04-03-2020, 10:52 PM
(This post was last modified: 04-03-2020, 11:11 PM by iStegosauruz.)
[div align=\\\"center\\\"]Background and Methodology[/div]
A few weeks ago, I explored the concepts of “Pythagorean Wins” and the “Linear Formula” as ways to predict how many games a team should be expected to win on a given season. I tested the formula on every season from Season 16 to now in my previous post and found that it is a fairly accurate measure of how many wins a team should expect. In both Season 19 and Season 20 it was predicted the eventual Ultimus winner.
I’ll save you having to slog through a lot of formulas and numbers again – if you’re interested in all of the math that goes into these calculations you can check out my previous post for a bit of a deeper dive and links to other websites where you can explore the topic in depth. For our purposes, the only thing you should probably have in your mind before going forward are the formulas. For both metrics the key factor are the total points a team scores on the year and the total points a team gives up on the year. Each metric has a different scaling constant than then takes those pieces of data and manipulates them.
For Pythagorean Wins, the formula is:
[div align=\\\"center\\\"]PYTH = ((PF^X) / ((PF^X + PA^X))) *13
Where X is calculated by:
X = 1.5 * LOG((PF + PA) / 13)[/div]
For the Linear Wins method, the formula is:
[div align=\\\"center\\\"]EXP(W%) = 0.001538 * (PF – PA) + 0.50[/div]
[div align=\\\"center\\\"]Number Crunching [/div]
After the first five games of the season I ran the numbers on how many games each team would be expected to win over the course of the regular, thirteen game season.
[div align=\\\"center\\\"][/div]
Five games into the season the New Orleans Second Line were projected to be the best team in the league, clocking in at a projected 10.062 expected wins. At that point in time the Arizona Outlaws were projected to be the worst team in the league, clocking in at 3.802 expected wins.
The results look marginally different after the rest of the season was played.
[div align=\\\"center\\\"][/div]
At the end of the season the Orange County Otters were projected to be the best team in the league, with projections expecting them to have won 9.786 games on average. The worst team in the league, on average, was still projected to be the Arizona Outlaws. They’re pegged for 3.439 wins, on average.
How do these numbers differ from each other and how do they differ from the actual results?
[div align=\\\"center\\\"][/div]
Pyth 1.0 are the projections for the first set of Pythagorean Win calculations I ran. Pyth 2.0 are the projections for the second round of Pythagorean Win calculations I ran. Pyth Diff. is the difference between the first round of calculations and the second round of calculations. A positive number means that as the season went on the team’s projections decreased, while a negative number means that as the season went on a team’s projects increased. Pyth Diff 2.0 is the difference between the second round of calculations and the actual amount of wins a team got on the season. A positive number means a team underperformed on the year, or that on average based off their points for and points against they should have won more games. A negative number means that a team overperformed on the year, or that on average based off their points for and points against they should have won less games.
The biggest overperformer on the year were the Chicago Butchers. After the first five games when I ran the first round of Pythagorean Win calculations, they were projected to win 7.173 games. At the end of the season, the Pythagorean Win formula estimates that, on average, they would win 3.747 games on the season. Their projections changed drastically over the course of the season – dropping 3.426 projected wins. They actually ended up winning five games, meaning they overperformed what they should have won on average this season by 1.253 wins.
The biggest underperformer this season were the Philadelphia Liberty. After the first give games when I ran the first round of Pythagorean Win calculations, they were projected to win 4.411 games. At the end of the season, the Pythagorean Win formula estimates that, on average, they would win 3.747 games on the season. Their projections changed moderately over the course of the season – dropping 0.664 projected wins. They actually ended up winning 3 games, meaning they underperformed what they should have won on average this season by 0.747 wins.
The team that saw the biggest increase in projected wins between the first set of Pythagorean Win calculations and the second set were the Yellowknife Wraiths. After the first set of calculations they were projected to win 4.944 games on the season. After the second set of calculations they were projected to, on average, win 6.684 games on the season. This is an increase in 1.740 expected wins. They ended up winning 7 games, meaning they overperformed what they should have won on average this season by 0.316 wins.
Based off the second set of Pythagorean Win calculations, and if this season is anything like Season 19 and Season 20, the Orange County Otters should win the Ultimus this season.
The Linear Formula shows a very similar model.
[div align=\\\"center\\\"]
[/div]
Using the Linear Formula, the biggest overperformer on the year were the Baltimore Hawks. The formula pegs them as winning 7.78 games on the season on average. They actually won 9 games this season, a difference of 1.22 wins. Their expected win percentage on the year was 9% lower than their actual win percentage.
