1.  Mariano Rivera

  

            Every morning I roll out of bed, look at who the Red Sox are playing, look at who the Yankees are playing, and do a little mental calculation of the odds.   Let’s see. ..we’re playing a pretty good team, they’re playing a bad team, but we’re at home, they’re on the road, and then, Rivera pitched an inning and gave up a run last night, so he’s probably not available.  .. .looks like it could be a decent day.

            But wait a minute.   I realized that I was assuming, as I was doing this, that the Yankees were less likely to win the game if Rivera was tired, that the Red Sox were less likely to win if Papelbon was tired, the Angels less likely to win if K-Rod was tired, etc.   What if it’s not true?   Is there actual evidence that the fatigue level of the closer is a factor predicting success for the team?   Or is that just something that seems like it might be true, but in fact gets lost in the laundry among the hundreds of things that might be used to predict the outcome of a game?

            The obvious way to study this issue is to study the Yankees and their Henry Fonda lookalike closer, Mariano Rivera.   Rivera has been the Yankees closer for ten years before this year (1997-2006).   More important than that,

1)      He’s been good every year,

2)      The Yankees have been good every year, 

3)      His role hasn’t changed very much over the years, and

4)      He’s generally been healthy.

Those things eliminate a lot of problems.   The ten years give us 1,620 games to study, which gives us fairly meaningful data. . .not perfect data, but pretty good data.   If we studied, let’s say, Bruce Sutter.  ..sometimes he’s healthy, sometimes he’s not, sometimes he’s great, sometimes he’s mediocre, sometimes he’s pitching just the ninth, sometimes he’s getting two- and even three-inning saves, sometimes his team is good, sometimes they’re bloody awful.   These things screw up the data, so that when you get done you don’t know what you have. 

So we’re studying Mariano and the Yankees.   How do we decide whether Rivera is tired?

I want to be careful about saying he is “tired”.   A pitcher can be tired, after all, for any of a thousand reasons; for all I know Mariano is spending his off hours hunting carabou, as so many of the players do now.   We only measure that part of his fatigue which results from his major league workload.   I developed a “Closer Workload Fatigue Store”, which is as follows:

5 times the number of batters faced yesterday,

Plus 4 times the number of batters faced the day before, 

Plus 3 times the number of batters faced the day before that,

Plus 2 times the number of batters faced the day before that,

Plus the number of batters faced the day before that. 

Twice during the ten-year study, in August of 1997 and again in August of 2005, Mo’s Workload Fatigue Score reached a peak of 89.   

On August 10, 2005, Rivera pitched two innings, facing 7 batters. 

On August 11 he pitched an inning and a third, facing 5 batters. 

On August 12 he didn’t pitch, but on August 13, 2005, he again pitched two innings, giving up 5 hits and facing 12 batters.   

Thus, on the morning of August 14, 2005, Rivera’s Closer Workload Fatigue Score was 89—

60 points for his 12 batters faced on August 13,

15 points for his 5 batters faced on August 11, 

14 points for his 7 batters faced on August 10. 

I got the data for this, obviously, from Retrosheet, and once more, let me express my deep appreciation to the volunteers of Retrosheet for making real baseball research possible. 

I figured Rivera’s Workload for every day of the regular season during the ten years, and then for every regular-season game the Yankees played.   When the Yankees played a double header and he pitched in the first game, I added six times the batters faced in the first game to his score going into the second game.  The peak point was 89, and sometimes he was at zero—after the all-star break, for example, and on opening day. 

When Rivera was on the Disabled List—meaning that he was totally unavailable for the game—I entered that as “100”, indicating that he was 100% out of action for that day.    If you were doing a different pitcher—Dick Radatz, for example, or Goose Gossage, or (God forbid), Mike Marshall, his workload would no doubt peak over 100; in fact, I would suppose that it would peak over 200.   Anyway, you couldn’t use “100” as a top end of the scale.   But I was just figuring Mariano, so 100 works for the days when he is “beyond fatigued”, so to speak. 

