An Alternative Universe in Which the Mets Made the Playoffs

Early last week, I wrote about whether the Nationals should rest Max Scherzer or maximize their chances of retaining home field advantage in the NL Wild Card game. Well, joke is on me, because they easily did both.

With that question centering around the Nationals' top tier pitching options, my esteemed colleague (a suffering Mets fan) posed this: would the Mets be the rare underdog that actually would have a better chance against the Nationals in a 5-game series, as opposed to a one game playoff?

Generally, an underdog wants a shorter time frame to try to pull off the upset - less time equals more randomness, and less of a chance for talent to win out. But the Mets are one of the few teams in baseball that could match the Nationals' pitching staff, with three aces in the top 10 of NL pitcher WAR (plus the NL Rookie of the Year, and still didn't make the playoffs).

So consider an alternative reality in which the Mets make the playoffs, and face the following proposition: they have to face the Nationals in a one game playoff, or a full five game NLDS (in both cases Washington has home field advantage).

Do you want to roll the dice on one game, with your best pitcher (Jacob DeGrom) up against their's (Scherzer)? Or would you rather have your lineup of DeGrom (#1 in NL pitcher WAR), Wheeler (#7), and Syndergaard (#10) go up against Scherzer (#2), Strasburg (#3), and Corbin (#6)?

Over 10,000 simulations, the Nationals win 61.8% of the time in the one game playoff (this also serves as Game 1 of the NLDS). Here are the game-by-game probabilities over a five game series:

Game	Home	Away	Home Pitcher	Away Pitcher	WSN Win Prob	NYM Win Prob
Game 1	WSN	NYM	Scherzer	DeGrom	61.80%	38.20%
Game 2	WSN	NYM	Strasburg	Wheeler	69.99%	30.01%
Game 3	NYM	WSN	Syndergaard	Corbin	41.45%	58.55%
Game 4	NYM	WSN	DeGrom	Scherzer	39.43%	60.57%
Game 5	WSN	NYM	Strasburg	Wheeler	69.12%	30.88%
Series	WSN	NYM			62.30%	37.70%

It's actually incredibly close - Washington would only have a 0.5% edge (62.3% favorites) in the NLDS scenario compared with the wild card game.

Outcome	In...	Prob
WSN	3	17.93%
WSN	4	17.39%
WSN	5	26.98%
NYM	3	6.7%
NYM	4	18.9%
NYM	5	12.1%

But, as expected, the Mets would still (barely) prefer the randomness inherent in one game over a five game series.

Should the Washington Nationals Rest Scherzer, Risking Home Field Advantage?

The Washington Nationals have clinched a wild card spot, but are only one game up on the Milwaukee Brewers for home field advantage in the NL Wild Card game. The Brewers have been red hot, with a 19-4 record in the month of September. 

Meanwhile, the Nationals have one of the best rotations in baseball, with Max Scherzer and Stephen Strasburg ranking #2 and #3 in the NL, respectively, in pitcher WAR this season.

Scherzer is their best pitcher. And he's currently in line to start the last game of the regular season on Sunday. However, that would burn him for the one-game playoff next Tuesday. So which is more valuable? Scherzer pitching in the NL Wild Card game, or the Nationals retaining home field advantage?

My colleague answered this question via FiveThirtyEight's pitcher ratings:

Using 538's Elo rating, they have Scherzer (30) as worth 11 more points than Strasburg (19). However, they have HFA listed at 24 points, which is actually doubled to 48 points if you take the HFA away from WAS and give it to MIL. So Strasburg at home is worth 43 points and Scherzer on the road is worth 6 points, a difference of 37 points! So they theoretically should keep Scherzer on normal rest this week as long as HFA is still on the line.

Per the Elo formula and FiveThirtyEight's ratings, the Nationals would be 54.4% favorites on the road with Scherzer, and 59.7% favorites at home with Strasburg. So they should maximize their chances at retaining home field.

I checked this using my play-by-play MLB simulator, assuming that the Brewers' top arm, Brandon Woodruff, would start in either wild card scenario. I found similar results: the Nationals win 57.5% of the time on the road with Scherzer, and 59.9% of the time at home with Strasburg. Both pitchers are really good! So home field is the deciding factor.

