September 30, 2014

Baseball Therapy

The Wild Card Penalty

by Russell A. Carleton

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It’s time for some Wild Cards! Tonight, the A’s will face off against the Royals. Someone will win the game, and their prize will be an all-expenses-paid trip to Anaheim for a best-of-five series against the Angels. The Royals will send James Shields to the mound and the A’s will counter with Jon Lester. No matter who wins, that team will not be able to call upon their ace until Game 3 of that Angels series. Good luck, fellas.

In 2012, when the Wild Card play-in game was introduced, there were two main arguments for its existence. One is that people love a win-or-go-home game, and that part is still true. The other had to do with justice, or at least some sense that the Wild Card should feel ashamed of sneaking into the playoffs and should show that shame by losing more often than it did. The problem was that since 1995, when baseball decided to both play in a three-division-per-league format and have a post-season, the Wild Card teams were a little too successful. In fact, Wild Cards won the World Series in 1997 (Marlins), 2002 (Angels), 2003 (Marlins again), 2004 (Red Sox), and 2011 (Cardinals). Wild Cards also won their respective league pennants in 2000 (Mets), 2002 (Giants), 2005 (Astros), 2006 (Tigers), and 2007 (Rockies). It didn’t seem fair that a team that didn’t win their division seemed to win their league so often. The Wild Cards were basically on equal footing with the division winners.

The Wild Card play-in game was supposed to fix things. By forcing the Wild Card wannabes into a cage match with each other prior to entering the Division Series, the Wild Card teams—plural now—would be punished by having to play an extra game, likely using their best starter, while the division winners lounged in a pool somewhere in Arizona. The winners would show up to Game 1 of the Division Series tired and in no shape to put up much of a fight.

On last Wednesday’s episode of Effectively Wild, astute listener Eric Hartman asked the question that no one ever really bothered to ask. How big is the “penalty” for playing in that game?

Warning! Gory Mathematical Details Ahead!

We’re going to try to isolate the “penalty” that a team pays for playing in the new Wild Card winner-takes-themselves-to-the-next-round game compared to the ancient pre-2012 system where the Wild Card was simply the fourth team in the bracket. We’re not going to calculate it for individual cases. There are several variables that could affect how much playing that extra game could help or hurt a specific individual team. What we’re going to do is to make a couple of assumptions and get a ballpark figure.

One man gathers what another man spills

The most obvious consequence of the play-in game is that a team that used to just waltz into the LDS now has to play for its playoff life. Now, we assume that the fourth place team, the team that used to get a free pass, will be the favorite in the play-in game, in general. They will be the home team, and the home team in general wins a baseball game 53 to 54 percent of the time. The fourth-place team also had a better record than the fifth-place team, so they are likely (slightly) better than the fifth place team. But if we assume that our fourth place team has somewhere between a 55 and 60 percent chance of advancing out of the play-in game, that’s 40-45 percent less than they had before the introduction of the second Wild Card.

At the same time, that’s an increase of 40-45 percent of getting to the LDS for the fifth place team in the league. Now, there will be years where the two Wild Card teams are both roughly each other’s equal, and then years where one Wild Card is vastly superior to the other. If the current rules had been in place in 2001, the Wild Card Oakland A’s and their 102 wins would have had to play a Twins team that won 85 games during the regular season. How fair is that?

But let’s turn our attention to the effects of having to play in the Wild Card game itself.

I can see you’re out of aces.

Okay, the Wild Card game has been played and the winner decided. The main thing that people often cite as a cost of playing in the Wild Card game is that a team will have to use its ace starting pitcher. It also seems to assume that all teams are constructed such that they have one unbelievably good starting pitcher and a bunch of bums. Teams that are constructed like this are at the greatest disadvantage, but let’s just go with the premise for a moment.

Let’s look at the schedule to see what our Wild Cards will be (and have already been) facing off against.

Date	American League	National League
Sunday 9/28	Game 162	Game 162
Monday 9/29	Day Off	Day Off
Tuesday 9/30	Wild Card Game	Day Off
Wednesday 10/1	Day Off	Wild Card Game
Thursday 10/2	ALDS Game 1	Day Off
Friday 10/3	ALDS Game 2	NLDS Game 1
Saturday 10/4	Day Off	NLDS Game 2
Sunday 10/5	ALDS Game 3	Day Off
Monday 10/6	ALDS Game 4 (if nec.)	NLDS Game 3
Tuesday 10/7	Day Off	NLDS Game 4 (if nec.)
Wednesday 10/8	ALDS Game 5 (if nec.)	Day Off
Thursday 10/9	Travel	NLDS Game 5 (if nec.)

