Implied Value of Playoff Games
One of the frustrating aspects of the current lockout negotiations (or at least the version that is laundered through the media, which after the reporting of Monday night/Tuesday morning February 28/March 1 one would be wise to be skeptical of) is the extent to which any kind of novel idea put forward by the MLBPA is immediately dismissed out of hand by MLB. Rob Manfred has spent the last several years pensively stroking his chin and saying “That’s interesting, we’ll consider it” to any suggestion made to change baseball, seemingly up to and including positioning clowns at random points in the outfield.
I was an opponent of a ten-team postseason format, so I certainly am no fan on the alleged compromise of a twelve-team postseason and still less of the owners’ cherished fourteen-team monstrosity, replete with a selection process made for reality shows and “bulletin board” material. That the owners would (allegedly) dismiss the notion of a “ghost win” in the first round so quickly appears to me to betray any claims that they are seeking a good faith solution at least on the issue of the postseason. Apparently Manfred et. al.’s obsession with using the minor leagues as a testing ground for various concepts stops at the shores of the Pacific Ocean, as a ghost win has been part of the NPB playoff format (although not at a comparable point in the playoffs as it is being proposed by the MLBPA).
In order to understand why a ghost win might make sense, I think it’s worth trying to quantify the value of a playoff game relative to a regular season game. To do this, I am going to propose that we can very easily calculate the implied value of a playoff game, proceeding from some assumptions that I think will be easier to explain as I go. I will be considering the seasons that have been completed under the current ten-team postseason which was introduced in 2012; of course, the 2020 season and postseason were played under different formats and will be ignored here. Before proceeding, I will warn you that this is mostly a thought experiment, and the results do not offer an actionable suggestion about how the playoffs should be structured – just a way to try to quantify what is implied about the value of playoff games by the results that the format could produce.
I will start from the premise that if a team can advance in the playoffs, knocking out an opponent that had a better regular season record, the difference in those teams’ record defines how much more the playoff games are worth than a regular season game. Let’s start with a simple example for the one-game wildcard playoff. In 2012, Atlanta had 94 wins and St. Louis 88, but the Cardinals could (and in fact did, although the actual outcome is irrelevant for the purpose of this exercise) advance at the expense of the Braves by winning a single game. This implies that the wildcard playoff was worth the equivalent of seven regular season games, so that if we credit St. Louis with seven regular season equivalent wins for their single playoff win, they would have 95 wins to Atlanta’s 94.
On the other hand, meeting in the first AL wildcard game, Baltimore and Texas both had 93 wins. Thus the wildcard game had an implied value of just one regular season game. If we let A designate the number of regular season wins for the team with the better record entering a single-game playoff, and B the regular season wins for the teams with the worse record, then we can calculate the implied value (I) by solving for:
A + 1 = B + I so
I = A – B + 1
For the eighteen wildcard games (nine seasons times two leagues), the average implied value of the wildcard game is 3.28 regular season games. Of course, this value is dependent on the actual differences between team records in those eighteen cases, and as sample data may not expect what we would expect over a longer period of time (or, even more difficult to quantify but more pertinent for this particular discussion, that might be expected under a different set of CBA parameters and their resulting impact on team roster building which would alter the expected distribution of wins across the league). This value was driven up significantly by the 2021 NL wildcard game, which had an implied value of 17 regular season games as it would have allowed the 90 win Cardinals to knock out the 106 win Dodgers. (For the purpose of these calculations, I just used raw regular season wins not including any wins in tiebreaker games and did not worry about any cases in which a team did not play 162 games. If teams were tied, I just picked the order randomly as this exercise is not about the particular teams involved but rather about the number of wins. Also, I have assumed that raw regular season wins are the proper measure, when in reality they are impacted by strength of schedule and don’t truly represent how impressive each team’s regular season game outcomes were).
I don’t know what a reasonable implied value is – it’s a subjective question that depends on how you feel about tradeoffs between the excitement of the postseason and the extent to which true team quality is revealed through the marathon of a 162 game season. As mentioned, my preference tilts heavily towards the latter, but regardless of where on that spectrum you fall, I think that thinking about this in terms of implied wins can help to quantify the extent to which playoffs can overturn the results of the regular season.
Let’s suppose that a 12-team playoff format was implemented. In this case, the two division winners with the best records would get a bye, and the other four qualifiers in each league would play a three-game series to advance into the LDS. How does the implied value of those series compare to those of the one-game wildcard playoff?
