02-13-2021, 01:46 PM
(This post was last modified: 02-14-2021, 09:09 PM by Asked Madden.)
Introduction
Many moons ago I wrote two media pieces that looked at expected wins using the pythagorean wins and linear wins formulas. Here's a handy link to the first one and here's a handy link to the second one. Due to the forum migration both the threads have their formatting really screwed up but they're still technically legible if you squint and turn your computer screen at an awkward angle.
I actually find this stuff kinda cool so I'll spare you the word fluff about the origins of the formulas and why they matter and all that mumbo jumbo and just get straight to the good part.
Both formulas try to peg how many wins a team should have using different metrics. Pythagorean Wins looks to point differential to determine how good a team is - i.e. how many wins they should have. There's a lot of value to the metric and its been shown to be pretty accurate in real life applications but I've also got plenty of issues with it as it applies to both the sim and real life because I can come up with issues with how tempo effects those metrics and get into a whole mind puzzle about that sort of stuff. But yeah, point differential. Its cool and can show you how good or trash your team is supposedly. Daryl Morey used it for the Rockets and they won a lot of games. Never a title but a lot of games nonetheless. Off topic but its really gotta suck to be a fan of Houston sports right now.
Linear wins is stolen from baseball - so it has plenty of room for criticism about how well it fits football - but some super smart stat nerds figured it out anyway. Its been found to have a pretty similar accuracy rate as Pythagorean Wins but varies somewhat and bumps my word count up with more charts and numbers to net me that sweet media money.
I actually find this stuff kinda cool so I'll spare you the word fluff about the origins of the formulas and why they matter and all that mumbo jumbo and just get straight to the good part.
Both formulas try to peg how many wins a team should have using different metrics. Pythagorean Wins looks to point differential to determine how good a team is - i.e. how many wins they should have. There's a lot of value to the metric and its been shown to be pretty accurate in real life applications but I've also got plenty of issues with it as it applies to both the sim and real life because I can come up with issues with how tempo effects those metrics and get into a whole mind puzzle about that sort of stuff. But yeah, point differential. Its cool and can show you how good or trash your team is supposedly. Daryl Morey used it for the Rockets and they won a lot of games. Never a title but a lot of games nonetheless. Off topic but its really gotta suck to be a fan of Houston sports right now.
The Pythagorean Wins Formula is:
PYTH = ((PF^X) / ((PF^X + PA^X))) *16
Where X is calculated by:
X = 1.5 * LOG((PF + PA) / 16)
Linear wins is stolen from baseball - so it has plenty of room for criticism about how well it fits football - but some super smart stat nerds figured it out anyway. Its been found to have a pretty similar accuracy rate as Pythagorean Wins but varies somewhat and bumps my word count up with more charts and numbers to net me that sweet media money.
The Linear Wins Formula is:
EXP(W%) = 0.001538 * (PF – PA) + 0.50
That funky 0.001538 is based on a linear model about how many points a team needs to add to their point margin to add 1% to their winning percentage. I'll let previous Steg from March of last year explain it cause he did a better job than I will now:
Quote:Although it is derived from NFL statistics and not sim engine statistics you can still fairly accurately determine what margin a team needs to increase their point margin by to gain an extra 1% on their expected winning percentage. Take 0.01 – equivalent to 1% - and divide it by the leading coefficient in the equation – 0.001538 – and you’ll find that a team needs an increase in 6.5 points in their point margin to gain an extra 1% to their expected winning percentage.
For clarity as well I scaled both formulas to fit to an 8 win season currently since thats how many games have been played thus far.
The Charts
![[Image: t99Vecs.png]](https://i.imgur.com/t99Vecs.png)
![[Image: 1b0bgp4.png]](https://i.imgur.com/1b0bgp4.png)
It really irks me those charts don't line up perfectly but whatever. Its media not my future Pulitzer Prize winning memoire. Couple of housekeeping notes about what all the charts mean.
The first chart is the Pythagorean model. Wins, Losses, Points For, and Points Against should all be self-explanatory. I hope. EXP is the X in the Pythagorean formula - so the logarithmic equation part. PYTH is the pythagorean win mark - so how many wins the model expects a team to have at this point in the season. Delta is the change between that and they're actual wins.
The second chart is the Linear model. That first column - "Linear" - is their linear win% based on the formula. Real Win% should be pretty self explanatory. "Linear scaled" is the formula scaled to 8 games in an actual numeric value type thing to show how many wins the team should have based on that win%. "Linear Diff" is how that scaled value of how many wins a team should have is different from the actual wins they have.
"Average Diff" looks at the average of the difference both models found. "Average Wins Diff" and "Average Losses Diff" look at the average of what a teams record should be based on both models.
The first chart is the Pythagorean model. Wins, Losses, Points For, and Points Against should all be self-explanatory. I hope. EXP is the X in the Pythagorean formula - so the logarithmic equation part. PYTH is the pythagorean win mark - so how many wins the model expects a team to have at this point in the season. Delta is the change between that and they're actual wins.