The biggest underperformer this season were the Philadelphia Liberty. The formula pegs them as winning 4.34 games on the season on average. They actually won 3 games this season, a difference of 1.34 wins. Their expected win percentage on the year was 10% higher than their actual win percentage.
The Chicago Butchers had the biggest decrease in their Linear Formula projections. After the first five games of the season the formula expected that they would win 6.8 games. After the season concluded, the Linear Formula projects that, on average, they would 4.34 games on the season. That is a difference of 2.46 wins. They actually ended up winning 5 games on the season, overperforming their projections by 0.66 wins.
The Colorado Yeti had the biggest increase in their Linear Formula projections. After the first five games of the season the formula expected that they would win 6.06 games. After the season concluded, the Linear Formula projects that, on average, they would win 6.98 games on the season. That is a difference of 0.92 wins. They actually ended up winning 8 games on the season, overperforming their projections by 1.02 wins.
[div align=\\\"center\\\"]Would the World Be Different?[/div]
If the average win projections each of these formulas had come true, would the world be any different? The final standings in the NSFC would be the same – the only potential difference would be whether the Butchers or Liberty were in last place. The final standings in the ASFC would be the same. The projected draft order for the first six picks would be the same – with the exception of the Butchers and Liberty potentially being swapped.
[div align=\\\"center\\\"]Conclusions [/div]
1. The Linear Formula and Pythagorean Win calculations are pretty handy for determining how good your team really was. The teams that underperformed can look for the areas they underperformed in while the teams that overperformed can try to strengthen certain areas as to not regress before next season.
2. Both metrics are fairly good at predicting the eventual record of most teams within about a game. There a few outliers, but for the most part after the first five games of the year the metrics were fairly accurate.
3. In Season 19 and Season 20, Pythagorean Wins accurately predicted the eventual Ultimus winner. If that is the case for this season, the Orange County Otters should win it. We'll have to wait and see if that projection holds.
[div align=\\\"center\\\"]Notes and Tidbits: [/div]
1. All the data for this is at the bottom of my previous study that should be linked above. The only thing I did was updated the excel spreadsheet with the new information. If you download the sheet you should be able to mess around with it on your own – the formulas are already programmed in.
2. I’m in the middle of another sim study that should be coming out in the next few days. It’s based on data for 82,800 simulations. I’m testing the best ways to build CBs. Should be very interesting, so be on the lookout for that.
A few weeks ago, I explored the concepts of “Pythagorean Wins” and the “Linear Formula” as ways to predict how many games a team should be expected to win on a given season. I tested the formula on every season from Season 16 to now in my previous post and found that it is a fairly accurate measure of how many wins a team should expect. In both Season 19 and Season 20 it was predicted the eventual Ultimus winner.
I’ll save you having to slog through a lot of formulas and numbers again – if you’re interested in all of the math that goes into these calculations you can check out my previous post for a bit of a deeper dive and links to other websites where you can explore the topic in depth. For our purposes, the only thing you should probably have in your mind before going forward are the formulas. For both metrics the key factor are the total points a team scores on the year and the total points a team gives up on the year. Each metric has a different scaling constant than then takes those pieces of data and manipulates them.
For Pythagorean Wins, the formula is:
[div align=\\\"center\\\"]PYTH = ((PF^X) / ((PF^X + PA^X))) *13
Where X is calculated by:
X = 1.5 * LOG((PF + PA) / 13)[/div]
For the Linear Wins method, the formula is:
[div align=\\\"center\\\"]EXP(W%) = 0.001538 * (PF – PA) + 0.50[/div]
[div align=\\\"center\\\"]Number Crunching [/div]
After the first five games of the season I ran the numbers on how many games each team would be expected to win over the course of the regular, thirteen game season.
[div align=\\\"center\\\"][/div]
Five games into the season the New Orleans Second Line were projected to be the best team in the league, clocking in at a projected 10.062 expected wins. At that point in time the Arizona Outlaws were projected to be the worst team in the league, clocking in at 3.802 expected wins.
The results look marginally different after the rest of the season was played.
[div align=\\\"center\\\"][/div]
At the end of the season the Orange County Otters were projected to be the best team in the league, with projections expecting them to have won 9.786 games on average. The worst team in the league, on average, was still projected to be the Arizona Outlaws. They’re pegged for 3.439 wins, on average.
How do these numbers differ from each other and how do they differ from the actual results?
