patrickfolz

Not really!

But you knew that already. The world hardly needs me to add to the thousands and thousands of articles dissecting the issue, but I’m writing one anyways because I’m pathologically narcissistic. Also, I frequently want to refer to the information I’m about to impart, but haven’t been able to find a clear resource on it, so I thought I’d make one, and then I thought I’d share it because, hey, that’s what the internet’s for.

To that end, I’ve attached an excel file with the championship game/series winners and losers for each American major sport league (MLB, NBA, NFL, NHL) for each year that said championship game/series held its current significance (for example, all Superbowl winners for the NFL, but no pre-merger champions), as well as some metrics and dissections of the data that I am about to discuss. I chose championship participants as the focus of investigation, because the championship participants clearly had a realistic shot at winning the championship (so neglecting sub-.500 playoff teams and the like, thanks NBA, though it of course includes MLB’s 83-79 2006 Cardinals), while not focusing on winners leaves out the vagaries of single-game or single-series results (hello 2001-02 Patriots).

This file is available freely, for now, in hopes that someone might find it useful. (Though hopefully not too many, lest I be driven into debt by excess bandwidth fees. Be gentle, I’m poor!) The data is compiled primarily from Wikipedia and my own knowledge, except where otherwise noted. If you spot something wrong, there is a 99.9% chance I typed it in wrong. If you want to change or add anything, feel free to do so, and if you send it to me (and it’s better) I will upload it and write a nice comment about you. More on the Excel file in the postscript.

Now about that “parity”[i]: the common line is that the NFL’s salary cap and free agency system encourages rapid player turnover, to ensure that the same teams don’t win year after year. So, do the same teams win year after year? There are many ways to attack that question; here is mine. I looked at championship game winners and participants throughout league history, across all sports. Since the beginning of NFL free agency in 1993 through now (June 2012), we have seen:

Since 1993:	MLB	NBA	NFL	NHL
Distinct Winners	11	8	12	11
Distinct Participants	19	16	22	19

Table 1: In each league’s respective championship game/series

So, at first blush it appears this line of reasoning has some merit: the NFL has had more distinct winners, and championship game participants, than any other sport, though MLB is right behind. However, this neglects a number of important complicating factors: the leagues have different numbers of teams, that number has changed in all four leagues over that timeframe, and two leagues cancelled a championship in that timeframe (MLB in 1994, NHL in 2004-05). Furthermore, the other leagues each began unrestricted free agency earlier than 1993: the NHL in 1972, MLB in 1976, and the NBA in 1988, so it’s worth looking at in a bit more detail.

In order to account for these issues, I introduce a “Participation Quotient”, defined for a given year as:

, where N_Pis the number of distinct participants (defined in terms of franchise, not location) since a specified start date, while N_t(year) is the number of teams in the league during a given year. For example, MLB from 1976-1993 inclusive gives the following results:

Table 2: Example calculation of PQ starting in 1976. Note that participants are counted by franchises, so the team that moved from Brooklyn to Los Angeles is counted as one entity, instead of treating LAD and NYB as separate participants in MLB history.

Season	Winner	Loser	N_P	N_t	PQ
1976	Cin	NYY	2	24	0.083
1977	NYY	LADBrk	3	26	0.115
1978	NYY	LADBrk	3	26	0.115
1979	Pit	BalStL	5	26	0.192
1980	Phi	KC	7	26	0.269
1981	LADBrk	NYY	7	26	0.269
1982	StL	Mil	9	26	0.346
1983	BalStL	Phi	9	26	0.346
1984	Det	SD	11	26	0.423
1985	KC	StL	11	26	0.423
1986	NYM	Bos	13	26	0.500
1987	MinWash	StL	14	26	0.538
1988	LADBrk	OakPhiKC	15	26	0.577
1989	OakPhiKC	SFNY	16	26	0.615
1990	Cin	OakPhiKC	16	26	0.615
1991	MinWash	AtlBosMil	17	26	0.654
1992	Tor	AtlBosMil	18	26	0.692
1993	Tor	Phi	18	28	0.643

Given infinite time and a constant number of teams, a league’s PQ will tend to unity, since N_P can only increase. However, expansion and contraction can reduce or increase PQ. Note that the NHL had a PQ > 1 throughout the “Original Six” era (setting the start date as 1926, the first year of the Stanley Cup being synonymous with the NHL championship), since prior to that more than six distinct franchises had participated in a Stanley Cup finals.

Taking 1993 as the start date, these are the 2011 PQs for each league:

	MLB	NBA	NFL	NHL
PQ	.633	.533	.688	.667

Table 3: PQ(2011) for each league, starting from 1993

Again, the NFL comes out a bit ahead, with the NHL and MLB close behind and the NBA far behind thanks to Lakers, Spurs, and Bulls dynasties eating up a bunch of championships. A die-hard MLB fan could set forth a convoluted argument that MLB actually has more parity since it comes in at a not-terribly-distant third despite the Yankees’ extraordinary and relatively unprecedented (since the 50s anyway) streak of appearances, noting that aside from them World Series participation has been extremely equitable (only Philadelphia and St. Louis appearing in more than 2 during that timeframe), and therefore could be seen as having more parity than the other leagues.

