Big Game Pitchers, Part II

January 21, 2014

                To determine whether or not someone is a Big Game Pitcher, we have to begin by determining what is and what is not a Big Game.

                I set up a point system to assign "Big Game Points" to every major league regular-season game played since 1952.    Some of you who are more clever than I am with programming and certain types of calculations could approach this by figuring what each team’s chance of reaching the World Series would be if they did win this game and what it would be if they didn’t win this game, and then identify the biggest games by finding the games which have the biggest impact on a team’s chance of reaching the World Series.    That’s a really complicated programming assignment, however, because you have to look at every other team in the league or the division to find the team with the best won-lost record, and then you have to look at every other team that could possibly beat you out for the Wild Card, etc.

                If you can do that, I don’t question but that your method would be better than my method, but I don’t know how to do all of that, so I took a different approach.    Every game starts with a base of 100 points, and the reason that every game starts with a base of 100 points is that if you don’t give each game a base, then, using the approach I am using, you would reach the conclusion that games in September were like a hundred times more important than games in April.    Games in September ARE much more likely to be "Big" games than games in April; in fact, in my system, there are no Big Games in April or May, but the value ratio isn’t a hundred to one, either; it’s more like four to one.

                OK, so each game starts out at 100 basis points, and we increase that by one point for each game that goes off the schedule, so that the second game of the season is 101, the third game 102, the fourth game 103, etc.

                Except that Big Games are for winners; if your team is 45-70 in August, then you’re not going to play any Big Games, whereas if you are 70-45 and in a pennant race, then you will.   So actually, we increase the game values by two points if a team wins a game, by one point if they lose, so that if your team is 45-70, then in Game 116 you have a Big Game Score of 260 (100 + 115 + 45), whereas if they are 70-45, then in Game 116 you have a Big Game Score of 285 (100 + 115 + 70).  

                We’re just getting started.    A game is a bigger game if you are playing a divisional opponent than if you are playing a team from the other division or the other league or a team from some other sport, so we add a 25-point bonus to each game played against a "direct" opponent.    Prior to 1969 all games were played against direct opponents, because prior to 1969 there were no divisions and there was no inter-league or inter-species play, so prior to 1969 every game gets the 25-point bonus, whereas now, not so much.

                A game is a bigger game when you are playing a good team than when you are playing a bad team; that is, from the Red Sox standpoint, it is a bigger game when we are playing the Yankees than when we are playing a last-place team, or, looking at it from the standpoint of the 2013 Arizona Diamondbacks, it is a bigger game when you are playing the Dodgers than when you are playing Rockies.   From the standpoint of the Cincinnati Reds, it is a bigger game when you are playing the Cardinals than when you are playing the Cubs, at least in 2013.   I am sure 2014 will be all different.

                Anyway, I initially factored this in by adding in the opposition’s wins minus losses (based on their record so far this season), but it became apparent that this adjustment was too large.    Suppose that your team has a record of 70-70, but the opposing team has a record of 90-50, and suppose it is a divisional opponent.   The "Big Game Score", with that adjustment, would be 100 + 140 + 70 + 25 + 40, or 355.  

                But that adjustment turned out to be too large, because what that does is make it a Big Game if your opponent has a really good won-lost record, regardless of your own won-lost record.    Think about it; if YOUR team was 90-50 and the other team was 70-70, the Big Game Score would be 335 (100 + 140 + 90 + 0).    Because the OTHER team is 90-50, it goes up to 355.   That’s not right.    At 90-50 you’re not really 40 games over .500; you’re 40 half-games over .500, so the appropriate adjustment is not 40 points, but 20.   That way, when a 90-50 team plays a 70-70 team, you have a Big Game Score of 335 for each team.  

                Except that you wouldn’t, ordinarily, because if your team was 70-70 and the other team was 90-50 and you were in the same division, it wouldn’t be a Big Game at all, because you’d be dead.   You would be virtually eliminated.

                Ah, there’s the rub.   We discount games, and discount them sharply, after a team has been eliminated.  After you’ve been eliminated, no game is a Big Game; it’s just playing out the string.  But this team hasn’t been eliminated; they’re merely dead as a doornail.   If I allowed this to stand as a Big Game based on the fact that the 70-70 team has not been mathematically eliminated, the Big Game lists would be polluted by many, many games of teams which had no realistic chance of winning.

Here we hit a truly interesting question:  When, exactly, is a team Virtually Eliminated?    It is much like my somewhat famous little heuristic:  The Lead is Safe.   Same problem:  where, exactly, do we draw the line between a team being in a difficult position, and virtually eliminated?

