Playoff Probabilities

Lady and Gents, I present to you a special blog post which you can read at your own leisure as you follow these glorious-or-frustrating football games this wonderful Sunday.  Warning: It's a long post, and there's a massive numbers geekout at the end, so reading it may require multiple attempts.

After 6 solid weeks of Fantasy play, we are essentially at the halfway point of the FF season.  The playoff picture is becoming more clear now, and as with any year, many developments, some expected (ugliness of Aaron's team due to autodraft, suspended players not playing, and the Panthers having no semblance of a running game, but still surviving much thanks to David Li's KB and being in a terrible division) while others not so much (the downfall of Jamaal and Megatron and the rise of DeMarco Murray), have unfolded.

With that said, here are a few observations from the season thus far:

• The top three teams in the league (Abraham, Jeff, Luke) have also scored the top three amount of points for.  Jeff is officially 2nd in the league, even though his team has the most points for thus far.  I think it's safe to say that these three teams have been the top three performers up to this point in the season, even if they haven't been the most consistent on a week-to-week basis (Luke).  My power rankings do not have Luke's team in the top 3 simply because his team has been feast-or-famine, and his RB situation is questionable, as are his WRs.  However, his team's performance has set him up nicely for playoff contention and a deep run with a 4-2 record and 3rd most in the points for category.

• The teams with the top two QBs in the league (Andrew Luck, Philip Rivers) also happen to be the top two teams in the league (Jeff, Abraham).

• The team with the best 3-combination-WRs in the league (Antonio Brown, Randall Cobb, Alshon Jeffery) also happens to be the top team in the league (Abraham).  I calculated this by ranking the players based on fantasy points scored, so Antonio Brown = 1 because he's scored the most points among WRs thus far, Randall Cobb = 5, Alshon Jeffery = 12.  Therefore, Abraham's WRs = 1 + 5 + 12 = 18.  The next best WR-combo is Steve Smith Sr. (3) + Mohamed Sanu (11) + Terrance Williams (15) = 29 from yours truly.  I don't think that's indicative of anything.  Third place goes to Jordy Nelson (2) + DeSean Jackson (10) + Emmanuel Sanders (23) = 35, all hailing from Eric's team - once again, doesn't appear to be indicative of much.  I do think it's significant, however, that Abraham has hands down the best-performing WRs in the league. 

• RB gets more interesting.  Justina has DeMarco, who is crushing it as the #1 RB, but her next best RB is Lamar Miller (14), giving her two best RBs a grand total of 15.  Who beats that?  Matt Forte (2) + Justin Forsett (8) = 10 for Jeff.  Marshawn Lynch (4) + Ahmad Bradshaw (7) = 11 for David Lin.  With Giovani Bernard (6) + Fred Jackson (11) = 17 coming up closely behind for David Li.  So Jeff wins the RB battle, and it shows in his record and points for.  Also keeps him, David Lin, David Li, and Justina at the top of my power rankings

• TE?  Gabs wins with Orange Julius.  Indicative of nothing, because the rest of his team has struggled.

• Kicker goes to Abraham with Stephen Gostkowski, but let's not kid ourselves with any sort of correlation there.

• Defense?  Philadelphia.  I think this is significant because they have scored a whopping 94 points, with the next best defense being Houston, which has scored 68.  Who owns Philadelphia Defense?  Chen San Jie aka Jeff.

• Therefore, it appears that if you can put together a team with top scorers in at least two positional categories, you have a good chance of domination in our league.  Cases in point: Jeff has Andrew Luck (#1 QB), Matt Forte + Justin Forsett (best-performing RB duo in the league thus far), and Philadelphia Defense (by far the best Defense).  Abraham has Philip Rivers (#2 QB), and Antonio Brown + Randall Cobb + Alshon Jeffery (by far the best-performing WRs in the league).  Oh, and the best kicker (Gostkowski).

• What about Luke's team?  How is he succeeding?  I'm of the opinion that he is winning by scrapping together players and hoping that they do well that week.  It's working the majority of the time, but consistency has been difficult to maintain.

• Granted, these numbers-converted-to-rankings aren't perfect, because they don't account perfectly for players who have had bye weeks and don't account for the disparity between, say, DeMarco Murray (#1 RB but with 122 points) and Matt Forte (#2 RB but with 93.5 points) - a 28-point difference - versus Matt Forte and Arian Foster (#3 RB but with 92.4 points) - a 1-point difference.  However, I think they are still telling to an extent.

What about Playoffs?

• Historically in our past 12-team leagues, a team that makes the playoffs has had no less than 6 wins.  Depending on how the other teams do, some years the number of wins went up to 7.  So I think it's safe to say that if a team is able to pull off 7 wins this season, they are guaranteed a spot in the playoffs.  Win 6 games, and you may or may not have a chance.

• Since I had some spare time, I decided to create a formula to calculate the chances of each team making the playoffs.  And thus begins the

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• These are the assumptions that I made (which may not be valid assumptions):
• If a team wins 7 games, they are in the playoffs.
• A team's past performance is indicative of how strong of a team they are, and that is also indicative of how well they will perform the remainder of the season.
• A team's strength of remaining schedule is based primarily on their opponents' past performance, and will influence how well the team will perform the remainder of the season.
• The amount of FAAB waiver wire money left for a team will influence, albeit not a significant amount, how well their team will perform the remainder of the season.