To calculate the implied value for a three-game series we’ll need to make some additional assumptions. A three-game series introduces the possibility that the team with the superior record (team A) wins one game before losing the series. If the team with the lesser record (team B) sweeps the three-game series, then we need to solve for I in the equation:
A + 1 = B + 2*I
So I = (A – B + 1)/2
For example, in the case of 2021 Dodgers (106 wins) v. Cardinals (90), the implied value would be (106 – 90 +1)/2 = 8.5 games, such that if the Cardinals win two games, they now have 90 + 2*8.5 = 107 regular-season equivalent wins, lifting them ahead of the 106 win Dodgers.
In the case in which the Dodgers win a game, we have to add a postseason win with value I to their side of the ledger, such that:
A + I + 1 = B + 2*I
So I = A – B + 1
Which in this case would be 17. To calculate the implied value of games for the series, we need to weight these two somehow. My solution is to weight them using the probability that the series goes two or three games, assuming the teams are evenly matched. For a three game series, this is very easy to calculate: there is a 50% chance that whichever team won game one will win game two, ending the series, and a 50% chance that whichever team lost game one will win game two, extending the series to three games. So the average implied value of each game in a Dodgers/Cardinals series is .5*8.5 + .5*17 = 12.75.
The average implied value for all of the actual 4/5 matchups (which is what the historical wildcard game would morph into under the new format) is 3. So each playoff game would be worth fewer regular season games than under a one-game playoff format, as is to be expected. However, the decrease is not as much as it might be if we ignored the possibility that the superior team will earn their own playoff win before bowing out.
When considering the 3/6 matchups, we run into the conundrum that it is possible in this case for the #6 seed to have a better regular season record than the #3 seed which is reserved for a division winner. This happened in the 2012 AL, as Detroit won the Central with 88 wins and Tampa Bay would have been sixth with 90 wins. Since I am not assuming any inherent value to winning a division, in such cases I will continue calculating implied value from the perspective of how much playoff games would have to be valued to give the team that had fewer regular season wins more win equivalents. The implied value for the 3/6 matchups is 4.5. Throwing out the DET/TB case from 2012, the implied value is 4.46, which I will use further below when comparing to the ghost win format.
Remember that for a one-game 4/5 playoff, the average is only 3.28, so even with a three-game series, these games have much higher implied value as the discrepancy between team regular season performance only grows.
Moving to the fourteen-team format sought by MLB, we need to consider the implied value for three-game series between 2/7, 3/6, and 4/5. The new addition is the 2/7, which introduces even larger variations, and a higher implied value of 9.91 regular season game equivalents. The maximum is 15 from the theoretical 2019 AL matchup between the 103 win Yankees and the 84 win Red Sox.
As the number of playoff teams grows, the playoffs will take on much higher implied value than they ever have before. It is hardly surprising that some segment of fans, players, and presumably even owners would find this troubling, and seek compromises that might be able to preserve some of the value of the regular season. Hence the concept of the ghost win, which under the MLBPA musings of a possible compromise would be applied to a notionally five-game series, giving the higher seeded team an automatic 1-0 lead at the start of the series.
But how effective would this be in lowering the implied value of these new playoff games? Here we run into a problem with our theoretical calculations in the cases in which the higher-seeded team has an inferior record, since that team would get the benefit of the ghost win. Since this is just a thought experiment, I will ignore any such cases.
There are two paths to victory for the lower-seeded team: either they win three games and their opponent zero, or they win three games and their opponent one. In the first case, we would have:
A + 1 = B + 3*I
So I = (A – B + 1)/3
In the second case:
A + I + 1 = B + 3*I
So I = (A – B + 1)/2
We need to weight these two possibilities, which is trickier. There are number of ways you could go about estimating the probability of each outcome, but I will make it as simple (and as unrefined) as possible. Over the course of these four games, the possible outcomes that result in the lower seeded team winning are:
WWWW (P = 6.25%)
WWWL (P = 6.25%)
WWLW (P = 6.25%)
WLWW (P = 6.25%)
LWWW (P = 6.25%)
Since we are assuming a 50% chance of winning a given game, all of these outcomes are equally likely. If these actually played out, only in the first two cases would the higher seeded team not get a win. Thus, given that the lower seeded team wins the series, there is a 40% chance that the higher seeded team does not get a win and a 60% that they do, so we will weight our two implied win calculations 40%/60%.
Now we can look at how the implied values compare for each of the matchups between a three-game series and a five-game series with ghost win (ignoring the aforementioned DET/TB case):
One way we might think about this is that we have accepted the one-game wildcard playoff (I don’t like it, but I’m not picketing outside Rob Manfred’s office over it either), which has an implied value of 3.28. A three-game series results in higher implied values than the wildcard playoff, but a five-game series with ghost win would have a lower implied value for the 3v6 matchup, so from this perspective it would not mark more of a degradation of the “sanctity” of the regular season than we’ve already accepted. There’s really not much that can be done to salvage the 2v7 matchup that would even be possible even if MLB wasn’t displaying stubborn rigidity - other than not have it.