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Friday, July 12, 2002

Baseball Schedules Aren’t Always Fair

Rich gives the West Coast fans something to complain about.

Just before interleague play was about to begin this year, A’s Manager Art   Howe was asked by a beat reporter if he liked the new interleague schedule,   where his club would be playing a whole new set of opponents, including both   of his former clubs, the Houston Astros and the Pittsburgh Pirates? Howe said,   "no," he would rather that interleague play would be done away with   entirely. He was particularly upset with the fact that while Oakland would be   playing 6 games against the San Francisco Giants, a quality opponent, the A’s   divisional rival, the Mariners, would be facing two lesser lights of the NL   West, the Rockies and the Padres. Little did Art know at that time that his   2002 club would post the best interleague mark ever for one season, 16-2, and   that the A’s would maintain the best overall interleague record since 1997.

The idea behind interleague play, of course, is not to increase fairness in   the major league schedule. The hope is to attract more fans to more games. And   for the most part, that seems to have worked well.

Nonetheless, the criticism that the schedule is unfair remains. Teams in each   of the 6 divisions compete for a division title - and the spot in the playoffs   that goes along with each crown - yet within those divisions, some teams have   distinctly more difficult schedules than their intradivisional rivals. And more   egregious is the schedule differentiation among clubs competing for each league’s   wild card. Due to the unbalanced schedule, where clubs are pitted 19 times against   intradivisional opponents but as few as 6 times against extradivisional foes,   teams in strong divisions are at a definite disadvantage. The very unbalanced   interleague schedule potentially makes the wild card race all that much more   unfair.

Fairness would be maximized by getting rid of interleague play, league divisions,   and the unbalanced schedule. This, of course, was the system until 1968. Both   leagues had 10 teams, and all 10 in each league played a balanced schedule of   162 intraleague games. With 9 opponents, you simply faced each one 18 times   in a season. However, this did not mean that the quality of opponents was perfectly   equal for all clubs, because a great team like the ‘68 Tigers necessarily had   an easier schedule than a sorry team like the ‘68 Senators. Why is that? Because   Detroit never had to face Detroit. And Washington missed out on getting to play   a team like Washington. But compared with everything else that has been tried   since, the pre-1969 set-up was the fairest possible.

In 1969, when the Royals and Pilots joined the AL, and the Padres and Expos   entered the NL, the leagues split into West and East divisions for the first   time. They could still play balanced schedules, but no longer was it certain   that the best teams would make the playoffs. Why not? Because in some years,   it would be the case that the best two teams were playing in the same division.   Take a look at the National League in 1973, for example:

        W  L  WL% GB
   CIN 99 63 .611 -- 
   LAD 95 66 .590 3.5
   SFG 88 74 .543 11.0
   NYM 82 79 .509 --

The Reds won the West, and the Mets won the East. But there was no doubt that   the Dodgers and Giants were better than New York was that year. Had the 1968   system still been in place, the Mets would have merely been a footnote as a   4th place ballclub. Instead, they nearly repeated the Miracle of 1969, after   first edging The Big Red Machine in the playoffs, and almost taking out the   Athletics in a 7 game World Series.

So with all the changes that have been made since the halcyon days of 1968,   how unfair is today’s schedule? Are we getting the best teams in post-season   play? As it turns out, that’s not the easiest question to answer. First and   foremost, 8 teams now make the playoffs - a fourfold expansion from 34 years   ago - so it is nearly certain that the best and second best teams will make   the post-season in 2002. (For a full explanation of how and why this doesn’t   always happen, see the excellent article by Jeff Hildebrand in the back of the   2002 Baseball Prospectus, in which he examines the interplay of the schedule,   the divisions, and issues of fairness).