• With those assumptions, this is what I did:

• I calculated each team's current strength based on a method I previously posted about.  
• Essentially, if a team scored the highest points in a week, they are awarded 11 points for that week.  2nd highest scorer gets awarded 10 points, and so on.  The lowest scoring team gets 0 points.  What this translates to is that the team with the most points that week would have won 11 out of the 11 games that week, and hence gets a "power score" of 11.  2nd highest scoring team would have won 10 out of 11, and therefore gets a "power score" of 10, and so on.  The lowest scoring team would have obviously won 0 of the 11 games that week, and gets a "power score" of 0.
• I averaged these points over the span of the last 6 weeks, and that provided a number that is supposed to be indicative of how strong that team has been up until now.  Or what I've called each team's "power score."

• The green means that team won that week while the red means that team lost.
• As you can see, Jeff's team has performed the best overall the first 6 weeks, followed by Abraham and Luke. 
• These numbers are somewhat reflective of the total "points for" column in our league, with the exception of some teams (Duke, Gabs, Eric, Aaron).  However, I am of the opinion that the "power score" is a better indicator of strength of someone's team over what their "points for" is.  So just accept that.

• I then calculated how many games each team needed to win in order to get 7 wins by the end of the season.

• I calculated strength of remaining schedule by adding the "power scores" of all the teams that each team is playing the rest of this season.  For example, in Week 7, I'm playing Duke, and his team has a "power score" of 3.667.  In Week 8, I play Aaron, whose team has a "power score" of 3.5.  I add up all the scores for the remaining teams I'm up against, and I get my remaining strength of schedule.  The higher the strength of schedule number, the harder a team's remaining schedule is.

 

• As you can see, Luke has the hardest remaining schedule (he finishes the season playing David Li, Jeff, me, Abraham, and Justina), followed by Duke, then Aaron.  Jeff, me, and David Li have the easiest remaining schedule.

• I also took into consideration remaining FAAB waiver wire money.  This was a straightforward input.  My reasoning is that someone with $95 remaining is better off than someone with $0 left, because at least that person has options.  Whether that money is put to good use is another question, so I didn't value remaining FAAB waiver wire money that highly (see below)

• I took all these factors, placed weights on their relative importance (power score [~80%], strength of remaining schedule [~20%], and FAAB waiver wire money remaining [<1%]) and created a "probability factor," which sums up the chances of each team winning their remaining games.  
• In theory, each team has a 50% chance of winning any given game.  However, with the above factors, I would argue that Jeff has a much better chance of winning his remaining games than Aaron does, simply because Jeff has a more proven team and a much easier remaining schedule. 
• I could have calculated this for each remaining game, but that would have taken too much time, so I calculated an average "probability factor" for each team - one number that applies to all of that person's remaining games, not necessarily contingent upon the opponent (except for the fact that strength of remaining schedule was factored in to the probability factor).

• You can read the chart like this: "Tim's average chance of winning any given game of his remaining 7 games in the season is 54.27%."  As previously mentioned, in theory, that percentage should be 50%.  With the aforementioned factors taken into consideration, the percentages for each team is no longer 50%.

• I then calculated each team's chances of winning "x" remaining games (which equals however many games that person needs to win reach 7 wins for the season) based on the above "probability factor" and binomial probability formulas David Lin helped me find.

And the final results...

• As you can see, Abraham has a 99.22% chance of making the playoffs, largely because he already has won 5 games, so all he needs to do is win 2 of the remaining 7, and he's pretty much in.  That gives him a slight advantage at this point over Jeff, who only has 4 wins, even though Jeff has a better "power score" and a much easier remaining schedule.

• Other shoo-ins include Jeff (97.23%), Luke (86.45%), and David Lin (84.34%), all who have 4 wins under their belts.

• The middle of the pack is led by Justina (63.8%), followed by a tight race between me (59.27%) and David Li (59.13%), and rounded out by Duke (48.72%).  While Duke's team isn't strong (11th rank in power score) and has a tough remaining schedule (2nd hardest), he has already won 4 games, so his chances of making the playoffs are considerably better because of it, since he only needs to win 3 more of the last 7 games.  If he had only won 2 or 3 games, his chances would have been much lower.

• As far as the bottom-dwellers, there will be 4 teams that likely won't make the playoffs.  Probability says those teams will be Eric (9.88%), Gabs (7.99%), Andrew (1.78%) and Aaron (0.91%).

• The gap between the bottom 4 and the middle 4 seems huge (Duke's 48.72% to Eric's 9.88%), but I think that just shows the weakness of the bottom 4.  Eric and Gabs both have only 2 wins, which means they need to win 5 of the last 7 games to make playoffs.  They are also 8th and 10th, respectively, in terms of their power score.

And for curiosity's sake, what if we set the bar lower, and assumed a team only needed 6 wins to make the playoffs?  This is how the final chart would look:

Much better chances, overall.  But obviously, the chances relative to each other remain the same.  Abraham still has the best chance while Aaron has the worst.

Now, you have to remember that these are mid-season calculations.  Even after this week, these numbers will probably change.  And as I mentioned earlier, a lot of assumptions were made (Perhaps we will see a season where one or more 6-win teams make the playoffs?  Past performance doesn't always predict future behavior?).  However, this gives us a snapshot of how teams have done thus far and how they are predicted to do the rest of the season.

Some of you might be saying, "Oh, so all you're telling me with all these number gooblygook is that Eric, Gabs, Andrew, and Aaron probably won't make playoffs?  I could have told you that just by looking at the standings!"  Well then, fine.  But now you have solid numbers to back that thang up.  And I have felt accomplished.

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