Playoff Odds

[Lefty Specialist]

Centerfield wrote: Lefty Specialist wrote: Plus, the Phils will probably be pitching a 'bullpen game' on Friday. Why do you say that? I thought they had that guy Asher lined up to pitch. He was pretty good in the early on against the Mets last week.

GKR said that originally they were going to pitch Asher on Friday and have the 'bullpen game' on Saturday. But then they moved Saturday's game to Fox (because of the keen national interest in the Phillies). Pete Mackanin didn't want to be an embarrassment by throwing 9 innings of bullpen on a national broadcast, so he'll probably pitch Asher on Saturday and strike the match on his bullpen game on Friday instead.

[Centerfield]

That is a terrific idea. Push back the capable starting pitcher and burn the bullpen in the first game of the series. Well played Philly.

[Lefty Specialist]

Centerfield wrote: That is a terrific idea. Push back the capable starting pitcher and burn the bullpen in the first game of the series. Well played Philly.

Well, they'll be resting from Monday on anyway.

[nymr83]

Lefty Specialist wrote: Centerfield wrote: That is a terrific idea. Push back the capable starting pitcher and burn the bullpen in the first game of the series. Well played Philly. Well, they'll be resting from Monday on anyway.

a "bullpen game" against a contender the last weekend of the season? that is an embarassment whether or not it is nationally broadcast.

[Frayed Knot]

It was supposed to be rookie Jake Thompson's start but they've opted to shut him down for innings limits. They had previously DL'd several other of their young guns (Nola, Eflin), had just one day off over the last 13 days of the season, and so essentially find themselves with just two rested and ready starters to cover the final three days.
Not an ideal situation, but hardly a big crime either.

[Frayed Knot]

OK, so our odds took bit of a hit last night with the double out-of-town wins (why couldn't one of them have just Tied!! like the Cubs & Pirates?!?).
The same eight scenarios still exist -- two outright misses plus six ties of some sort -- for us NOT clinching a free and clear WC spot this weekend, but seeing as how the overall number of possibilities have gone down and the ones that disappeared and are no longer possible (Cards and/or Giants losing 4 straight!) were all good ones for us, the chance of one of those eight non-clinching situations showing up got a little larger.

There are now 64 combinations still possible (4 x 4 x 4) and 56 of them get us in (87.5%) although weighting the outcomes to reflect that 2-1 or 1-2 splits are more likely for all the teams than are 3-0 or 0-3 sweeps puts the odds at:
Eliminated by Sunday = 0.78% -- (Mets get swept while Cards win 3 + Giants win 2, or Mets get swept while Cards win 3 + Giants win 3)
2-Way Tie w/StL = 2.93%
2-Way Tie w/SFG = 0.59%
3-Way Tie = 4.10%
METS WIN!!! = 91.6%

BP says 96.5% - which is probably where it should be if you figure 91.6% plus the odds of surviving any two or three way play-in tussles.

[Frayed Knot]

So did we ever establish how the tie is broken if we tie the Cardinals for the two WC slots?
There's one and only one combination in which that situation can come up (out of a possible 27): if we lose both remaining games, the Giants lose both of theirs, and the Cardinals win twice.
Those outcomes would leave us and the Cards tied at 86 wins with Giants on the outside looking in with 85. There'd be no play-in game at that point but I'm not sure of the tie-breaking procedure to determine who's #1, who's #2 and therefore where Wednesday's game is to be played.


So aside from that, like I said there are 27 remaining combinations of outcomes (3 x 3 x 3)
- We wind up in the #1 WC slot in 22 of them, 20 of them free and clear of both teams plus two others where we're tied w/the Giants for slot #1 which is the same as winning outright since we hold the tie-breaker. ODDS = 89.07%
- In two other cases we wind up with WC #2 all to ourselves: Mets lose twice + Giants win twice + Cards either lose once or lose twice. ODDS = 4.69%
- There's the one case mentioned above where we tie with the Cards for WC #1 with SF out of it: ODDS = 1.56%

So that's 25 of the 27 cases where we're assured of playing one game for the right to meet the Cubs. TOTAL ODDS = 95.32%

That leaves the two we don't want to see where we'll be forced into a Monday play-in or maybe even a Monday/Tuesday play-in:
- Mets lose both, Giants win both, Cards win both: This puts us in a play-in vs StL for WC #2. ODDS = 1.56%
OR
- Mets lose both, Giants win once, Cards win both: that outcome throws us all into a 3-way tie and multiple play-in games which I don't even know how they'd be set up. ODDS = 3.13%

[Benjamin Grimm]

The Cardinals have the home field over the Mets because the next tiebreaker after head-to-head is record within the division.

The Mets, so far, are 39-35 against N.L. East teams, and the Cardinals are 40-34 against the Central. If the Mets end up tied with the Cardinals, it would mean that the Mets ended up 39-37 and the Cardinals 42-34.