However, I won’t do that, and instead will note that this timeframe encompasses only 19 seasons. A few (un)lucky breaks in the leagues’ conference championship games could sway the number quite a bit. I’m comfortable saying that MLB, the NFL, and the NHL, are basically “tied” as far as PQ from 1993 goes, with the NBA notably more dominated by a small handful of teams.

Using 1993 as the start date is a bit artificial for the non-NFL teams, though, since they have had more time to master the free agency process than the NFL. What if we compare results for the first 19 seasons after the introduction of free agency? I will also include the results for the 19 years prior, for comparison’s sake.

	MLB	NBA	NFL	NHL
PQ before UFA	.583	.522	.536	.500
PQ after UFA	.643	.567	.688	.571

Table 4: PQ in the year before unrestricted free agency (based on 19 years prior), and then for the 19 years since free agency

In the aftermath of free agency, the NFL once again has the highest PQ, with MLB a close second, then a gap separates them from the NBA and NHL. Free agency in the NFL has given it the quickest ‘acceleration’ in number of teams that have participated in the championship, no matter how we slice it, though MLB has also consistently done well in that regard.

It’s also worth noting that, acknowledging the enormous caveat that taking 19 years before unrestricted free agency is utterly arbitrary (starting from league inception, MLB, the NBA, and the NHL all reached unity PQ at some point before their respective expansion eras began), unrestricted free agency has resulted in more teams reaching the championship over that timeframe in every league. Not that anyone was really arguing otherwise, but it’s good to see that it achieves this purpose (if only just, in the case of the NBA).

I thank and congratulate you, gentle reader, for making it this far, and if you wish to depart at this point I give you my blessing. What follows is largely (though not entirely) speculative discussion ofhow NFL’s parity compares with MLB’s, and briefly touch on how this relates to the other leagues.

There is another major factor that contributes to NFL teams’ success cycles besides free agency: injuries. NFL careers are very short compared to other leagues, only about 3.5 years (jumping to 6 if fringe players are neglected). The average MLB career is 6.6 years (jumps to 9), and the NBA and NHL come in at 6.6 and 5.7 respectively (data for significant careers could not be found [in the time I cared enough to search for it]). Thus, we expect there to be more championship participant turnover simply because injuries force more roster turnover, and regression dictates that good players are likely to be replaced with ones who aren’t quite as good.

Except, is this true? Certainly some teams are better at acquiring (and keeping) talent than others, so they may be able to maintain excellence despite turnover. Furthermore, career length has a long tail at the upper end (i.e. some players have very long, decade-plus careers, while no one has a career less than 0 years, with many concentrated in the 0-3 year range). And from a tactical standpoint, some positions (like QB) are able to affect the game more significantly than others. Thus, if a team happens to acquire a Peyton Manning or Brett Favre, a player who has a long and excellent career at a significant position, that team is likely to be able to maintain success for a much longer timeframe than one might expect based on FA turnover and injuries[ii].

MLB, on the other hand, has no salary cap so theoretically, teams could keep their players indefinitely (obviously practical considerations dictate otherwise), and careers are longer than those of other sports, yet its PQ parity is similar to that of the NFL. I have just discussed a reason that the NFL’s ‘good team’ (some subset of which will become championship participants and contribute to PQ) turnover might be less than expected at first blush. Are there any reasons we might suspect MLB ‘good team’ turnover is more rapid than uncapped spending and career length might suggest? I posit a few:

