Baseball’s Head-to-Head Rule
Recently, I argued that the post-wildcard baseball rule giving division championships to teams with tied overall records but barely-untied head to head records was silly. My point was that when comparing the records of two teams with equal win/loss records within a single division, the fact that Team A has beaten Team B more times than B has beaten A tells you nothing about which team played better baseball. Sure, A beat B more often than B beat A, but why should that count any more than the fact that inevitably, there exists a Team C which B has beaten more often than A has? It all balances out, as it must, else the total W/L records would not be equal. I’m more wary of drawing similar inferences between divisions, as teams within any one division generally play each other more often than they play teams from other divisions. If, for example, the National League Worst had had a single team that was worthy of the playoffs, that team would have almost certainly had a better W/L record than Angels or the Braves, not because it played better baseball, but because its usual opponents put up less of a fight. Still, the AL West and the NL West shouldn’t be too far off, as the leaders in both divisions had one chief opponent who, until relatively late in the season, put up a credible fight. For us it was the A’s, who fell apart a couple of weeks before the end. For the Yanks and the Red Sox, it was each other, who stuck it out to the bitter end - and who were about as close to evenly matched as any two MLB teams ever could be.
Now is the time to test my theory. In the ALDS, both teams lost, but not by comparable margins. The Red Sox rolled over and played dead for the White Sox, much as the National League Worst “champions” the Padres did against St. Louis. At the same time, their allegedly equal Yankees really only seriously flubbed one game against the Angels (Friday’s), but came within a game of winning the series and finally lost with the tying and potentially winning run on base tonight. This suggests that the Angels are slightly better than the Damned Yankees this year, who in turn were either very close (as baseball rules dictate) or identical (in my opinion) to the Red Sox.
Now’s the time to test my theory. If the White Sox mow over my Angels just like they did to John Kerry’s Botsox, then we can safely assume that the Red Sox and the Yankees were exactly equal teams, and that the Angels - whose W/L record in another division tied theirs, and whose ALDS record just barely bested one of them - was excruciatingly close. But, of my Angels put up a real fight - or, for that matter, actually end up winning the series - then the mere fact that the Yanks came as close as they did to beating us in the first round is evidence that they really were a better team than Boston after all.
Finally, here’s an alternative theory, which may hold no matter how the ALCS pans out: none of this crap means squat, and I’m simply overanalyzing it to death. In that case, I plead not guilty by reason of being so friggin’ tired of debating Harriet Miers’s nomination that I’m desperate to blog about something else. So fisk me.
UPDATE: ALCS Game 1 pretty much ended any chances of testing my theory. No predictions as to how the series will pan out, but if the Angels can beat the White Sox on the second red eye in as many days, after the White Sox had three days off, it’s too late for the Angels to fare comparably to the Red Sox. Then again, as commenter Jody rightly noted, “there’s no transitivity in baseball!”
October 11th, 2005 at 6:36 am
Not so quick, oh wise one…
(1) Since the Yankees had a worse record against the rest of MLB than did the Red Sox, the Red Sox ought to have done better in their playoff match-up than the Yankees were expected to do.
(2) You don’t address the Angels-White Sox head to head record. If, for example, the White Sox swept the season match-ups, then should they ought to beat the Angels in 4… regardless of whether the Yankees or the Red Sox were the ‘better’ team.
(3) The White Sox have had time to get their pitchers rested and their rotation set for the upcoming series, while the Angels haven’t… this will have an effect on how the Angels measure up to your standard.
(4) Home field advantage: both the Angels and White Sox had it in the first round, while obviously they both don’t now. All other things being equal, this ought to hurt the visiting team, making a comparison to first round games harder to pull off.
And, you’re right… tis nice to have something other than Miers to go on about… even if it is just baseball.
October 11th, 2005 at 6:44 am
(In my best Tom Hanks voice, which isn’t really that good anyways)
Transitivity? Transitivity? There’s no transitivity in baseball!
October 11th, 2005 at 7:02 am
(1) Whatever the head-to-head record means (not much IMO), comparing not-head-to-head rates seems even further off.
(2) I don’t know the Angels-White Sox head to head record, but it doesn’t mean much anyway. Teams play very different baseball in the post-season, where every game is a do or die, than they do in the regular season, where the desire to win any particular game has to be balanced against the need to preserve resources for future games. It’s possible that games between the (perceived) top two in a division get played a little more like the playoffs, e.g., the Yanks know they can advance a full game in the standings if they beat the Red Sox, or fall a full game if they lose to them, while winning or losing against anyone else will move them only half a game. The Angels and the White Sox, being in different divisions, never had that incentive, so each game they played against each other was just another regular season game.
(3) That’s very possible. It’s equally possible that part of the reason the Chisox slaughtered the Bosox was that the Chisox clinched their division title early, while the Bosox and the Yanks went down to the wire, both as to the division title and as did the Wild Card consolation prize. Note, however, that this should have had the same effect on the Yankees, who should have been too burned out in Game 1 to beat the well-rested Angels anywhere, let alone in Anaheim. Yet, Game 1 was NY’s best game against LA/Anaheim/whatever.
(4) Home field advantage can explain the close series, maybe, e.g., the Angels vs. the Yanks (setting aside the fact that the Angels’ overall home vs. away records are pretty close to identical - or balancing it against the fact that the Yanks’ respective home vs. away records aren’t). However, it doesn’t explain going down in three straight, particularly given that one of those three games was played at home.