As Ben and Sam pointed out on Wednesday’s episode, it’s not as big a deal as people assume. Look at all of those off-days! Still, the NL division winners have a full four days off. They will have the luxury of setting up their rotation exactly as they want to, lined up in nice neat order for Games 1 through 4, and if necessary, their ace comes back for Game 5.

For a team that has to “burn its ace” for the Wild Card game, the ace will not be able to come back until Game 3, but in both leagues he will be on full rest (there’s no way to pitch him on short rest.) If a team was involved in a fight down the stretch and needed to use their ace for Game 162 to ensure that they got into the playoffs, he could be fully rested for Game 2 in the ALDS, and Game 1(!!!) of the NLDS, assuming they got that far.

So, here’s the configuration of starters that an American League team would theoretically use in a series, assuming no rainouts or other such issues.

Game #	Division Winner	Used Ace in Wild Card Game	Used Ace in Game 162 & #2 starter in WC game
1	Ace	Starter #2	Starter #3
2	Starter #2	Starter #3	Ace
3	Starter #3	Ace	Starter #2
4	Starter #4	Starter #4	Starter #4
5	Ace	Starter #2	Ace

Because of the way the off-days fall, a team could have its Game 2 starter pitch Game 5 on full rest. A team who used their ace starter in Game 162 would still get the benefit of having two full-rest starts from him, including in Game 5 and one each from #2, #3, and #4. A team that uses its ace in the Wild Card Game would get two starts from its #2 starter, rather than its ace. The actual penalty that a team would pay would depend on who those two pitchers are. But if we use a couple of benchmarks. I looked at all pitchers in 2014 who had 150 or more innings. The fifteenth (your average “ace”) best FIP belonged to Stephen Strasburg at 2.99. The forty-fifth-best (average “second starter”) FIP was James Shields at 3.59. We’re talking about 0.6 runs over nine innings, so roughly half a run in a seven inning start. That’s the aggregate difference for the five-game series in pitching. Over 162 games, that would pro-rate to 16.2 runs. By missing that start from the ace (and giving it to the #2 starter), it makes our Wild Card team roughly a win and a half worse than it had been. The 89 win team becomes and 87-and-a-half win team.

I believe you meant a pitch-pipe, not a pitcher

Now, there will be some out there who focus on this line:

Game #	Division Winner	Used Ace in Wild Card Game	Used Ace in Game 162
1	Ace	Starter #2	Starter #3

They will say that the big problem is that our Wild Card team is surely at a disadvantage in Game 1 (most likely true) and that Game 1 “sets the tone” for the series. By not starting their ace, our Wild Card team is in more danger of losing Game 1. Since 1995, the team that wins game one of a five-game series goes on to win the series 71.1 percent (54 out of 76) of the time. This may have something to do with the fact that the winner of Game 1, by definition, only has to win two of the next four games while the loser must win three of four. It’s also true that the better team (who also usually has home field advantage) is more likely to win the first game and the series in general. But perhaps there’s something to it.

I looked at that same set of series from 1995-2013 (best-of-5 LDSes) and identified Game One winners. What’s interesting is that the team that won Game 1 won 53.6 percent (120 out of 224) of the remaining LDS games despite only having home field advantage in slightly more than half of them (113 out of 224). The effect can’t be explained by a difference in team quality either. Using regular season records and the log5 method, I figured out how many games the Game 1 series winners “should” have won. The answer was 113.5. So, Game 1 winners really do outperform expectations in the remaining games in the series, by about three percentage points. Here’s a post-season cliché that actually holds some water. Game 1 really does set a tone for the series. It doesn’t reduce the Game 1 loser to nothing, but three percentage points over 162 games is 4.86 games.

How much does starting the second guy in your rotation hurt your chances in Game 1, compared to starting your ace? That one is harder to figure, but if we just shove Stephen Strasburg’s 2.99 FIP multiplied by 162 games into a Pythagorean formula and assumed an average offense (4.07 runs per game), that team would win 63.7 percent of its games (103-59!). Using James Shields’s 3.59 FIP, we get an expectation that the team would win 55.7 percent of its games (90-72). That’s all a bit slapdash, but it’s probably close enough. By starting a lesser pitcher in Game 1, our Wild Card team has roughly an 8 percent reduction in the chances that it will win Game 1, and thus, that it will pay a 3 percent penalty because the wrong tone was set. If you pro-rate that all out to 162 games, that handicap from tone setting is worth .39 wins on average, before we know the result of Game 1.

