# Scheduling and Relative Strength

Following on from league schedule chat, I got thinking about the level of luck involved in the schedule and what the chances were of teams getting different amount of wins, considering the number of points they scored each week. It’s important to understand, of course, that just because a team scored a lot of points, it doesn’t mean they could have been consistent winners. If they scored massive amounts in just 3 weeks and at or below average the rest of the season they could look like big time Charlies when actually they were … erm … small time Freddies? Also, some weeks the entire league scored highly so a high score is merely par (weeks 8, 10 and 13 all featured average team scores of 190+), while other weeks the points were low so a high score had the chance to dominate (week 2 had an average score of only 158.7).

The point is that it definitely matters when you score those points, as well as how many of them you score.

So given I have the full weekly scoring available I decided to run some scenarios. In fact, practically every scenario. Sort of. There are some weakness which I am going to acknowledge up front.

So what I did was rank everyone’s score from first to last in the league in each week. From this you can derive the chance of winning in any given week. If you top scored you had a 100% chance of winning. If you were the 5th top scorer you had a 55.55% chance of winning (you could beat 5 teams out of 9 – 5/9 = 55.55%) and thus a 44.44% chance of losing. And so on.

By multiplying your chance of winning in week 1 by your chance of winning in week 2 and so on we can work out the chance of you winning every single game. If we create a list of all possible scenarios (ie every combination of win or lose for every week of the season), we can then work out the likelihood of each scenario. Add up all the scenarios that result in 7 wins and you have the % chance of that outcome.

The caveats:

1. In week 10 Dyna Hard and Kelkowski had the same score. They didn’t play each other so there was no tie, but this would add a tie into the possible outcomes. This would change the number of scenarios across a 13 week season from 8,192 to 1,594,323. To avoid doing this I have knocked Dyna Hard down by 0.05 points so there’s no tie that week. This means that I slightly under-estimate Dyna Hard’s position in the end results and slightly over-estimate Kelkowski’s, but the difference is minimal.
2. I have not done this based on feasible schedules that fit with our ‘play your division twice, the other division once’ rules. This is purely done on the basis of how many teams could you beat each week. This means that while it may say a team has a small percentage chance of winning every week or losing every week, this may not actually be the case because that may rely on playing The Sadness or Kelkowski every week.

However, what this does do is provide an analysis of relative strength across the division as well as estimate the role schedule luck played in each team’s performance.

So first off I want to walk you through an example. East Flanders had a 0.13% chance of losing all 13 games in the season. The table below shows the ranking of each weekly points score for the team, the chance of losing in that individual week, and the cumulative chance of losing each week, one after the other:

 Score Rank Chance of Losing Cumulative Chance of Losing Week 1 6 55.56% 55.56% Week 2 4 33.33% 18.52% Week 3 10 100.00% 18.52% Week 4 8 77.78% 14.40% Week 5 8 77.78% 11.20% Week 6 7 66.67% 7.47% Week 7 10 100.00% 7.47% Week 8 8 77.78% 5.81% Week 9 9 88.89% 5.16% Week 10 7 66.67% 3.44% Week 11 8 77.78% 2.68% Week 12 2 11.11% 0.30% Week 13 5 44.44% 0.13%

A decent start and end to the season didn’t cover up a pretty terrible middle.

So doing this for every win/loss combination for every team gives the following table of likely win totals:

The figures highlighted in bold are the percentage chance the team had of recording the number of victories they actually did record. So Champions of the Sun ended up with 6 wins and there was a 24.75% chance of that happening based on their weekly scores (accepting the caveats listed earlier), while Dyna Hard had just a 9.86% likelihood of getting exactly 5 wins, as they managed across the year.

So for all bar two teams, the chances of ending with the record they ended with was between 22.52% and 29.19%, though only 3 teams ended with the record they were most likely to.

So the next stage is to look at the cumulative win chances – ie adding the percentage chances up as you move along. So each column in the table below shows the chances of winning between zero and n games (n being the number at the top of the column).

