LIVE SUPER BOWL PROBABILITIES
The chances each remaining team will make it to the SB and win it are tracked live as each game progresses. The probabilities take into account the current game's live win probability, weighted by pre-game estimates of team strength and home field advantage. It also accounts for all future permutations of remaining games, weighted according to their likelihood of occurring. Those future games are also weighted by team-strength and home field according to seed.
I started out yesterday directly computing the probabilities, but because of the dynamic match-up scenarios that occur due to seeding rules, I decided to make things much easier on myself and create a Monte Carlo model. For example, who Denver plays depends on who wins the wildcard games, and who gets home field for the AFC conference championship game depends on who wins all the other games, and so on. Direct computation gets really hairy really quickly, and it's too prone to error to do it in a rush. So it was much easier to simulate a single iteration of the playoff tournament, then rerun it with weighted random outcomes n-thousand times. The proportion of times when a team makes it to the SB becomes their probability of making it to February.
The drawback is a small degree of imprecision. The estimates will occasionally dither by +/-0.01 just due to sample error. But that's the trade off I made to make sure I got it right.
The widget updates automatically every 30 seconds which is probably more often than necessary, but why not?
Since yesterday I've added SB outcome probabilities, and I may add a column for the probability for each team of making past the division round if I get around to it.
The NFC Champion odds are wiggling around a little bit each update, even though the only game being played right now is an AFC game.
ReplyDeleteWhat variables are changing the NFC probabilities?
(I've seen SEA's probability wiggle between 0.48 and 0.54, for example.)
Because the nfc team will have to play an afc team to win the superbowl. Whichever afc team comes out has a huge impact on nfc super bowl odds.
DeleteThese are their odds of winning the conference, not the Super Bowl.
ReplyDeleteWhere did Philly go?
ReplyDeleteI don't know! Trying to find the bug now. Time-pressure live debugging should be an olympic sport.
ReplyDeleteFixed it!
ReplyDeleteCan you post live Division and Conference winner odds?
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteNot sure how a 53% win probability for San Francisco translates into a lower SB-appearance likelihood than GB. Unlike SD/Cincy, there's no difference in the difficulty of their respective playoff roads after a win.
ReplyDeletePaul, I agree. I'm pretty sure that's just error in the model. Unlike the playoff odds which only relied on 1 set of potential matchups, I'm using a Monte Carlo model for this. It's running 10k iterations, which is why the numbers can dither +/- .01.
ReplyDeletePaul Thomas: that might be a simple transposition of the final results. 0.08/0.09 = 0.47/0.53, to within rounding errors.
ReplyDeleteFigured it out. I gave GB a boost to their NYPA b/c so much of it was w/o Rodgers. Right now their GWP is .60 rather than .54, which gives them a small edge over SF tomorrow.
ReplyDelete"Not sure how a 53% win probability for San Francisco translates into a lower SB-appearance likelihood than GB."
ReplyDelete53 to 47 is so close as to not matter. According to this site, that is well below the threshold of home field advantage. perhaps GB has better "WP" in the later games than SF does. however, i agree, it does have the unpleasant result of the less favored team being more favored.
"Figured it out. I gave GB a boost to their NYPA b/c so much of it was w/o Rodgers. Right now their GWP is .60 rather than .54, which gives them a small edge over SF tomorrow."
ReplyDeleteyikes. that sounds subjective.
It's based on the analysis I did for my NYT article 3 wks ago. I'm going to re-examine it tomorrow w/ more data and it will probably incr further.
ReplyDeleteThe probabilities must be pretty shaky to give New Orleans a 22% chance of beating Seattle on the road and then winning a second road game...while Carolina has only a 14% chance of winning at home against GB/SF and then winning an undetermined second game.
ReplyDeleteI've got NO as a measurably stronger threat to SEA than CAR. HFA is baked in. Free to disagree, but they are far, far from "pretty shaky."
ReplyDeleteBrian,
ReplyDeleteI noticed you said you were using a Monte Carlo calculation for this, but wouldn't it be more efficient to simply calculate the analytical solution here using recursion? Their are only 2^11 = 2,048 possible outcomes from the outset of the playoffs, it seems like a Monte Carlo simulation may be overkill for this many outcomes. Also, this way you wouldn't get any of that +/- 0.1 wiggling.
Just a thought.
I really like the new tools, great work!
amp, I did that for the playoff chances last week and it worked fine b/c there was only 1 layer of games. Here there are 4 layers (rounds to the tournament) and due to the complications of HFA caused by seeding, the MC approach was much simpler and far less prone to error. But if I had more time I'd go with direct computation.
ReplyDeleteI think there is a bug - GB is give better odds than SF now and SF is winning... (17:31 EST)
ReplyDeletedo you have GB and SF reversed? SF chances dropped throughout the first quarter while SF game probability improved.
ReplyDeleteI will third the suggestion that GB and SF might be reversed. The in-game probability shifted as expected when GB scored that TD. This probably shifted towards SF (around 5:45 EST).
ReplyDeleteWill check.
ReplyDeleteYou guys were right. Thanks. Fixed it just after halftime.
ReplyDeleteI anxiously await the "GB should give up the touchdown" article.
ReplyDeleteI don't think they could. GB was definitely in the chokehold zone, but the way the clock and field position worked, they were near the border of indifference. If you throw in the conditions and the fact that chance that SF doesn't fall for it (kneeling at the 1), then the right call is to force the stop and hope for an unsuccessful FG.
ReplyDeleteWill the team strengths be updated with the results of this weekend's games, or will they be based on the final efficiency ratings?
ReplyDeleteThey get updated, but at this point in the season things don't move much.
ReplyDeleteNE seems to be left out right now. Not that I mind :)
ReplyDeleteJust call your mortgage broker and put everything you have on Denver ML, because the so-called "powers that be" will never let Pete Carroll win a super bowl. "Why's that" you ask? Because he is a 9\11 truther, and they will not put up with his questioning of the official version. Watch, Denver will win it on some extremely controversial call. If Seattle is up in this game, you can bet some 'funny' calls will not go their way. Just watch, and pay attention.
ReplyDelete