When it comes to testing fairness of the schedule, we are mostly talking about   how marginal playoff contenders are affected. That is, the 3rd, 4th, 5th, and   maybe 6th best teams in each league that are competing for a wild card spot.   One point Hildebrand covers is the fact that, over time, teams in a 4-team division   are at a distinct advantage over clubs in a 6-team division. But again, for   the most part, that distinction affects not the best or second best team in   a league. Rather, most years, it impacts the teams competing for the last playoff   spot.

To get back to the question at hand about fairness in today’s particular schedule,   I first examined all 30 teams’ schedules up to the All-Star break. To do that,   I calculated the win-loss records of each team’s opponents, extracting the games   that each team in question played against its opponents. That sounds confusing,   but looking at the example of one team makes the methodology clear.

Here’s how I handled the Blue Jays. Toronto has played 86 games, so far. 11   of those games have been against the Red Sox, 6 versus the Athletics, 3 against   the Dodgers, and so on. The Red Sox’s record against all teams is 52-33 (.612).   However, against Toronto, Boston is 10-1. Therefore, the Red Sox’s record against   all non-Toronto teams is 42-32 (.568). So for those 11 games, the Blue Jays   are credited with playing a .568 team. Against Oakland, Toronto won 5 of its   6 games. The A’s overall record is 50-38 (.568). But against all non-Toronto   teams, Oakland is 49-33 (.598). So for those 6 games, the Blue Jays are credited   with playing a .598 club. Counting all the teams that they have played so far,   Toronto’s weighted opponents have a mean winning percentage of .530. (That happens   to be the most difficult of any team in baseball.)

Here is how the divisions break out:

   TOR 86 .530
   BAL 85 .513
   BOS 85 .511
   TBD 85 .510
   NYY 85 .504
   KCR 85 .498
   CWS 88 .489
   MIN 89 .485
   CLE 85 .478
   DET 85 .478
   SEA 88 .518
   OAK 88 .516
   ANA 86 .491
   TEX 86 .490
   NYM 87 .518
   ATL 88 .513
   PHI 86 .509
   MON 87 .489
   FLA 88 .484
   CIN 87 .506
   MIL 88 .506
   HOU 86 .492
   CHN 86 .489
   STL 85 .488
   PIT 87 .469
   COL 88 .525
   LAD 88 .511
   ARI 87 .507
   SFG 87 .505
   SDP 88 .504

Among the teams now contesting for a division title, the pre-All-Star schedule   has favored the Yankees over the Red Sox, the Indians over the Twins and White   Sox, the Angels over the A’s and Mariners, the Marlins and Expos over the Braves   and Mets, the Cardinals over the Reds, and the Giants and Diamondbacks over   the Dodgers. Some of these discrepancies have been big (such as in the AL West   and the NL Central); others are quite small (such as in the NL West); and others   are probably not significant (such as in the NL East, where despite a disadvantage,   the Braves are still well ahead).

To see how each club’s post-All-Star schedule compares, I used a slightly different   methodology. I took each club’s opponents’ Pythagorean record (based on all   games played so far this season), and multiplyed that by the games each club   will play against it in the second half. Because of the labor involved in subtracting   the runs scored and runs allowed in each head-to-head match up, I did not extract   those runs when calculating P-records. For example, the Expos played the Reds   3 games prior to the All-Star break. Those two teams will play 3 more times   after the break. To weight the difficulty of that match-up for Montreal, I simply   used Cincinnati’s Pythagorean Winning Percentage (.473), instead of recalculating   it after subtracting out the runs the Reds scored and allowed against the Expos.   In most cases, I don’t think this discrepancy will greatly affect the results.