• MLB free agents are more likely to depart while they are still effective? The NFL’s franchise tag gives teams a mechanism to keep their most prized players no matter what (more or less). In MLB, on the other hand, once a player is through their arbitration years they are free to sign with anyone. Thus, top players like Prince Fielder, Alex Rodriguez, and Carlos Beltran regularly hit the free agent market in their primes. Very rarely do top NFL QBs or DEs, to name a couple important positions, reach the open market with their best years ahead of them. I can’t prove this (paging smart people with free time!) but I suspect it’s true.
• MLB talent has less spread? MLB has a relatively larger talent base to draw from (even neglecting international signings, which MLB has far, far more of, there are  ~670,000 America HS baseball players for ~750 Major League positions = 893 HS/ML players vs. 1.1 million HS football players for ~1700 NFL positions = 648 HS/NFL players) who are then brought into a robust multi-tiered development system. The end result is that I suspect that even the worst MLB players are closer to some theoretical maximum level of baseball performance than the worst NFL players are to theirs. Basically is Casey McGehee (worst regular third-baseman in 2011) better at baseball than, like, Curtis Painter is at football? (I don’t follow the NFL all that closely; is someone else clearly worse? Don’t say Tebow). I have no idea how to even begin to go about proving that, but I suspect it’s true. If player talent is spread less, then team talent is spread less (assuming a realistic distribution of players amongst teams), and if team talent is spread less then, all else being equal, worse teams are more likely to be able to defeat better ones, and thus make the playoffs and subsequently the championships.
• Fewer playoff participants encourages finals turnover? The NFL takes 12 teams into its postseason tournament; MLB took 8 (as of 2011), and it was effectively capped at two from any one division. Thus, if a championship participant declines slightly in talent such that it goes from being in the top-8 to the top-12, it loses the opportunity to make the championship at all in MLB, not so in the NFL (this is especially significant if the talent spread amongst teams is relatively small, as I suspect it is in MLB). Also, if the first-, second- and third-best MLB teams are all in the same division (say, NYY, BOS, and TB), and the teams are close in terms of talent, one of them could make the World Series one year and miss the playoffs the next. If similarly-talented teams are more likely to rotate in and out of the playoffs, championship participant turnover will go up. I suspect this is a big part of it; Jayson Stark and others have noted that MLB playoff participant turnover is higher, percentage-wise, than the NFL’s.
• A seven-game MLB series is more random than one NFL game? Or more accurately, are two seven-game MLB series less random than two or three NFL games (depending on top seed status)? Basically, are MLB playoffs more “random” than the NFL’s? I want to examine this in a bit more detail (but not too much, it’s hard!)

First of all, there are a couple of factors I can’t really account for. Great way to start, eh? For one, the talent spread in the NFL playoff pool is likely greater than in MLB (both by the nature of the leagues and because the NFL simply has more teams involved). For two, the NFL’s regular season is more random than MLB’s, so the true talent of the teams in the playoffs is relatively less certain.

Tom Tango estimated that true variance matches random variance at 69 MLB games and 12 NFL games, but of course MLB plays 162 games while the NFL only plays 16. The thresholds are 36 for the NHL and 14(!) for the NBA. If we define the number of games to reach this threshold as T, we see that the NFL season is only 1.33T long, while MLB and the NHL are 2.35T and 2.28T respectively, and the NBA is at 5.86T. This roughly corresponds with the PQ results, that the NFL has the most PQ turnover, followed by MLB and the NHL, and finally by the NBA. This is to be expected, because both T and advancement to the championship game derive from the same underlying principle: the predictiveness of an individual game. In other words, how likely is it that the better team actually wins a given game?

As a quick and dirty estimate, we can break each game down into a series of discrete events, and assume that the team that “wins” the most events wins the game. If we consider a team that has a 51% chance of “winning” each event, using a binomial distribution the odds of winning a given game can be estimated:

	MLB	NBA	NFL	NHL
Events Per Game:	80 (Plate Appearances)	200 (Possessions)	150 (Plays)	62 (Shots)
Favored Team Wins:	.527	.584	.565	.512

Table 5: Odds that a 1% superior team wins a given game in each league

This passes my personal ‘sniff test’ for MLB, NBA, and NFL, and I don’t know jack about the NHL[iii] so I’ll call it good. The NFL plays single-elimination playoffs featuring either 2 (2/6 teams) or 3 (4/6 teams) rounds before the championship, but the other sports all play series. Using binomial distribution to estimate the likelihood of a team with those respective winning percentages of advancing each round, we find the odds of reaching the championship for a team that is 1% better in true talent throughout the playoffs as:

	MLB	NBA[iv]	NFL[v]	NHL
Odds of Advancement:	.308	.302	.227	.147

Table 6: Odds a consistently 1% better team advances to the championship

These results suggest that the NHL playoffs are much more of a “crapshoot” than the other leagues’, which I guess is how they’re perceived, so good[vi]. They also suggest that the NFL playoffs are a lot more “random” than MLB or the NBA. More randomness should increase the number of distinct participants, so this squares with what PQ says about NFL versus MLB and the NBA, but it puts the NBA and MLB on similar footing. I suspect this is because the talent distribution is much less uniform amongst NBA playoff teams than MLB’s (and the NFL’s, for that matter), making the “consistently exactly 1% better” assumption even less correct than in the other cases.

In summary, I’ve found that the NFL and MLB have had a similar proportion of their teams reach their respective championships. Both have more parity, in this sense, than the NBA or NHL. Further, it appears that the NFL’s parity derives in some significant part from the NFL’s relatively random playoffs. Accounting for that, and the fact that MLB’s season results are more indicative of true talent than the NFL’s, suggests that MLB teams may actually be better able to become championship-caliber on a true talent level than NFL teams. The extreme variance in the NFL makes this difficult to sort out. Hopefully this piece, and the resource, will serve as a jumping-off point for further analysis, be it my own or someone else’s.