It is a truly interesting question which will lead us into some truly un-interesting math.   I have written a formula to determine when a team has been Virtually Eliminated, and I will explain that formula to you in a moment, but first let me say this.   There is no right answer here.   There IS no exact moment at which a team is "virtually" eliminated.   Is a team virtually eliminated when they are 5 games back with 5 to play, or not?    I don’t believe anybody has ever come back from that situation to win—but it certainly isn’t impossible.   If enough teams were exactly five games back with exactly five to play, sooner or later one of them would come back to win.    Are you virtually eliminated if you are six and a half back with eight to play?   Five and a half back?    There is no right answer here.

We are flying in the face of Yogi Berra’s most famous axiom:  It ain’t over ‘til it’s over.    Saying that it ain’t over ‘til it’s over is a totally unsatisfactory and totally unworkable answer from the standpoint of this particular problem, so we have to determine when it ain’t over, but she’s packed her bags and bought a bus ticket and called her momma.    This is how we do that.

First, figure the team’s Virtual Elimination Percentage; I’ll explain how in a moment.

Second, figure the Schedule Completion Percentage; I’ll explain how in two moments.

Third, if the Virtual Elimination Percentage, raised to the power 1.8, is greater than the Schedule Completion Percentage, then the team is Virtually Eliminated.

The Virtual Elimination Percentage is figured as the highest win total in the division (or in the league, if you have no divisions in your league), plus the number of losses for the focus team, divided by three plus the number of scheduled games (which is 162 in modern baseball.)   (If the number of losses for the focus team plus the number of wins for the first-place opponent exceeds 162, the team has been mathematically eliminated.   The "+3" is put in this formula as a protection to ensure that we don’t classify a team as Virtually Eliminated in the last four or five days of the season.   In the closing days of the season, if you’re not mathematically eliminated, then you have a realistic chance to win, no matter what.)     Anyway, if your team is 70-70 and the first-place team is 90-50, then your Virtual Elimination Percentage is .9697, or 160 divided by 165.

The Schedule Completion Percentage is easy; that’s just the percentage of your scheduled games (not including ties) that you have played.   If you’re 70-70 and scheduled to play 162 games, your Schedule Completion Percentage is .8642.   

Raise the Virtual Elimination Percentage (.9697) to the power 1.8; you have .9461.   That is greater than .8642, so. 70-70, with another team at 90-50, you have been Virtually Eliminated.   

Stick with me a minute.   Suppose the first-place team is 90-50.   If your team is 80-60, your Virtual Elimination Percentage is .9091; raise that to the power 1.80, you get .8424.  That is LESS than the Schedule Completion Percentage, so your team has NOT been virtually eliminated.    At 78-62, you haven’t been Virtually Eliminated—but at 77-63, you have been.    We have to draw a line somewhere; that’s where we draw it.   13 games out with 22 to play, you’re dead. 

I intended for this to work out so that we could use the SQUARE of the Virtual Elimination Percentage, rather than raising it to the power 1.80, but. ..raising it to the square turned out to be just too damned tolerant, too lenient.  (Thanks, Obama.)  Using the square, rather than the power 1.80, a team was not virtually eliminated if they were 77-63 when another team was 90-50.   My judgment is that, in that situation, you ARE virtually eliminated.  77-63 against 90-50. . .you’re absolutely not winning.

Actually, raising it to the power 1.80 is too tolerant, too.  1.60 or 1.70 would probably be more realistic, but I wanted to err on the side of caution.   I do not want to declare a team dead as long as they could still rally and win, even if it would take a miracle.    But—and this is a tremendously key point, so I’m going to repeat this phrase about four times—when you err on the side of caution, it is still an error.    When you err on the side of caution, it is still an error.     I am not looking to declare a team "dead" if they are not COMPLETELY dead.   A doctor in an emergency room will continue to work on a trauma victim, knowing full well that the patient is dead, because there is no percentage in declaring him dead when he might somehow, conceivably, still be brought back to life.    When declaring someone dead, you always err on the side of caution.   Same here; when declaring a team dead, we err on the side of caution—BUT WHEN YOU ERR ON THE SIDE OF CAUTION, IT IS STILL AN ERROR.

The importance of this is to acknowledge that our system is not perfect, and to declare, furthermore, that it cannot be made perfect.    A system of this nature will always contain error.   But I’m mirroring the way that real teams think about this.   I will tell you this:  that in 2004, when the Red Sox were down to the Yankees three games to none in the playoffs and had just been humiliated 19-8, we met back in the bowels of Fenway Park, where an important person in the Red Sox system said, "We have to look at it like we are still going to win this thing, like we are going to go out and win the next four games.   Of course we know it won’t happen, but that is how we HAVE to look at it."   And. . .son of a bitch, they did it.    In real life, you never concede defeat until there is just no conceivable way you can come back and win it.  So. ..I don’t declare a team Virtually Eliminated until there is just no conceivable way they can come back and win it.