And for the Brewers to maximize their chances of winning, they have to chase either pitcher early: Scherzer's average start in Milwaukee is 6.08 innings in a Brewers win, but 6.49 innings in a Nats win. Strasburg's average start in Washington is 5.79 innings in a Brewers win, but 6.25 innings in a Nats win.

"What are the odds?" Of Rolling 7 Doubles in a Row (Dice)

In backgammon, each game begins with each player throwing a single die to determine who goes first. In the event that each player's roll is the same, "then both players roll again until they roll different numbers". The following question was posed to me: what are the odds that each player rolls the same number... 7 times in a row?

There are 6 potential numbers on each die, so over two dice there are 6 * 6 = 36 possible combinations. Additionally, there are 6 possible pairs: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). So 6 / 36 = 1 / 6 ~= 0.167% chance of tying on one roll. But when this is replicated 7 times in a row: (1 / 6) ^ 7 = 0.00036%, or 1 in 279,936.

N	Chances	1 in ...
1	16.67%	6
2	2.78%	36
3	0.46%	216
4	0.08%	1,296
5	0.01%	7,776
6	0.002%	46,656
7	0.00036%	279,936
8	0.0001%	1,679,616
9	0.00001%	10,077,696
10	0.000002%	60,466,176

That's far less likely than having a doctor on your flight or getting the same taxi driver twice in a large city, but way more likely than two teams sharing identical box scores on the same day or three people in the same family all being born at the exact same time (on different days).

What if you play backgammon a lot though? How long would you have to play in order to expect to see a streak of 7 dice ties in a row?

The math is explained on this nice "Probability of Runs" calculator, but you would need to play 232,845 games of backgammon until there would be a better than 50/50 chance of seeing a run of ties like this. The average number of games needed until you would see this happen is even larger: 335,922 games of backgammon.

Preseason NCAAF Rankings for 2019

As I did in 2018, 2017, 2016, 2015, and 2014, I've compiled my preseason NCAAF rankings that take into account player turnover and recruiting classes.

There's a slightly new wrinkle this year though. As before, I used my final MDS Model ratings from last season as the base, and then factored in ESPN's Preseason FPI and the S&P+ projections (which are now housed over at ESPN with Bill Connelly leaving SB Nation), but this year I've also included Ed Feng's rating system from The Power Rank. Once the season starts, this "preseason" rating will be faded out as the season progresses, carrying less and less weight with each ensuing week.

As I have in the past, I missed Week 0, but got these ratings out before the first full weekend of games.

In the below list, the "Trend" indicates whether the respective team's new ranking rose or fell relative to last year's preseason ratings. No team movement in or out of FBS this year though!

My goodness are Alabama and Clemson evenly matched, and in a class of their own:

Alabama: 0.95035035751657
Clemson: 0.949045941382027

Rank	Team	PRESEASON	Trend
1	Alabama	0.950	UP
2	Clemson	0.949	UP
3	Georgia	0.851	UP
4	Oklahoma	0.813	UP
5	LSU	0.808	UP
6	Ohio State	0.806	DOWN
7	Michigan	0.793	UP
8	Notre Dame	0.792	DOWN
9	Auburn	0.784	DOWN
10	Penn State	0.743	DOWN
11	Florida	0.740	UP
12	Washington	0.732	DOWN
13	Texas A&M	0.731	UP
14	Mississippi State	0.723	DOWN
15	Michigan State	0.712	DOWN
16	Oregon	0.695	UP
17	Wisconsin	0.691	DOWN
18	Missouri	0.690	UP
19	Miami (FL)	0.669	DOWN
20	Utah	0.667	UP
21	South Carolina	0.660	UP
22	Florida State	0.654	DOWN
23	Oklahoma State	0.653	DOWN
24	Iowa	0.645	UP
25	USC	0.644	DOWN
26	Texas	0.636	DOWN
27	Stanford	0.635	DOWN
28	UCF	0.630	UP
29	Virginia Tech	0.629	DOWN
30	Tennessee	0.627	UP
31	Iowa State	0.627	UP
32	TCU	0.625	DOWN
33	Boise State	0.622	DOWN
34	Washington State	0.622	UP
35	Baylor	0.610	UP
36	UCLA	0.605	UP
37	Minnesota	0.603	UP
38	Ole Miss	0.602	DOWN
39	Kentucky	0.593	UP
40	Nebraska	0.585	UP
41	North Carolina State	0.583	DOWN
42	Syracuse	0.581	UP
43	Memphis	0.577	UP
44	Arizona State	0.575	UP
45	West Virginia	0.571	DOWN
46	Virginia	0.570	UP
47	Northwestern	0.569	DOWN
48	Texas Tech	0.568	DOWN
49	Purdue	0.568	UP
50	Duke	0.566	DOWN
51	Pittsburgh	0.563	UP
52	Appalachian State	0.554	UP
53	Brigham Young	0.552	UP
54	Indiana	0.547	UP
55	Arizona	0.546	DOWN
56	North Carolina	0.544	DOWN
57	Vanderbilt	0.536	UP
58	Cincinnati	0.535	UP
59	Wake Forest	0.532	DOWN
60	California	0.529	DOWN
61	Arkansas	0.524	DOWN
62	Kansas State	0.523	DOWN
63	Louisville	0.515	DOWN
64	Boston College	0.514	DOWN
65	Fresno State	0.508	UP
66	Houston	0.503	DOWN
67	Temple	0.495	UP
68	Georgia Tech	0.495	DOWN
69	Utah State	0.495	UP
70	Maryland	0.490	UP
71	San Diego State	0.489	DOWN
72	South Florida	0.479	DOWN
73	Marshall	0.477	DOWN
74	Northern Illinois	0.469	UP
75	Toledo	0.468	DOWN
76	Colorado	0.464	UP
77	Western Michigan	0.459	UP
78	Florida Atlantic	0.453	DOWN
79	Army	0.452	UP
80	Ohio	0.449	DOWN
81	Southern Miss	0.447	UP
82	Arkansas State	0.440	DOWN
83	Georgia Southern	0.438	UP
84	Air Force	0.437	UP
85	Southern Methodist	0.425	DOWN
86	Troy	0.425	UP
87	Illinois	0.421	UP
88	North Texas	0.417	UP
89	Louisiana Tech	0.412	DOWN
90	Wyoming	0.403	DOWN
91	Tulane	0.400	UP
92	Middle Tennessee	0.397	DOWN
93	Florida International	0.394	UP
94	Tulsa	0.387	UP
95	Oregon State	0.380	UP
96	Miami (OH)	0.380	DOWN
97	Nevada	0.379	UP
98	Rutgers	0.374	DOWN
99	Western Kentucky	0.373	UP
100	Hawaii	0.373	UP
101	UAB	0.363	UP
102	Eastern Michigan	0.360	UP
103	Navy	0.349	DOWN
104	Buffalo	0.348	DOWN
105	Louisiana-Monroe	0.345	UP
106	Kansas	0.341	DOWN
107	Colorado State	0.339	DOWN
108	Louisiana-Lafayette	0.336	UP
109	UNLV	0.325	DOWN
110	Ball State	0.324	UP
111	East Carolina	0.309	UP
112	Texas State	0.307	UP
113	Liberty	0.285	UP
114	Georgia State	0.276	UP
115	Coastal Carolina	0.274	UP
116	Central Michigan	0.274	DOWN
117	San Jose State	0.269	UP
118	New Mexico	0.260	DOWN
119	Akron	0.255	DOWN
120	Kent State	0.250	UP
121	Bowling Green	0.244	DOWN
122	Charlotte	0.234	UP
123	New Mexico State	0.234	DOWN
124	UTSA	0.229	DOWN
125	Massachusetts	0.218	DOWN
126	South Alabama	0.213	DOWN
127	Old Dominion	0.206	DOWN
128	Connecticut	0.201	DOWN
129	Rice	0.162	DOWN
130	UTEP	0.118	DOWN