Probabilistic Standings Simulations – Mixed Auction LABR

Introduction

Well, we are down to the final week of fantasy baseball. After a short 60 game season in 2020, we are blessed to be approaching game 162 here in 2021!

We here at RotoGraphs, are hoping that you are right in the thick of the competition for your league’s fantasy championship title. For me – I am right in the middle of an intense battle with one of the legends of rotisserie baseball, Ron Shandler, as well as our own Jeff Zimmerman.

The league that I am referring to is the Mixed Auction LABR league. I was one this division of LABR’s inaugural members back in 2020.

Above is a photograph of some of the participants of the live 2020 auction draft from Tampa, Florida. Due to COVID, this year’s draft was held online. LABR is one of the longest running (if not THE longest currently running) expert leagues of rotisserie baseball. It is an honor simply to be invited to compete.

The Mixed auction LABR league is a very standard 12-team 5×5 rotisserie league. We use the standard scoring categories (R, RBI, HR, SB, BA, W, K, SV, ERA, WHIP), and standard rosters (14 B, 9 P). Scoring periods are weekly, trading is allowed, and the initial draft is of the auction variety. Last year, I went into great detail recapping my draft – a two-part article that can be found here and here.

As many of you might already know, as a risk management actuary – my day job consists of running simulation models to recommend purchasing decisions to the upper management of my company. I simulate possible fires, hurricanes, medical malpractice claims, and other liabilities that we may be on the hook for.

Borrowing several actuarial methods, I adapted some of these models in order to develop a proprietary in-season fantasy baseball tool. It is a probabilistic final standings simulator. Using the current league accumulated standings, a source of projected ROS statistics, a volatility and a correlation model – I run 4000 iterations of what might happen for the remainder of the season.

Analyzing these 4k sims allows me to generate associated probabilities for winning the league, finishing in 2^nd place, etc. The model also directs me to the categories that need the most attention, so that I can maximize in-season waiver wire pickups. It can also assist with finding possible trades.

In today’s article, rather than diving into the math behind the probabilistic simulation tool’s methodology – I will introduce the reader to many of the resulting output charts and graphs. Plus, in using the Mixed Auction LABR league as the example, it will provide us with an update on my chances for winning this prestigious expert league in 2021.

Current Standings

Below are the league standings as of the morning of September 27, 2021:

At the start of game play this week, I am currently trailing Ron Shandler for the league lead by 2.5 points. Jeff Zimmerman trails by 5.5 points.

Simulated Standings

For today’s probabilistic simulation, I use the following rest of season projections:

• Derek Carty’s THE BAT X for hitters
• Derek Carty’s THE BAT for most pitching statistics
• Jared Cross’s Steamer for projected saves

For each of the 4000 iterations of model, the accumulated statistics to date are combined with a randomly generated possible final week of the 2021 season. For some simulations, a team may generate a large number of homers. Sometimes few round-trippers emerge. On average, the accumulated stats for week 27 will match the input projections.

I have summarized the resulting final outcomes in the table below. The first two columns add projected statistics without accounting for process variance of the simulation. The rest of the table includes it.

Here is where variance makes all of the difference. If every team exactly generated its projected/expected results, Ron Shandler would be in line to win the league by a single point.

However, when considering that some teams have good weeks while others had bad ones – despite my current 2^nd place standing – the model indicates that I have a 59% chance to win the league. I am actually the favorite! Unfortunately, Jeff stands to only have about a 2% chance (1 in 59 to be more exact) of winning LABR.

Below is the full listing of the LABR fantasy teams with their probabilities of final place standing:

You can see above that the top 3 teams are essentially locked into the top 3 slots. Ryan Hallam will assuredly finish in 10^th place. A number of teams in the middle can either rise or drop some 3 spots in the standings.

Next is the resulting point density chart for the top five teams in the league. It gives the probabilities that each team will finish with a specific number of fantasy points. Ron Shandler has about a 40% chance of ending up between 86-87 points, while I have about the same chance to achieve a score of 87-88. In one terrible simulation for me, I fall all the way to 78 points, but on the upside – I can possibly reach 94.

Finally, let’s take a closer look at the categories at risk for each of the top 3 teams:

For Ron, there is a large gradient in stolen bases. Ron could potentially lose as many as 3 points in the category. However, in ERA – Ron can potentially gain 4 points in the final week. He is point-locked into a number of categories – including RBI, W and SV.

Jeff’s best chance of gaining point lies in saves and ERA. That may explain the fact that he had been activating 6 relievers in each of the past few weeks.

My largest concerns are the runs and batting average categories. I can quite easily lose two points in runs. There is a wide range of outcomes for BA. As HRs & RBIs are already settled (near 0% chance to move), this influenced my decision to start Isaiah Kiner-Falefa for the final two weeks over the more valuable Kyle Seager. With the opportunity to gain two points in wins, I decided to activate nine starting pitchers, leaving all of my excellent closers (Edwin Diaz and Emmanuel Clase) on the bench for the ultimate week.

As a side note – notice that the ratio categories are some of the most volatile ones above. While most fantasy players believe that counting stat categories are easier to gain ground upon [late in the season], it isn’t true. I would argue that ratio categories most often are the ones with larger point gradients.

Conclusion

Most if not all of your final lineup decisions in rotisserie leagues will be made with regard to the categories. You at home are undoubtedly doing a very similar analysis for each of your roto squads, without applying exact probabilities to it.

Today’s probabilistic simulation was meant to reinforce this concept. Look carefully at your rosters and risk-assess the potential categorical tradeoffs in your lineup decisions. This will be the most effective way to secure your fantasy titles – both this year, and in years to come.

In addition, I desire feedback from you. Which charts/graphs would you find most helpful on a regular basis? What other types of applications in fantasy would this analysis be of assistance to you? Your comments and suggestions are deeply helpful.

Best of luck in the final week of 2021!