All I want is a couple days off…

One other problem that the Wild Card winner will face will be that after a long, grinding season, they had to play another game while the Division winner was resting. I’ve previously found that a day off in the middle of the season actually boosts a hitter’s production by a point and a half of OBP. While both teams have gotten some off-days in there, the Division winner got an extra one, and over the course of a series in which they might get 150 plate appearances or so, they might squeeze out an extra quarter of a hit or walk on average in the series. Turning an out into a hit or walk is actually worth a lot. (It could be a home run!) If we say that the transition is worth one run, then a quarter of a run over five games is worth 8.1 runs over 162, most of another win.

However, no one ever talks about tired hitters. They always talk about the poor bullpen arms. In the Wild Card game, there’s an incentive to over-extend the good relievers to throw two innings instead of one, but then again, the Wild Card team gets a day off after. Even more than that, there’s little evidence that bullpens (as a unit) do better or worse than normal after a day off. The problem is that bullpen usage in the playoffs is so different from the regular season that we can’t use regular season data to model the effects. There’s probably some effect from Wade Davis pitching in both the seventh and eighth inning of a game (note: yes, this is legal) but it’s not clear what.

But let’s add it all together. Because a team likely used its ace starter in the Wild Card game, they will have to give a start that he otherwise would have taken in the LDS and to their no. 2 guy. We estimate that, on average, to be worth a win and a half, pro-rated out to 162 games. In specific circumstances, it could be more, it could be less, but that’s probably mid-range. There is also the reduced chances of winning Game 1 and having to play catch up in a short series that’s also worth .4 wins. The hitters, because of having an extra game to play bleed away .8 wins, and the relievers are something of an unknown. So, we estimate that playing in the Wild Card game saps the team that wins of something on the order of 2.5 to 3 wins of value. That seems pretty substantial and almost entirely attributable to the new rules around the play-in game.

Three of our Wild Card contestants won 88 games this past year (Kansas City won 89). The winner of the AL game will face off against the Angels (98 wins) while the NL winner will get the Nationals (96 wins). The Halos and Nats will also have home field advantage.

Let’s compare the chances that an 88 win team would have playing against a 97 win team over a 5 game series to the chances that an 85 win team would have playing against that same 97 win team. Again, using log5, we find that an 88 win team could be expected to win about 44.4 percent of the time. Ignoring home field advantage for a moment, we would estimate that over a 5 game series, an 88 win team would prevail about 40 percent of the time. For an 85 win team, we expect them to win 42.6 percent of games and 36.3 percent of all five game series.

The “Wild Card penalty” is worth roughly 4 percentage points of chance of advancing to the League Championship Series. There are plenty of assumptions powering that number and maybe a leap of faith or two, but this is once again a case where the order of magnitude (it’s in the single digits) is more important than the third decimal place. Once in every 20-30 cases (so once every 10-15 years), a Wild Card team that might have won its LDS will end up losing its series because of the effects of the Play-In Game.

The Real Reason for the Play-In Game

No matter who wins tonight’s A’s-Royals game, they are at a disadvantage. Even if the Royals had simply walked into the Division Series like they did during the heyday of the Spice Girls, they’d have their work cut out for them. If the Wild Card team loses, it’s convenient to think that they did so because the Wild Card play-in game knocked the wind out of them. It will probably have more to do with the fact that they became a Wild Card because they finished with the fourth or fifth best record in the league and are matched up against the best. That said, we can reasonably say that the Wild Card game has some deleterious effect on its victor. Maybe not as much as was originally thought, but enough to register when you do some #GoryMath. Most of the lack of a penalty comes from the fact that there are just so many days off that playing one extra game in the middle there is an annoyance, but hardly backbreaking. These guys have been playing most every day since April.

One surprising thing that we did find is that all of the emphasis on Game 1 actually has some warrant. The winner of Game 1 of the LDS gets more of an advantage than would otherwise be expected for just having won one of the five games to be played, if necessary. (And by playing in the Play-In Game, our Wild Card team loses some of its chance to win Game 1.) Every once in a while, one of those playoff clichés turns out to be true!

If MLB really wanted to make the Wild Card suffer, it would probably have to do so by cutting back the number of off-days in the playoffs. Maybe force the Wild Card to play the next day after its wild victory. But of course, that affects the TV schedule. And part of the fun of the playoffs is that you get to see the best players on the best teams because they are properly rested. So maybe baseball should just admit that the real point of the Wild Card game is to make for two really compelling prime-time games for people to watch.

Russell A. Carleton is an author of Baseball Prospectus. Follow @pizzacutter4
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