[div align=\\\"center\\\"][/div]
Pyth 1.0 are the projections for the first set of Pythagorean Win calculations I ran. Pyth 2.0 are the projections for the second round of Pythagorean Win calculations I ran. Pyth Diff. is the difference between the first round of calculations and the second round of calculations. A positive number means that as the season went on the team’s projections decreased, while a negative number means that as the season went on a team’s projects increased. Pyth Diff 2.0 is the difference between the second round of calculations and the actual amount of wins a team got on the season. A positive number means a team underperformed on the year, or that on average based off their points for and points against they should have won more games. A negative number means that a team overperformed on the year, or that on average based off their points for and points against they should have won less games.
The biggest overperformer on the year were the Chicago Butchers. After the first five games when I ran the first round of Pythagorean Win calculations, they were projected to win 7.173 games. At the end of the season, the Pythagorean Win formula estimates that, on average, they would win 3.747 games on the season. Their projections changed drastically over the course of the season – dropping 3.426 projected wins. They actually ended up winning five games, meaning they overperformed what they should have won on average this season by 1.253 wins.
The biggest underperformer this season were the Philadelphia Liberty. After the first give games when I ran the first round of Pythagorean Win calculations, they were projected to win 4.411 games. At the end of the season, the Pythagorean Win formula estimates that, on average, they would win 3.747 games on the season. Their projections changed moderately over the course of the season – dropping 0.664 projected wins. They actually ended up winning 3 games, meaning they underperformed what they should have won on average this season by 0.747 wins.
The team that saw the biggest increase in projected wins between the first set of Pythagorean Win calculations and the second set were the Yellowknife Wraiths. After the first set of calculations they were projected to win 4.944 games on the season. After the second set of calculations they were projected to, on average, win 6.684 games on the season. This is an increase in 1.740 expected wins. They ended up winning 7 games, meaning they overperformed what they should have won on average this season by 0.316 wins.
Based off the second set of Pythagorean Win calculations, and if this season is anything like Season 19 and Season 20, the Orange County Otters should win the Ultimus this season.
The Linear Formula shows a very similar model.
[div align=\\\"center\\\"]
[/div]
Using the Linear Formula, the biggest overperformer on the year were the Baltimore Hawks. The formula pegs them as winning 7.78 games on the season on average. They actually won 9 games this season, a difference of 1.22 wins. Their expected win percentage on the year was 9% lower than their actual win percentage.
The biggest underperformer this season were the Philadelphia Liberty. The formula pegs them as winning 4.34 games on the season on average. They actually won 3 games this season, a difference of 1.34 wins. Their expected win percentage on the year was 10% higher than their actual win percentage.
The Chicago Butchers had the biggest decrease in their Linear Formula projections. After the first five games of the season the formula expected that they would win 6.8 games. After the season concluded, the Linear Formula projects that, on average, they would 4.34 games on the season. That is a difference of 2.46 wins. They actually ended up winning 5 games on the season, overperforming their projections by 0.66 wins.
The Colorado Yeti had the biggest increase in their Linear Formula projections. After the first five games of the season the formula expected that they would win 6.06 games. After the season concluded, the Linear Formula projects that, on average, they would win 6.98 games on the season. That is a difference of 0.92 wins. They actually ended up winning 8 games on the season, overperforming their projections by 1.02 wins.
[div align=\\\"center\\\"]Would the World Be Different?[/div]
If the average win projections each of these formulas had come true, would the world be any different? The final standings in the NSFC would be the same – the only potential difference would be whether the Butchers or Liberty were in last place. The final standings in the ASFC would be the same. The projected draft order for the first six picks would be the same – with the exception of the Butchers and Liberty potentially being swapped.
[div align=\\\"center\\\"]Conclusions [/div]
1. The Linear Formula and Pythagorean Win calculations are pretty handy for determining how good your team really was. The teams that underperformed can look for the areas they underperformed in while the teams that overperformed can try to strengthen certain areas as to not regress before next season.
2. Both metrics are fairly good at predicting the eventual record of most teams within about a game. There a few outliers, but for the most part after the first five games of the year the metrics were fairly accurate.
3. In Season 19 and Season 20, Pythagorean Wins accurately predicted the eventual Ultimus winner. If that is the case for this season, the Orange County Otters should win it. We'll have to wait and see if that projection holds.
[div align=\\\"center\\\"]Notes and Tidbits: [/div]
1. All the data for this is at the bottom of my previous study that should be linked above. The only thing I did was updated the excel spreadsheet with the new information. If you download the sheet you should be able to mess around with it on your own – the formulas are already programmed in.
2. I’m in the middle of another sim study that should be coming out in the next few days. It’s based on data for 82,800 simulations. I’m testing the best ways to build CBs. Should be very interesting, so be on the lookout for that.