October 11th, 2005 at 7:24 am
I tend to agree with this particular tie-breaker with 162 games, and 10-9 between the teams. But:
1) At least in this case, the ‘extra’ game was played in Boston (if it were the other way round there might be some grounds for complaint)
2)Since both got knocked out in the first round, it scarcely matters now.
and, finally,
3)They did both get a CHANCE to play in the post-season! Here in Philly, we were arguably playing better ball than the Braves at season’s end (but that’s not unusual –Atlanta typically gets a division lead that allows it to coast a bit in September) and undoubtedly better than the West “champs”, but suffered just one two many losses at division rivals in the race most of the way. (And, not to whine –OK I will– but we had an amazing streak of horrible officiating calls that cost us a handful of games down the stretch!)
So, though I prefer Boston to the Yankees, I didn’t shed too many tears over their second-place finish.
October 11th, 2005 at 9:52 am
I’m going to go with the alternative theory. The regular season generally means nothing come the playoffs.
October 11th, 2005 at 10:12 am
I think ultimately, and I know you know this, but hey, it comes down to the fact that a tie needs to be broken between 2 teams then we should look first to how those two teams played against each other. Sure, the Yankees may have had a worse record against say (like I know) the the Texas Rangers, than the BoSox but for breaking a tie, that doesn’t get you anywhere. And if the TR have been knocked out of the playoffs, who cares that the BoSox were better against the Rangers than the Yankees, the Rangers data point has become irrelevant. (Maybe the BoSox left-vs-right balance was strong vis-a-vis the Rangers), but ultimately it remains that the Yankees and BoSox had played 19 games and the Yankees record vis-a-vis the BoSox was 10-9, the BoSox being 1 Game Back.
And, ultimately, if the rule is prior existing, than the rule may have it’s own effects, the Yankees might have played differently against the BoSox, with greater intensity during the season, as a result of recognizing how ties are broken, whereas perhaps as the season is winding down, being a couple games ahead, a team may be more willing to let numero uno pitching Ace rest and perhaps lose a game because they hold the tie-breaker.
Not having such a tiebreaker rule (say requiring a 1 game playoff) does what though? It requires the tied teams to play another game giving the other resting opposing teams an advantage, by providing them with one more day of rest for their pitchers (and generally).
October 11th, 2005 at 11:40 am
I object to your method of measuring which team is better. Why should future games be any more indicative of a team’s quality than past games?
A baseball game is a random coin flip with a biased coin. Some coins are more likely to come up heads than tails (reflecting the fact that some teams are better than others), but only by some probability p. The “best” team is the team for which p, taken over all possible coin tosses is maximum (although I’m not sure how I would compute the “taken over all possible coin tosses”).
We don’t know p, all we know is the outcomes of the trials. But there are a lot of trials so we can measure p with some confidence. To maximize the confidence in the measured p, though, you want to take as many trials as possible, and not just some small subset, such as those that occur in the playoffs.
October 11th, 2005 at 11:40 am
The Red Sox and the Yankees were 95-67– and so were the Angels. The White Sox were 99-63 and swept Boston. The Angels and Yankees fought to the last out. I don’t see a problem.
October 11th, 2005 at 11:49 am
That option gets my vote. :)
Every matchup is different. In football, the Cincinnati Bengals have been bad forever, but always played tough against Pittsburgh. In fact, one season, the Bengals went 3-13, with two of their three wins coming against the Steelers. They matched up very well against the Steelers, and not so well against everyone else.
In baseball, your Angels lost five of six to the Blue Jays during the regular season. The Blue Jays simply matched up well against you.
(Then again, the White Sox went 3-4 against the Red Sox during the regular season, and we see how that turned out…)
October 11th, 2005 at 11:56 am
Xrlq:
Oh, and I have to object to your classification of the White Sox having clinched “early.” They didn’t clinch their division (or even a playoff spot) until Sep. 29, with only three left to play. They didn’t clinch home field until Sep. 30, with two left to play. That’s hardly what I’d call “early.”
October 11th, 2005 at 1:04 pm
Joel: I doubt anyone played any differently on account of the tie-breaker rule, but will concede that once Boston and NY recognized each other as their only credible competititors, they probably did play more aggressively against each other simply because they knew a full game in the standings was at stake each time rather than the usual half game.
Doc: I don’t think future games are better indicators than past games, but I do think “must win” games are a better indicator of a team’s potential than the average “any given day” game played during the season. I also think that all other things being equal, more games is a better indicator than fewer games.
TGirsch: I’d forgotten how long it took them to clinch. Nevertheless, two exhibition games at the end (or three, depending on how badly they wanted home field advantage vs. how confident they were that the Angels and the Yankees would each lose at least one game to clinch it for them) is still enough to give them a leg up on either Boston or New York.
October 12th, 2005 at 10:10 am
Your point is probably correct, although it does seem like in football, where the tiebreakers are more common and more important, teams do respond more to the tiebreaker rules.
October 12th, 2005 at 8:34 pm
Apparently, some umpires have a difficult time applying laid down rules. Who know what affect that has on your theory though.
October 12th, 2005 at 8:42 pm
After tonight, I suspect you have more important rules to interpret than the head to head playoffs.