Here, then, are the weighted schedules of all teams following the All-Star   break:

   TBD 77 .536
   TOR 76 .505
   BAL 77 .496
   BOS 77 .487
   NYY 75 .473
   DET 77 .518
   CLE 76 .502
   MIN 73 .484
   KCR 77 .482
   CWS 74 .469
   TEX 76 .539
   ANA 76 .522
   OAK 74 .503
   SEA 74 .490
   PHI 76 .515
   MON 75 .512
   FLA 74 .511
   NYM 75 .501
   ATL 74 .488
   PIT 75 .508
   CHN 76 .492
   MIL 74 .491
   STL 77 .480
   HOU 76 .478
   CIN 75 .474
   SDP 74 .530
   COL 74 .510
   LAD 74 .504
   SFG 75 .501
   ARI 75 .493

Judging the difficulty of each team’s schedule for the second half, based on   how the clubs it still must face did in the first half, is far from perfect.   In some cases, those just aren’t the same teams. Seattle, for example, has not   yet played the Indians. So the Tribe they will face 7 times in August is one   without Bartolo Colon, perhaps without Jim Thome, and with a gimpy Omar Vizquel   (who is now playing with a torn labrum). Nevertheless, we get a pretty good   idea who is favored by the games each has yet to play.

In the AL East, the Yankees (again) have it easier than the Red Sox; in the   Central, the Twins have a tougher-looking run than the White Sox; in the West,   the Mariners appear to have it much easier than the Angels and Athletics; in   the NL East, the Braves should benefit from their remaining games; in the Central,   there is not a lot of difference among the top-tier teams; and in the West,   Arizona has a small edge over the Giants and Dodgers.

Combining the pre-break results with the expected post-break results, we can   see which teams in each division are most and least likely to benefit from their   2002 schedules. Here are the weighted results for all 30 teams for all 162 games:

   TBD 162 .523
   TOR 162 .518
   BAL 162 .505
   BOS 162 .499
   NYY 162 .489
   DET 162 .497
   KCR 162 .490
   CLE 162 .489
   MIN 162 .485
   CWS 162 .480
   TEX 162 .513
   OAK 162 .510
   ANA 162 .505
   SEA 162 .505
   PHI 162 .512
   NYM 162 .510
   ATL 162 .501
   MON 162 .500
   FLA 162 .497
   MIL 162 .499
   CIN 162 .491
   CHN 162 .490
   PIT 162 .487
   HOU 162 .485
   STL 162 .484
   COL 162 .518
   SDP 162 .516
   LAD 162 .508
   SFG 162 .503
   ARI 162 .501

In the divisional races, these are the teams that will likely be the beneficiaries   of their schedules: the Yankees (.010) over the Red Sox; the White Sox (.005)   over the Twins; the Mariners and Angels (.005) over the A’s; no real advantage   in the NL East; the Cardinals (.006) over the Reds; and the Diamondbacks (.007)   over the Dodgers. With the possible exception of the AL East, none of those   looks like a dramatic difference. However, in the wild card races, at the extremes,   the schedule may have more of an impact on who makes the playoffs.

Here are the top contenders in the American League:

   OAK 162 .510
   ANA 162 .505
   SEA 162 .505
   BAL 162 .505
   BOS 162 .499
   NYY 162 .489
   CLE 162 .489
   MIN 162 .485
   CWS 162 .480

If the race were to come down to Oakland and Chicago, the White Sox’s schedule   advantage may end up keeping the A’s out of the post-season. Chicago’s edge   is clearly significant. All else held equal, that could amount to almost 5 games   in the standings over 162 games.

Here is the NL picture:

   LAD 162 .508
   SFG 162 .503
   ATL 162 .501
   ARI 162 .501
   MON 162 .500
   FLA 162 .497
   CIN 162 .491
   HOU 162 .485
   STL 162 .484

Though not as extreme as in the AL, it’s possible that the Cardinals enjoy   an almost 4 game advantage over the Dodgers (after 162 games), based on the   schedule alone.

My purpose in this examination is not to call for a reversion to 1968 or to   push for any changes at all. I happen to like divisional races, the unbalanced   schedule, and interleague play. My only goal was to see just how much effect   the schedule can have on who does and does not make the playoffs. Insofar as   the current schedule seems to have hardly any effect on most divisional races,   that’s all the more reason to not go back to olden times. And while it is true   that there is a significant degree of unfairness when it comes to winning the   wild card, I think it’s most important to recognize that that is only a determination   of who is the third, or fourth, or fifth best team in a league. The best teams   still make it to the post-season, and from there, as the 1973 Mets showed, anything   can happen.


