2023 Simulated Schedules

See the 2022 Simulated Schedules.

Introduction

With the 2024 season coming up, let’s look back at last season and see how different the outcome could have been if the schedule had been different.

Every week, each team ‘plays’ another team in the league. However, there is no real interaction between the two teams. Each team tries to score the most points they can, independent of their opponent. That is, Team A’s owner will roster the players he thinks will get the most points that week, regardless of whether he is playing Team B, C, or D.

Using this premise we’ll perform the following workflow:

• Generate a new season schedule
• Use the number of points each team actually scored in each week to determine the outcome of every game
• Calculate the season standings from the new schedule

Some questions we’ll answer:

• What were the chances of team X placing where they did last season?
• What were the chances of each team placing first/last for the season?
• What were each team’s chances of making the playoffs?

Lastly, we’ll look at some interesting and unlikley rankings that could have occured.

Just The Regular Season

Unfortunately, this analysis is only for the regular season. The reason I can’t include the playoffs is because of the first-round byes that four teams have. These byes mean that I don’t have team point totals for four teams from week fifteen. When we simulate a new schedule, those four teams that had byes might not have them anymore, but since they didn’t play that week, we can’t determine the game outcome.

If you guys enjoy this analysis then next year I can include the playoffs. We’ll just have to have the four teams with first-round byes tell me the players they would roster for that week if they didn’t have a bye.

Schedule Generation

At the start of the season Sleeper randomly generates the season schedules. The regular season is fourteen weeks long. In the first eleven weeks, each team plays every other team once. Then, the first three weeks are repeated for the last three weeks.

Ideally, we could generate every possible schedule, which would give us an exact distribution of each owner’s rankings. The exact number of possible schedules is a tricky combinatorics problem, but I’ve estimated it to be somewhere around 10^25 (a 1 with 25 zeros after it). With this many possible schedules, we can’t generate them all, but we can generate a very large number that will give us a fairly accurate picture of the ‘true’ distribution.

Season Results

It’s been a few months since the season ended, so as a reminder, here are the final standings from the regular season.

Rank	Username	Points For	Points Against	Record
1	pacc	2008.96	1765.22	9-5
2	thezirconisdragon	2000.73	1895.99	9-5
3	herbietime	2114.47	1990.59	8-6
4	alecwilson	2107.20	1854.36	8-6
5	empireyikesback	1798.42	1662.93	8-6
6	burgertownthicnred	1769.67	1778.89	8-6
7	therealfergus	1814.81	2027.19	6-8
8	mackjyers21	1730.29	1818.54	6-8
9	shakylegs	1650.25	1838.57	6-8
10	tonygordzilla22	1625.72	1735.48	6-8
11	black8yellownation	1495.60	1615.37	6-8
12	namebrant	1645.83	1778.82	4-10

10 Million Simulations

I simulated 10 million possible schedules, and recorded the final season rankings for each. Lets look at some of the results.

Ranking Counts

These are the raw counts from the 10 million simulations. For example, herbietime placed first in 5,191,110 simulations, whereas tonygordzilla22 placed first only 36 times. Some interesting things to note:

• Every team except herbietime could have placed last
• Every team except blackandyelllownation could have placed first

There could be schedules were herbietime placed last or blackandyellownation placed first. However, they didn’t occur in the 10 million simulations performed here.

	1	2	3	4	5	6	7	8	9	10	11	12
herbietime	5191110	2466258	1263125	638384	281700	108655	38014	10242	2192	300	20	0
thezirconisdragon	2074697	2171155	2116925	1910464	908055	432684	211870	104144	44943	18354	6032	677
pacc	1301049	2361512	2587268	2017290	952164	439508	200778	89029	34619	12850	3618	315
alecwilson	1209358	2309450	2423388	2001998	1123941	556264	243843	95928	28520	6519	771	20
empireyikesback	100340	300327	652351	1275076	2215778	2300439	1551716	906495	443471	187408	59043	7556
therealfergus	79027	231050	524234	1112273	2232044	2101218	1603096	1077066	611100	301181	112416	15295
mackjyers21	29770	97803	239929	529663	1024433	1574398	2006172	2136204	1266054	688986	334023	72565
burgertownthicnred	12441	50768	148201	374902	863380	1594773	2346878	2212003	1351781	705852	291124	47897
shakylegs	1832	8321	27895	79198	204288	428686	818694	1486333	2669906	2335301	1514670	424876
namebrant	340	2944	13802	46325	136744	302059	591635	1072327	1910769	2822535	2315996	784524
tonygordzilla22	36	403	2825	14000	54992	151888	361161	736419	1446341	2425927	3904713	901295
black8yellownation	0	9	57	427	2481	9428	26143	73810	190304	494787	1457574	7744980

Ranking Percentage

This is the same table as above, however, now it shows as a percentage. I’ve also highlighted the ranking that each team actually had in the 2023 season. Now, we can see the herbietime had about a 51.9% chance of taking first place, a 24.6% chance of taking second, and a 12.6% chance of taking third, which he did.