So if the Mets have to play the Cardinals on Monday to break a two-team tie it will be in St. Louis.

[Frayed Knot]

OK, so that makes it:
WC #1 = 89.07%
WC #2 = 6.25%
2-Way Tie w/Cards = 1.56%
3-Way Tie = 3.13%


BP puts us in at 98%, which, if you add my WC #1 odds to WC #2 odds then give us a 50/50 shot at prevailing in a 2-Way play-in and a 1/3 shot at surviving a 3-Way play-in
89.07 + 6.25 + 0.78 + 1.565 = 97.665

I suspect BP is checking their work against mine but I don't know that for sure.

Edited October 1, 2016 by Guest

[Benjamin Grimm]

And then, for the three-team tie, there's this. I hope I'm interpreting everything correctly.

• If Club 1 and 2 have identical records against one another, but each has a better record against Club 3, then Clubs 1 and 2 would follow the two-Club tiebreak rules to break their tie to pick the first designation.

The Mets and Cardinals are both 4-3 against the Giants, and 3-3 against each other, so in this scenario the Giants are Club 3. Since the Cardinals win the tiebreaker against the Mets, they'd be Club 1.

Three-Club Tie for Two Wild Card Spots: After Clubs have been assigned their A, B and C designations, Club A would host Club B. The winner of the game would be declared one Wild Card winner. Club C would then host the loser of the game between Club A and Club B to determine the second Wild Card Club.

So the Cardinals are Club A, the Mets are Club B, and the Giants are Club C. The Mets would play the Cardinals on Monday in St. Louis. If they win, they get Tuesday off while the Giants and Cardinals play each other. If the Cardinals win, the Mets stay in St. Louis to play Wednesday's Wild Card game. If the Giants win, both teams fly to New York to play Wednesday's game at Citi Field.

If the Mets lose Monday's game, they're not eliminated. They'd go to San Francisco* to play the Giants on Tuesday, and if they win they'd fly back to St. Louis to play Wednesday's Wild Card game.

* I would have guessed that this game would be played in New York, but the rule does say that Club C would be the host.

[Frayed Knot]

Benjamin Grimm wrote: If the Mets lose Monday's game, they're not eliminated. They'd go to San Francisco* to play the Giants on Tuesday, and if they win they'd fly back to St. Louis to play Wednesday's Wild Card game. * I would have guessed that this game would be played in New York, but the rule does say that Club C would be the host.

I guess that's based on the idea that the only club who doesn't get the chance to lose and still survive, SF in this case, should have that game at home and also not have to suffer the logistical nightmare of taking a last-minute (and possibly cross-country) flight only after the results of the first game are known for a game the next day. The loser of play-in game #1 at least knows where they're headed if/when they lose.

[Gwreck]

[crossout:27o17c0d]In the scenario where 3 teams tie for 2 wild card slots, "Club B" is the preferred designation, because you get two chances to make the wild card game. Yes, both are on the road, but it's far better to have two chances than one.

I would expect the Cardinals to be "Club B" and for the Mets to be "Club A" if it came to a 3-team tiebreak.

The Mets would host the Cardinals in a tie-breaker game on Monday. If the Mets win that game, they host the Wild-Card game on Wednesday.[/crossout:27o17c0d]

Nevermind

Edited October 1, 2016 by Guest

[Benjamin Grimm]

Don't both Club A and Club B get two chances? It's only Club C that's limited to one chance, because the loser of A vs. B will always go on to play C.

[Gwreck]

Ah, I see now. Club C faces EITHER Club A or B. It is not a guarantee that they face Club B.

[Chad ochoseis]

So aside from that, like I said there are 27 remaining combinations of outcomes (3 x 3 x 3) - We wind up in the #1 WC slot in 22 of them, 20 of them free and clear of both teams plus two others where we're tied w/the Giants for slot #1 which is the same as winning outright since we hold the tie-breaker. ODDS = 89.07% - In two other cases we wind up with WC #2 all to ourselves: Mets lose twice + Giants win twice + Cards either lose once or lose twice. ODDS = 4.69% - There's the one case mentioned above where we tie with the Cards for WC #1 with SF out of it: ODDS = 1.56% So that's 25 of the 27 cases where we're assured of playing one game for the right to meet the Cubs. TOTAL ODDS = 95.32% That leaves the two we don't want to see where we'll be forced into a Monday play-in or maybe even a Monday/Tuesday play-in: - Mets lose both, Giants win both, Cards win both: This puts us in a play-in vs StL for WC #2. ODDS = 1.56% OR - Mets lose both, Giants win once, Cards win both: that outcome throws us all into a 3-way tie and multiple play-in games which I don't even know how they'd be set up. ODDS = 3.13%

Subtle error here in the calc - assuming 50% probability of a win of any given game, each team has a 25% likelihood of winning 0 games, a 50% likelihood of winning 1, and a 25% likelihood of winning 2. The calc above doesn't take into account that a team is twice as likely to win exactly one game than zero or two.