What this is saying is that the higher the cumulative number the luckier you would need to be to get that number of victories, while approximately 50% is where you would expect to be. So in 95.54% of scenarios Here Comes The Brees would win 8 or fewer games and only in 4.46% of scenarios would they win over 8 games. As we can see, there was only a 13.60% chance that Dyna Hard would win 5 or fewer games.

We can also reverse this and produce a table which shows the chances of reaching a minimum number of wins:

This shows that The Brees had only a 14.66% chance of getting at least the 8 wins they managed, while Dyna Hard were as close to guaranteed as you could reasonably expect to get to hit the 5 wins they did, with over a 96% chance of reaching that level. The Dynasty of Sadness were the second luckiest franchise, with only a 35% chance of getting 5 wins, although they had a better chance of getting 4 wins than East Flanders, while the Champions of the Sun were very lunlucky to register just 6 wins.

So what can we do with all this data? Well, we can use it to create an expected win number. By looking at where the 50% position falls in the above 2 cumulative tables and taking the average of the 2 positions we can see the expected number of wins for each team based on their performance.

 Team Expected Wins Exp. Win Rank Actual Wins Diff. % Difference Kelkowski Don’t Play By No Dyna Rules 8.59 1 8 -0.59 -4.52% Dynasore Losers 8.34 2 8 -0.34 -2.61% DynaForOne Firebirds 7.33 3 7 -0.33 -2.50% Dyna Hard 7.12 4 5 -2.12 -16.27% Champions of the Sun 6.89 5 6 -0.89 -6.88% Tamworth Two 6.43 6 6 -0.43 -3.34% Dynablaster Bombermen 6.11 7 7 0.89 6.88% Here Comes The Brees 5.88 8 8 2.12 16.30% East Flanders Dungeoneers 4.18 9 5 0.82 6.31% The 4th Dynmension: Dynasty of Sadness 4.12 10 5 0.88 6.74%

So most teams were within 1 win of where they would be expected to end up, but Dyna Hard and Here Come The Brees were both over 2 wins difference from what their week to week performance merited.

All told I am pleasantly surprised at how little difference the schedule made for most people. This may be a case of there being so few games it’s harder to separate from the mean, but then again, 20% of the league – a not insignificant proportion – were over 2 games different from their expected level.

What can be said at this point is that we don’t really know if this is a problem or not. Will there always be teams who get very lucky or unlucky or was 2014 an anomaly? Should we look to provide a degree of stabilisation to try to get the best performing teams over the course of the season into the playoffs? Or should we embrace randomness?

Kommish Komment Korner (again)

The fact that the match-ups, in a randomly assigned order, can make a large difference to the outcome of the season – something beyond the control of the GM – seems an unfair punishment (or reward) and if something can be done that removes an element of that, while maintaining the excitement of head-to-head match-ups, my view is it should be included.

What we have is not broken, but there are a few cracks in the facade and it would be nice to address those so that we have a league which is both fun and robust. The magic of the cup will remain, regardless, in the playoff stage. What the regular season should at least try to do is ensure that the best teams end up in the playoffs while the worst teams get the best picks in the draft in order to better themselves and make themselves more competitive. In 2014 the playoffs were 3/4 right in that regard, but it’s not as though the 4th part of that equation was a borderline case. Had Dyna Hard come 5th, just behind Champions of the Sun, the issue wouldn’t have been a talking point (and I realise I am the only one talking about it really so you may not consider it one anyway). But I think it is tough to argue that Dyna Hard merit the first pick of the draft ahead of DoS and East Flanders.

I’m not suggesting a revolution, I’m suggesting evolution. The league is one year old and we knew we wouldn’t get things right the first time. We need to adapt to make the league as good and as fair as possible. I don’t want playoffs to be decided based on all-play or total points or anything. We all put in a lot of time and effort and it is better that we have a system that rewards that time and effort and, where appropriate, skill as best as possible.

This won’t change for 2015 and the above analysis will be repeated after the 2015 season to see how different the league was from actual performance. There will then be a vote sometime in the new year about whether we should change the schedule and/or ranking system for teams. Cases will be made and, whatever the outcome, we will move forward, older and allegedly wiser.