But this policy causes us to include in the list of Big Games a certain number of games by teams which have, in fact, only the slightest chance of winning.  We discount a team’s Big Game Score, after the team is Virtually Eliminated, so that no game by a team which has been Virtually Eliminated will be included in the Big Game lists.

Small note. . .sometimes the math is screwy in the opening days, so there is a codicil in the procedure that says that no team is Virtually Eliminated until they have lost at least 40 games.   Also, there is a rule in the system that says that if your won-lost record is 0-0 (Opening Day), add 100 points to the Big Game Score.   Because of that, the Big Game Score for Opening Day is 200, or, since teams are normally playing in-division on Opening Day, normally 225.    This has nothing really to do with the study, since 225 isn’t a big enough number to designate the afternoon’s amusement as a Big Game, but it does mean that on a bad team that is virtually eliminated in June, their biggest game of the season is Opening Day.   I put that rule in because it is realistic, but it doesn’t have anything to do with the study.

    But I still had a problem, at this point, which was that I had too many games being listed as Big Games by teams that were not Virtually Eliminated, but which could not honestly be said to be in a pennant race.   A team is 60-65 in late August and 15 games behind; under the right circumstances, it can show up as Big Game, which is not right because if you are 15 games behind in late August, it is not a Big Game.    I had to put in an "Early Elimination Penalty".

What is the Early Elimination Penalty?   Well, if

a)  A team has lost at least 40 games,

b)  Their "Virtual Elimination Percentage" exceeds their Schedule Completion Percentage by at least .2000, and

c)  That team also has no chance at a Wild Card,

Then we apply an Early Elimination Penalty, which has the effect of removing that team’s games from the Big Game list.   

With, however, two more obscure and annoying provisos—

1)  That we don’t apply the Early Elimination Penalty to any team with a winning record before the first of September, and

2)  That we don’t apply the Early Elimination Penalty to any team with a winning record in the Wild Card era, even in September. 

All of that sounds complicated and obscure, and it is—but even with all of those outs and exclusions, the Early Elimination Discount is applied to 42,751 games in our study, so. . .it’s not like it’s a trivial adjustment.    It is a necessary adjustment to prevent the Big Game List from being polluted by teams that couldn’t find a pennant race with a bloodhound, even though they have not been either mathematically eliminated or virtually eliminated.

When you get through all of that, of course, you have to figure out whether a team has been not merely Eliminated or Virtually Eliminated, but also whether they are still in the hunt for a Wild Card.    And when we have done all of that and eliminated all of the teams which need to be eliminated, we will have a Big Game Score for every team in every game of every season.


COMMENTS (13 Comments, most recent shown first)

I'm probably not the first to be reminded of this, but the "early season" question is interesting in light of the 1984 Tigers (now, there's a "direct" Jack Morris reference, eh?).

As anyone on this site will recall, that team jumped out to a 35-5 record to start the season and then cruised to the pennant, ultimately winning the Series handily.

So... are we saying that none of their games, after about Memorial Day, were "big games" (at least not for them)?

I, too, am anxious to see how many big games Jack started (and how that stacks up with the rest of the field); But I will be specifically watching for anything in the 1984 season.

And... incidentally, Morris doesn't even win that Game 7 if Pendleton's double drives in a run (no, I'm not going to talk about the particulars, just saying that if a run scores, Smoltz and the Braves likely win).
And... haven't some of us argued here that Gene Tenace certainly COULD be considered a marginal Hall of Fame candidate? At the least, there is an article here that compares him favorably with Jim Rice (who also might NOT be a legitimate Hall of Famer, but at least is a marginal candidate). That's about enough stumping.
9:37 AM Jan 22nd
mskarp - it leaves that 'how sensitive the results are' question open, in the abstract … but not necessarily in the real world. Mathematicians and lab scientists could always question the 'approach' used in a court of law.

When I use a points system to determine that "Black" works better as an eBay keyword than "Brown," yes, the question is open as to how sensitive that result was to the fact that I measured results in the winter rather than the spring. But guess what?

1. My sales went up. Period.

2. I can TRIANGULATE my results, isolating variables and using trial-and-error to get ever-increasing sales.

Bill is going to present results that work better than what we had before, and results that position others to improve them. Mathematicians will cheerfully question the slop in the method. Non-mathemeticians will continue to enjoy improved insight into the real world.