Rich Rifkin Posted: July 12, 2002 at 06:00 AM | 9 comment(s) Login to Bookmark
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   1. MattB Posted: July 12, 2002 at 12:35 AM (#605533)
I agree with Tim. The only potential difference here that rises above the level of statistical noise is the great White Sox/ Oakland wild-card chase. And it only becomes "unfair" if the White Sox use their easy schedule to parlay their first half sub-.500 record into a whipsaw advance over Oakland, Anaheim AND Boston to win the Wild Card. (They are currently 13 games behind Boston in the loss column, and it would require a monumental tripartate collapse of historic proportions for them all to drop behind Chicago.)

On the margins, I couldn't care less if the fifth best team in the league makes the postseason instead of the fourth. As long as the best team in each league makes the postseason, I don't think anyone has anything to complain about. The second best has no "rights" to complain about losing.

And what are the chances that an unbalanced schedule will result in the best team having the fifth best record in the league (or the third best in their division)? I'd say significantly less than the same results coming from half a dozen bad hops, two games where the ump has an inconsistent strike zone, and one scheduling quirk where you have your 2, 3, and 4 pitchers up against their 1, 2, and 3 pitchers.
   2. Alan Shank Posted: July 12, 2002 at 12:35 AM (#605534)
"And while it is true that there is a significant degree of unfairness when it comes to winning the wild card, I think it's most important to recognize that that is only a determination of who is the third, or fourth, or fifth best team in a league. The best teams still make it to the post-season, and from there, as the 1973 Mets showed, anything can happen."

Your definition of "the best teams" is based on their W-L record, which is affected by the division they're in and the schedule, so it's sort of a circular argument. Even if one accepts that definition, it's only the "best" two teams that will make it, since the team with the best record will win its division and the team with the 2nd best will either win its division or the wild card.

I think the biggest problem with the current setup is the 3-division arrangement, not interleague or the unbalanced schedule. As you pointed out, a team in a 4-team division has a better chance of reaching the playoffs, over time. The biggest problem, however, is the chance that a mediocre team will win its division and make the playoffs. As you said, anything can happen (see 1987 Twinkies). In 1994, baseball may have been saved by the strike from the embarrassment of having a sub-.500 division "champion."

Look at this year's AL Central. Over at the "High Boskage House" baseball site, Eric Walker rates the teams by the Pythagorean projection, not of their runs scored/allowed, but of their TOP and TPP, which are his own run-estimation tools. I think this is a better estimate of a team's strength than W-L or Pythagorean based on runs. The NL Central teams look like this:
MIN .503
CWS .498
CLE .439
KC .393
DET .368
One of those teams is certain to make the playoffs, and then... doesn't the AL have home field in the WS this year?

What the unbalanced schedule does, more than anything else, is hide the weakness of a division. If Texas had had more games against the other weak AL West opponents in 1994, they might very well have been at least over .500. It's like inter-breeding.

I think the best way to examine different alignment and schedule options is to do a study like Bill James did in the 1989 Abstract, which was, I believe, the first one he didn't write. It was called "How Often Does the Best Team Win?", or s.t. like that. He developed an algorithm that assigned "true quality" figures to all the teams, tweaking it until he got a distribution of team wins very close to that in real baseball when the computer "played" the season. This way, the "true quality" of all the teams is known; of course, when you play the season, the "best" team does not always come out with the best record. I have a "C" program that does the same type of study. It's amazing the amount of variation you get. I even did a study where each team was exactly a .500 team, and had seasons where teams won or lost 100 games!