• The first column is each team’s chance of placing first
• The last column is each team’s chance of placing last

	1	2	3	4	5	6	7	8	9	10	11	12
username
herbietime	51.9111	24.66258	12.63125	6.38384	2.817	1.08655	0.38014	0.10242	0.02192	0.003	0.0002	0.0
thezirconisdragon	20.74697	21.71155	21.16925	19.10464	9.08055	4.32684	2.1187	1.04144	0.44943	0.18354	0.06032	0.00677
pacc	13.01049	23.61512	25.87268	20.1729	9.52164	4.39508	2.00778	0.89029	0.34619	0.1285	0.03618	0.00315
alecwilson	12.09358	23.0945	24.23388	20.01998	11.23941	5.56264	2.43843	0.95928	0.2852	0.06519	0.00771	0.0002
empireyikesback	1.0034	3.00327	6.52351	12.75076	22.15778	23.00439	15.51716	9.06495	4.43471	1.87408	0.59043	0.07556
therealfergus	0.79027	2.3105	5.24234	11.12273	22.32044	21.01218	16.03096	10.77066	6.111	3.01181	1.12416	0.15295
mackjyers21	0.2977	0.97803	2.39929	5.29663	10.24433	15.74398	20.06172	21.36204	12.66054	6.88986	3.34023	0.72565
burgertownthicnred	0.12441	0.50768	1.48201	3.74902	8.6338	15.94773	23.46878	22.12003	13.51781	7.05852	2.91124	0.47897
shakylegs	0.01832	0.08321	0.27895	0.79198	2.04288	4.28686	8.18694	14.86333	26.69906	23.35301	15.1467	4.24876
namebrant	0.0034	0.02944	0.13802	0.46325	1.36744	3.02059	5.91635	10.72327	19.10769	28.22535	23.15996	7.84524
tonygordzilla22	0.00036	0.00403	0.02825	0.14	0.54992	1.51888	3.61161	7.36419	14.46341	24.25927	39.04713	9.01295
black8yellownation	0.0	9e-05	0.00057	0.00427	0.02481	0.09428	0.26143	0.7381	1.90304	4.94787	14.57574	77.4498

Playoff Chances

This table aggregates the previous one into a more readable format. Each column is the percentage of simulations where each team placed better, equal, or worse than their actual ranking for the season. The last column in the percentage of simulations where they placed in the top six teams.

Here was can really see who got lucky and unlucky with the schedule.

• Pacc took first place, a 13% chance, but he had an 87% chance of placing worse than that.
• Namebrant took last place, a 7.8% chance, but he had a 92.2% chance of placing better (better luck next year Brant).
• The playoff teams were about as expected except for burgertownthicnred sliding into the playoffs with a 30.5% chance and kicking therealfergus to the losers bracket despite his 62.8% chance.

Rank	Username	Better	Equal	Worse	Playoff
1	pacc	0.00	13.01	86.99	96.59
2	thezirconisdragon	20.75	21.71	57.54	96.14
3	herbietime	76.57	12.63	10.80	99.49
4	alecwilson	59.42	20.02	20.56	96.24
5	empireyikesback	23.28	22.16	54.56	68.44
6	burgertownthicnred	14.50	15.95	69.56	30.44
7	therealfergus	62.80	16.03	21.17	62.80
8	mackjyers21	55.02	21.36	23.62	34.96
9	shakylegs	30.55	26.70	42.75	7.50
10	tonygordzilla22	27.68	24.26	48.06	2.24
11	black8yellownation	7.97	14.58	77.45	0.12
12	namebrant	92.15	7.85	0.00	5.02

For you visual minded guys, here’s a chart of the previous table:

Some Interesting Rankings

Here are some interesting rankings from all ten million simulations. The columns in these tables are given:

• The Chance >= column contains the percentage of simulations in which that team placed greater than or equal to their given ranking.
• The Playoff column contains the percentage of simulations in which that team made the playoffs

Most Common Ranking

The most common ranking order appeared 15,053 times:

Rank	Username	Chance >=	Playoff
1	herbietime	51.91110	99.49
2	thezirconisdragon	42.45852	96.14
3	alecwilson	59.42196	96.24
4	pacc	82.67119	96.59
5	therealfergus	41.78628	62.80
6	empireyikesback	68.44311	68.44
7	burgertownthicnred	53.91343	30.44
8	mackjyers21	76.38372	34.96
9	shakylegs	57.25153	7.50
10	namebrant	68.99480	5.02
11	tonygordzilla22	90.98705	2.24
12	black8yellownation	100.00000	0.12

Unlikely Top 3

In this ranking, mackjeyers, burgertownthicnred, and shakylegs take the top spots despite each having a less than one percent chance of doing so.

Rank	Username	Chance >=	Playoff
1	mackjyers21	0.29770	34.96
2	burgertownthicnred	0.63209	30.44
3	shakylegs	0.38048	7.50
4	herbietime	95.58877	99.49
5	alecwilson	90.68135	96.24
6	pacc	96.58791	96.59
7	thezirconisdragon	98.25850	96.14
8	therealfergus	89.60008	62.80
9	empireyikesback	97.45993	68.44
10	namebrant	68.99480	5.02
11	tonygordzilla22	90.98705	2.24
12	black8yellownation	100.00000	0.12

Lopsided Playoffs

Here, we have the bottom three teams in terms of playoff chances all making the playoffs.

Rank	Username	Chance >=	Playoff
1	herbietime	51.91110	99.49
2	pacc	36.62561	96.59
3	thezirconisdragon	63.62777	96.14
4	namebrant	0.63411	5.02
5	tonygordzilla22	0.72256	2.24
6	black8yellownation	0.12402	0.12
7	alecwilson	98.68242	96.24
8	empireyikesback	93.02522	68.44
9	burgertownthicnred	89.55127	30.44
10	therealfergus	98.72289	62.80
11	mackjyers21	99.27435	34.96
12	shakylegs	100.00000	7.50

End

We can see that no matter how good or bad your team is, you can still get incredibly lucky or unlucky with the season schedule. Let me know what you guys think about this analysis and if you want to see anything else.