3:54 AM Jan 22nd
mskarpelos is right, I think, that the partisans will fail to be convinced, but the reason for that is more likely to be that the number of games defined as 'big' is going to be a whole lot higher than they (the partisans) expect. Ask a Morris advocate how many big games Jack started in his career and he will hem and haw and finally say, "Um, five?" Ask him to identify them and he will probably only be able to come up with the 7th Game in 1991.

But that's not why I'm still waiting to be convinced.

The method described here attempts to identify big games objectively rather than by perception. Or rather it attempts to identify the conditions that will cause a game to be perceived as 'big', since if Morris or anybody else is a 'big game pitcher' it's because he pitches expecially well in games he perceives to be big, even though the casual fan may not.

If that's right, this method will underestimate the perception of the importance of an early-to-mid-season game played by teams who expect to be rivals. Even early-to-mid-season games between the Red Sox and Yankees (or the Diamondbacks and Dodgers, or the Cardinals and Reds, or the A's and Rangers) are perceived as big, regardless of the teams' records at the time.

I'm not sure how significant this is. Maybe it's a good thing to make it harder for games in the first half of the season to qualify as 'big', maybe it's not.

In any event I wait with bated breath to learn how many big games Jack Morris actually started.
9:45 PM Jan 21st
I'm uncomfortable generally with basing any analysis on seemingly arbitrary numbers like 1.8, 100, 25, etc. They're not really arbitrary, of course. Bill has a good sense of what works, and he's obviously revised those numbers over several iterations of working through the analysis. Nevertheless, such an approach leaves open the question about how sensitive the final results are to the arbitrary numbers Bill has chosen. I can easily see partisans of one position on the question of someone's Hall of Fame candidacy playing around with the arbitrary numbers to try and favor their candidate's position. The reason Bill can reasonably use this quirky approach is the same reason that Robert Parker can give a quirky wine a very high rating. Both have a tremendous feel for what works, and both have well deserved reputations for fierce independence and objectivity. Nevertheless, if we ever hope to settle the matter of what truly constitutes a big game, we're going to have to do the work Bill describes as too hard (i.e. figuring the odds of making the playoffs if a team wins or loses a particular game and identifying those games with the biggest differential). I'll still follow Bill's series of articles, but I doubt whatever he comes up with will convince a true partisan in the debate.
7:22 PM Jan 21st
I think Brian's formulation is right if the games aren't between the rivals. In Bill's example, four of four games have to go right (random chance, 1/16) for the trailing team to catch up; but if the games aren't against each other, eight of eight do for the win (1/256) or seven of eight to tie (8/256).​
4:54 PM Jan 21st
This type of "points system," as first (?) used in the Hall of Fame monitor and in the Similarity Scores, is creative and very useful.

10 or 15 years ago, I presented it to a sabermetrician who was a math major and he found the whole paradigm to be VERY annoying. He sort of considered it beneath his dignity, so to speak. ;- )

But the fact is, it allows us to triangulate problems that would otherwise be inaccessible, allows us to surround an answer and spiral in on it. I used it to identify better keywords on eBay, for example.

Does any other sabermetric source use this approach? If so, they probably started doing so fairly recently, right?

I wonder whether Bill "invented" this particular "fuzzy logic" approach, or "borrowed" it from some place else he'd seen.

4:15 PM Jan 21st
Steven Goldleaf
So "virtually eliminated" just means you got to run the table to win? Polysyllabificatious sesquipediallianism victorious!!!
3:39 PM Jan 21st
Brian. ..your formulation, at a glance, appears to be about the same as mine. You've stated in one sentence or half a sentence what I explained in three paragraphs, so congratulations to you for that, but if I understand what you're saying, it comes down to essentially the same thing, with some exceptions. If your record is 93-65 and your opponents are 96-62, the magic number is two and you're three games behind, but I certainly would not say you were Virtually Eliminated; you just need to sweep them. But generally, 95% of the time. . .I think they're the same.
2:03 PM Jan 21st
I always figured virtual elimination as being when the magic number gets to be less than the games behind. I wonder how often that would agree with your results...
1:21 PM Jan 21st
Don't forget the final day of the 2011 regular season; a day so full of drama that MLB immediately changed the rules to prevent it from ever happening again.
8:41 AM Jan 21st
I would guess that the most important game is a tie between any game 163 and Brewers-Orioles game 162 in 1982.
8:22 AM Jan 21st
Arrgh! We have to wait until tomorrow to find out the most important game of the last 60 years. Or maybe later.
8:00 AM Jan 21st
We face the same problem here as in defining clutch. Any definition of a clutch situation you provide, I can find an exception. By the time you account for the exceptions, you end up with a small sample size of data for a player.
7:59 AM Jan 21st
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