The trouble with trying to study the current setup this way is that there is no algorithm for playing the schedule, since the schedule is so arbitrary. You'd have to actually have the program read the schedule, or at least have a data file indicating in some way each team's inter-division and interleague opponents.

I really hate interleague play, but there are some aspects of the unbalanced schedule that I like, particularly when you get two or three contending teams playing each other the last week of the season. Ideally, I would like to see two more teams (fat chance!) so we'd have 32 teams, divided into four 8-team divisions.

That leads to the question of the extra round of playoffs. Clearly, the extra round reduces the probability that the best team in each league, however you define it, will reach the World Series. Baseball doesn't care about that, of course. But with the 4 X 8 setup, they could still allow four teams/league in, whether it would be the two division winners plus the next two best records, or just the first- and second-place finishers. Eight-team divisions would substantially reduce the chances that a weak team would reach the playoffs.

Alan Shank
Al's Baseball Tidbits

   3. jimd Posted: July 15, 2002 at 12:36 AM (#605562)
There are really two different issues wrapped up here; one is schedule fairness, the other is the relative importance of the regular season vs. the playoffs.

Even during the 16-team era, the two best teams were not guaranteed to make the World Series. They may have been in the same league, and they probably were about half the time. No W-L analysis will prove the point, one way or the other, because there is no direct way to compare the relative quality of the leagues, just indirect inferences from changes in the statistics of players moving from one league to another.

However, it was always fair, because the teams competing for a given playoff spot always played the same schedule (at least they were supposed to when the schedules were printed; there always were games postponed and often they were not made up).

The advent of division play did not make things unfair. Each division had its own reserved spot and its teams played the same schedule. What changed was the guarantee that the best team made it into the World Series. It was obvious when one division in a league was distinctly inferior to the other. Also, upsets at this pre-World Series playoff level did not settle too well with the traditionalists.

Unfairness began, in a small way, when each league expanded to 14 teams (AL 1977, NL 1993). A fair schedule didn't fit into 162 games, so a couple of unmatched games resulted when division rivals compared schedules.

The wild card combined with the unbalanced schedule increased the unfairness dramatically. Neither by itself is unfair. A wild card in a balanced schedule is fair. An unbalanced schedule with no wild card is fair, as long as each team in a division plays the same schedule.

The introduction of the wild-card arises from a different concept of fairness. It is argued by some that it is somehow unfair for an inferior team to be in the playoffs while a superior team stays home even though it lost its division to an even better team. This attitude arises when the playoffs become more important than the regular season. From this springs the concept of a wildcard playoff spot which rewards the best runner-up team, which undermines the concept of the pennant race. Once a wild-card is introduced, a pennant race can no longer happen at the highest level (the two best teams in baseball or nearly so), but only at the level of the weaker teams that fill out the playoffs (the race is for the wildcard spot or for a division title weaker inferior to the wildcard team).

The wild card was introduced by the NFL in 1970 after the merger/realignment with the AFL. The members of the new divisions did not (and could not) play anything like the same schedule, and the wildcard concept was peddled as a mechanism to prevent the best team in the conference from missing the playoffs due to an unfortunate inequity in the scheduling. The NFL was also still smarting from heavy criticism arising from a situation in 1967 when the two best records in the league (11-1-2) were in the same division and one team did not make the playoffs due to the tiebreaker rules (another newly introduced concept; before that year championship ties had always been broken on the field, but the TV schedules did not permit that luxury anymore). The criticism was more of the tiebreaker rule concept (which could not be dumped) but it was defused by the wildcard by saying "See, the best team still makes the playoffs".

Baseball would have no need of the wildcard concept as long as division rivals played the same schedules (so fairness is maintained) and schedules were heavily unbalanced (to mask any inequities of division strength).
   4. Cris E Posted: July 18, 2002 at 12:36 AM (#605572)
jimd touches on a very important point: wildcards and unbalanced schedules are both trying to do the same thing (ensure tat the best teams make the post season), but they interact in ways that undercut that mission.