The second chart is the Linear model. That first column - "Linear" - is their linear win% based on the formula. Real Win% should be pretty self explanatory. "Linear scaled" is the formula scaled to 8 games in an actual numeric value type thing to show how many wins the team should have based on that win%. "Linear Diff" is how that scaled value of how many wins a team should have is different from the actual wins they have.
"Average Diff" looks at the average of the difference both models found. "Average Wins Diff" and "Average Losses Diff" look at the average of what a teams record should be based on both models.
Non-Math For Those Who Like to Read
So you've made this far. Congrats. If you don't like interpreting charts on your own and would prefer I serenade you with you my words you've come to the right section of the article. I'm gonna treat this as a sarcastic meme section so we're gonna hand out some awards at the bottom to the "Most Sim Screwed" team and "Most Sim Blessed" team.
By the Pythagorean model Berlin is almost perfectly performing at their expected level with a 0.03 difference between their Pythagorean win total and their real win total of 4-4. Sarasota is also pretty balanced - a difference of 0.06, as is Honolulu - a difference of -0.15.
Only a couple of teams have huge gaps in their expected wins. The model really hates San Jose. It thinks they've overperformed to the tune of their record being 1.54 wins better than it should be. Same with Yellowknife and Arizona who it believes should have 4.2 and 5.2 wins now respectively - a difference of 0.75 and 0.76 from their actual 5 and 6 wins. Poor New Orleans only has 3 wins but the model thinks they should have 4.4 if thats any consolation.
On the Linear side of things Berlin manages to get even more balanced with the difference in their performance and expected performance being literally 0.01 wins. I never expected to see the 0.03 from their Pythagorean metric get any closer to zero but it somehow did. Yellowknife and San Jose stay as the two most overperforming teams but get knocked a little harder with Yellowknife's wins difference moving to -1.88 and San Jose's to -0.81. Arizona gets really close to join the -1.5 difference club with a -1.4 because the model only expects them to have 4.6 wins right now. Honolulu is in the -1 club but a bit farther off of -1.5, slotting in it at -1.13 and an expected win total of 4.87.
Baltimore's had a rough season thus far but gets a nice boost from the Linear model which expects them to have 1.79 wins now. Austin, Philadelphia, New Orleans, and Orange County all get nice boosts as well which bring them all to around the 4-4 mark if the season had gone like the model expected.
Awards Time (No it wasn't a joke)
And the award for "Most Sim Screwed" goes to...
The New Orleans Second Line
3-5 is probably not where New Orleans expected to be at this point of the season but the average of the models says they should be 1.33 wins better and slot in at 4.33-3.67.
A close runner up is Baltimore with the models thinking they should be an average of 1.22 wins better for a record of 1.22-6.78. Its not much but a wins a win.
And the award for "Most Sim Blessed" goes to...
The San Jose Sabercats
The New Orleans Second Line
3-5 is probably not where New Orleans expected to be at this point of the season but the average of the models says they should be 1.33 wins better and slot in at 4.33-3.67.
A close runner up is Baltimore with the models thinking they should be an average of 1.22 wins better for a record of 1.22-6.78. Its not much but a wins a win.
And the award for "Most Sim Blessed" goes to...
The San Jose Sabercats
Wowie San Jose is overperforming compared to almost every other team. The models think that on average they're 1.66 wins better than they should be. Thats a pretty chunky difference.
Arizona is in a pretty distance second all things being considered with the models thinking they're only 1.08 wins better on average.
So How Bout Them Standings?
Baltimore Hawks On average, the models predict the standings should look like this at this point in the season:
NSFC
Colorado Yeti
5.05-2.95
Chicago Butchers
5.05-2.95
Sarasota Sailfish
4.80-3.20
Yellowknife Wraiths
4.19-3.81
Berlin Fire Salamanders
4.02-3.98
Philadelphia Liberty
3.20-4.80
NSFC
Colorado Yeti
5.05-2.95Chicago Butchers
5.05-2.95Sarasota Sailfish
4.80-3.20Yellowknife Wraiths
4.19-3.81Berlin Fire Salamanders
4.02-3.98Philadelphia Liberty
3.20-4.80
1.22-6.78The bottom three teams stay the same in the NSFC however the current top seed Yellowknife Wraiths fall out of the playoff picture and into the fourth seed while third place Colorado Yeti vault to the top of the conference (they're tied with Chicago in average predicted record and have the tiebreaker over them). Sarasota slides into the playoff picture in the third seed after the Wraiths fall out.
ASFC
Honolulu Hahalua
5.36-2.64Arizona Outlaws
4.92-3.08San Jose Sabercats
4.34-3.66New Orleans Second Line
4.33-3.67New York Silverbacks
4.18-3.82Austin Copperheads
3.06-4.94Orange County Otters
2.87-5.13The top three teams stay completely the same, however New Orleans replaces New York as being the team "on the bubble" for potentially making the playoffs. Austin leapfrogs Orange County to get out of the cellar while the Otters chances of missing the playoffs for the first time in franchise history only increase.
![[Image: bZJ57LU.gif]](https://i.imgur.com/bZJ57LU.gif)