There are four possible outcomes for each team - win none (one outcome), win one (two outcomes), or win two (one outcome). So 4^3 = 64 outcomes in total.

The only outcomes under which the Mets don't win the wild card are these:

Cards win 2, Mets win 0, Giants win 1. 2 out of 64 ways that this can happen (1 way for the Cards to win 2 * 1 way for the Mets to win 0 * 2 ways for the Giants to win 1). If this happens, there's a 3-way tie [crossout]and the Mets still have only a 1/3 probability of not winning a wild card. So the probability of Mets losing the WC this way is (2/64)*(1/3) = 2/192[/crossout]

OE - in a 3 way tie, the Mets have a 1/4 probability of not winning a WC, because of the way the tiebreaker works. So prob of Mets losing this way is (2/64)*(1/4) = 2/256

Cards win 2, Mets win 0, Giants win 2. Only one way that this can happen, and it leads to the Mets and Cards tying for WC2, so there's still only a 1/2 probability that the Mets lose the WC even if it were to happen. So the probability of the Mets losing the WC this way is (1/64)*(1/2) = 1/128.

The outcomes are mutually exclusive, so you can add them. [crossout]2/192[/crossout] 2/256 + 1/128 = [crossout]7/384[/crossout] 1/64 probability that the Mets don't get the WC.

So there's a [crossout]377/384 = 98.2%[/crossout] 63/64 = 98.4% probability that the Mets do get the WC. I'm not motivated enough to figure out the probabilities of WC1 and WC2.

The real probability is much higher, of course, because of strength of opponents (also, the Dodgers still have something to play for, and the Pirates and Phillies don't).

[Frayed Knot]

Chad Ochoseis wrote: Subtle error here in the calc - assuming 50% probability of a win of any given game, each team has a 25% likelihood of winning 0 games, a 50% likelihood of winning 1, and a 25% likelihood of winning 2. The calc above doesn't take into account that a team is twice as likely to win exactly one game than zero or two. There are four possible outcomes for each team - win none (one outcome), win one (two outcomes), or win two (one outcome). So 4^3 = 64 outcomes in total.

I took those into consideration in my calculations. Rather than treating a 1-1 finish as two different outcomes I counted it as one but with twice the likelihood of happening as compared to either 2-0 or 0-2.

And, yes, the 3-way playoff outcome is more complicated that I stated. I actually should have given the Mets a 2 of 3 shot at coming out of it since 2 of the 3 teams will survive but, like you said, it's not that simple either.

[ashie62]

Alot of sliderules are breaking.

I think the Mets are guaranteed a game Monday. Thats all I got. I'm stumped.

[Frayed Knot]

Odds are 100% of a game a CitiField on Wednesday.

[Chad ochoseis]

Frayed Knot wrote: Odds are 100% of a game a CitiField on Wednesday.

One minute ahead of me! This has been a fun thread for those of us who know more about math than baseball.

[Frayed Knot]

Eight possibilities left and half of them will disappear within the next three hours or so.


If Cardinals [u:6kwfayzu]Lose[/u:6kwfayzu] on Sunday AND ...
- Giants Win Saturday + Win Sunday -- SF is WC #2
- Giants Win Saturday + Lose Sunday -- SF is WC #2
- Giants Lose Saturday + Win Sunday -- SF is WC #2
- Giants lose both days = Tie for WC #2


If Cardinals [u:6kwfayzu]Win[/u:6kwfayzu] on Sunday AND ...
- Giants Win Saturday + Win Sunday -- SF is WC #2
- Giants Win Saturday + Lose Sunday -- Tie for WC #2
- Giants Lose Saturday + Win Sunday -- Tie for WC #2
- Giants Lose both days -- StL is WC #2



Giants as WC = 50.0 %
Cards as WC = 12.5 %
Tie for WC = 37.5 %




C'MON TIE!!!!

[Frayed Knot]

And then there were four ... and only one causes a tie.

Giants Win + Cards Win = Giants as #2 WC
Giants Win + Cards Lose = Giants as #2 WC
Giants Lose + Cards Lose = Giants as #2 WC
Giants Lose + Cards Win = Monday Play-in Game for #2 WC

So it's around an 87.5% shot that we get the Giants and 12.5% that we get a Wednesday visit from the Cardinals - unless you have reason to suspect that one team has a notable advantage over another in either of tomorrow's two games or in a potential Monday play-in.

[Benjamin Grimm]

And the Cardinals would be the home team if there's a Monday game, because of their 4-3 record against the Giants.