An unbalanced schedule ensures that your division champ is the best team in the division. The wildcard tries to ensure that you get the best teams in the League by reaching past division winners to examine the regular season results. The trouble is that you can't compare teams across the league if the schedules aren't largely similar. And you don't need to be completely accurate about the division winner being the best team in the division if you have a safety net like the wild card.

I was going to state my preferences for a playoff structure (ie. an occasional Cinderella or bridesmaid makes for good history, so no wildcards and no crying in baseball) but I'm not sure the best way to get there. (Well OK, the best way is four divisions per league and no wild card, but I was thinking "best possible".) I guess I care more about a meaningful regular season than the getting the "right" teams in the playoffs, so unbalanced without wildcard would be best followed by balanced with wildcard followed distantly by what they're doing now.
   5. jimd Posted: July 18, 2002 at 12:36 AM (#605576)
Here's the thing. To me it's an either-or situation.

If you think the playoffs are the more important, then you want wild-cards. Play a balanced schedule and scrap the divisions; take the top N teams by record for the post-season tournament. The only thing the divisions do is make the bad teams seem a little less bad; fourth place sounds so much better than eleventh place. Realize that there are no more pennant races, just exciting Nth-place playoff races, that will often be more interesting than the eighth-place races in hockey. The fans of the teams involved will always be excited; neutral observers less so because the team is just playoff filler anyway, unless it turns into Cinderella. Since top-quality teams would tend to be of playoff quality for a period of years, some very good playoff rivalries will develop.

If you want pennant races, then you want divisions. Scrap the wild-cards and drastically unbalance the schedule (assuming that you can't bear to give up inter-divisional play altogether). But keep the schedules identical within the division to keep it fair. The imbalance will hide the relative strengths of the divisions (though statheads like me will run math models to draw conclusions from small samples), while at the same time increasing fan interest in the team rivalries. Realize that any attempt to bring in runner-up teams will undercut the pennant races. There will probably be an exciting pennant race or two each year. If inter-divisional play is severely restricted or eliminated, then the playoff matchups will be more intriguing due to mutual unfamiliarity.

Each format has its drawbacks and its charms. But you can't have pennant races AND have the N best teams make the playoffs.
   6. jimd Posted: July 22, 2002 at 12:36 AM (#605616)
Please, no 9 game World Series. 7 is ideal. 9 drains some of the tension away. They dumped that idea 80 years ago after a 3-year trial.

A note on scheduling. 162 game baseball schedules have a rhythm that must be observed or they won't be acceptable. They should be decomposable into 52 blocks (26 weeks, 2 series a week), 46 3-game series and 6 4-game series. (Look at your favorite teams season schedule and you'll see what I mean.) You can rearrange a pair of 3-game blocks to create a 2-game and a 4-game series, do it a few times even, but you don't want too many 2-game series, because the players and fans hate them. You do need three or four 2-gamers, usually for Opening day (to include a weather date), and to create an All-Star break, with a couple of 2-game series in the following week. (51 blocks also works with 42 3-gamers and 9 4-gamers; in this schedule, no 2-gamers are needed after the All-Star break.)

   7. jimd Posted: July 24, 2002 at 12:37 AM (#605635)
Mathematically, you guys are on the same page:
"pro-rated intraleague winning percentage"
(division wins/3 + wins vs. other 2 divisions) divided by 84

If you multiply that formula by 252, you get points:
(division wins + 3*(wins vs. other 2 divisions))

We can agree to disagree on the 9-game series. In a 7-game series, every game is either an elimination game, a tie-breaker game, or has the potential to tie the series, except for a small "dead-spot" at 2-0. (I videotape this game for later, and pay attention to my neglected wife if and when this situation is reached.) A 9-game series increases this "dead-spot" to include 3-0 and 3-1 as well (my wife will be in favor of this change). As I pointed out earlier, 80-odd years ago they tried it for 3 years and didn't like it (1919-1921).

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