1400) San Jose Sabercats 3-31
(1596) Arizona Outlaws - (1551) Orange County Otters 16-23
Sabercats had a very big win here that boosted them a lot and made them not be in last place at the end of the season after spending weeks there. Expected results in every game.
New totals after the end of the regular season:
Arizona Outlaws: 1580 (-16)
Orange County Otters: 1567 (+16)
Yellowknife Wraiths: 1528 (-21)
Colorado Yeti: 1502 (+21)
San Jose Sabercats: 1425 (+25)
Baltimore Hawks: 1398 (-25)
Playoffs Week 1:
(1528) Yellowknife Wraiths - (1502) Colorado Yeti 6-13
(1567) Orange County Otters - (1580) Arizona Outlaws 13-36
The playoffs ended up being really interesting. With the home-field advantage, the Yeti had a huge advantage despite being the worst of the four teams. They got into the final with the home-field advantage. Arizona with a huge win that boosts them over 1600 and with home-field advantage, they were in a great spot. We also had the best two teams play in the first round, in an early final, but still with a huge favorite in the Outlaws thanks to home-field advantage with 67%.
New totals after playoffs week 1:
Arizona Outlaws: 1603 (+23)
Orange County Otters: 1544 (-23)
Colorado Yeti: 1517 (+15)
Yellowknife Wraiths: 1513 (-15)
San Jose Sabercats: 1425 (-)
Baltimore Hawks: 1398 (-)
Playoffs Week 2:
(1517) Colorado Yeti - (1603) Arizona Outlaws 6-29
Outlaws were a 76% favorite to win the final game, thanks to home-field advantage and a big lead in ELO rating.
FINAL RESULTS AFTER SEASON 1:
Arizona Outlaws: 1618 (+15)
Orange County Otters: 1544 (-)
Yellowknife Wraiths: 1513 (-)
Colorado Yeti: 1502 (-)
San Jose Sabercats: 1425 (-)
Baltimore Hawks: 1398 (-)
Funny in the end, a final team is only in 4th place and only barely above the average team in ELO rating with 1502 (1500 being the average).
I am sorry this was so long and clunky, once I am caught up with season 2 it will be nice and pretty each week, maybe even as a graphic. Season 2 will probably come tomorrow. The ratings will continue with where we left off, though probably there will be some regression to the mean, the way fivethirtyeight.com does it, probably bringing everyone closer to 1500 again by maybe 25%, with the expansion teams starting at 1400.
Some cool facts at the end summarized:
Highest rating: Arizona Outlaws: 1618 (after last week)
Lowest rating: San Jose Sabercats: 1390 (after week 11)
Biggest upset: San Jose Sabercats beating Colorado Yeti on the road in week 9, 30-17 with only a 17% win probability and an ELO deficit of 268 after adding home field advantage.
*ELO Rating - season 1 - kckolbe - 08-25-2017
Very interesting, but I now need Season Two. Given all of the moves due to the expansion teams, you might be better off doing them from scratch instead of carrying over S1.
*ELO Rating - season 1 - manicmav36 - 08-25-2017
It's always cool to see something made for a different purpose apply so we'll where it wasn't intended. Nice write-up!
*ELO Rating - season 1 - JuOSu - 08-25-2017
(08-25-2017, 07:05 AM)kckolbe Wrote:Very interesting, but I now need Season Two. Given all of the moves due to the expansion teams, you might be better off doing them from scratch instead of carrying over S1.
According to 538.com, expansion teams would start at 1300 and they carry over every year, but do regression to the mean and I will probably stick with that. Season 2 will come soon!
*ELO Rating - season 1 - timeconsumer - 08-25-2017
![[Image: giphy.gif]](https://media.giphy.com/media/7rj2ZgttvgomY/giphy.gif)
BTW I wouldn't put this in stats analysis either. You'll get paid more for it here because of the huge word count.
*ELO Rating - season 1 - Kristy95 - 08-25-2017
(08-25-2017, 07:21 AM)timeconsumer Wrote:
BTW I wouldn't put this in stats analysis either. You'll get paid more for it here because of the huge word count.
Hahaha Shia LeBouf
*ELO Rating - season 1 - Sweetwater - 08-25-2017
(08-25-2017, 10:21 AM)timeconsumer Wrote:
BTW I wouldn't put this in stats analysis either. You'll get paid more for it here because of the huge word count.
He should get some extra credit for doing the stats though
*ELO Rating - season 1 - Valtookan - 08-25-2017
Pretty cool write up.
In week 6 and 7 of this article you called us the Arizona Hawks not the Outlaws; just a pointer.
Besides that I really liked the look back. Can't wait to see the S2 Elo. I really think we are just going to dominate that one.
*ELO Rating - season 1 - kckolbe - 08-25-2017
@JuOSu
Quote:Funny in the end, a final team is only in 4th place and only barely above the average team in ELO rating with 1502 (1500 being the average).
There is a VERY good chance of that happening this year with the Hawks, who will likely be 5th best in the league by ELO.
*ELO Rating - season 1 - DeathOnReddit - 08-25-2017
Whats crazy is that in season 2 we're so much better.