The essential conclusions of this study are as follows:

1)      Rivera pitched less often when his Workload Fatigue Score was high,

2)      Rivera was less effective when his Workload Fatigue Score was high, and

3)      The Yankees’ winning percentage dipped quite significantly when Rivera was tired.  

I sorted the data in several different ways to ward against conclusions suggested by random groupings in the data.  Perhaps the most useful split was the split dividing the Yankee games into four groups:

1)  High Fatigue

2)  Fatigue Fairly High

3)  Fatigue Fairly Low

4)  Low Fatigue

These are Mariano’s Games Appearances and ERA by the four groups:

                                    &n​bsp;                     Games    ERA

1)  High Fatigue                        &nb​sp;             90      2.71

2)  Fatigue Fairly High                          164      2.18

3)  Fatigue Fairly Low                          185      2.00

4)  Low Fatigue                           ​;         201      1.60

There are 405 Yankee games in each group (more or less. . .a couple of games were cancelled, so I cut a couple of the groups to 404.)  When he was most rested Rivera pitched in essentially one-half the games, and posted a 1.60 ERA.  As his Closer Workload Fatigue Score increased he pitched less, and his ERA ascended. 

In the top group Rivera pitched in only 90 games of 405, but this is a little bit misleading because the top group includes the games for which Rivera was on the Disabled List.   There were 98 Yankee games over the ten years for which Rivera was on the Disabled List, so actually Rivera pitched in 29% of the Yankee games (90 of 307) even when his fatigue score was highest, a rate of 48 appearances per 162 games. 

This was one thing that surprised me in the study—that the slope of the line indicating likelihood of appearing in the game was not more steep than it is.   What I take from that realization is this:  that in modern baseball the closer’s role is so limited and defined that the closer is almost always available for one inning of work.    I would have thought that there would be days when Rivera’s recent workload was so high that he was simply not available for this game, and no doubt there are some such days.   But there aren’t very many of them.   The point of the modern “closer usage” rules is, in a sense, to make the closer always available if you really need him. 

In this data sort the Yankee winning percentage also declines as Rivera becomes less available and less effective:

                                                          Games    ERA   Yankee WPct

1)  High Fatigue                         &nb​sp;            90      2.71          .602

2)  Fatigue Fairly High                          164      2.18          .588

3)  Fatigue Fairly Low                          185      2.00          .633

4)  Low Fatigue                                    201      1.60          .620

The Yankee winning percentage is higher when Rivera is more rested.  However, there is a “random sort glitch” in that one which causes me to suspect that this is actually understating the effect.   The .602 percentage in the top group there includes the 98 games for which Rivera was on the Disabled List, and the Yankees actually played extremely well (67-31) when Rivera was on the DL.    If you take those games out of it, the “high fatigue” winning percentage drops to .577—the lowest point on the chart.   This becomes even more clear when we split the data into five groups of 324 Yankee games, rather than four groups of 405:

                          &n​bsp;                               Games    ERA   Yankee WPct

1)  High Fatigue                           &​nbsp;          63      2.57          .608

High Fatigue NOT INCLUDING DL     63      2.57          .575

2)  Fatigue Fairly High                          123      2.36          .586

3)  Middle group                                  137      2.16          .594

4)  Fatigue Fairly Low                          152      1.67          .630

5)  Low Fatigue                                    165      1.77          .635

In the bottom group in this sort, when Rivera is most rested, Rivera appears in 82 games per season and the Yankees win 103 per season.   In the top group, when he is least rested, Rivera appears in 45 ganes per season and the Yankees win 93 per season.   (There’s a tie game in there screwing up the calculations, if you’re trying to extrapolate from this.)  

 I am not a gambler, I don’t write to gamblers specifically, and I don’t claim to know the things that gamblers can profit from knowing.   However, it would seem to me that if you have a gambler’s focus, this would be an extremely important “razor” to sort the data, to decide whether to bet for or against the Yankees.   Fifty, sixty points of winning percentage is a huge edge.  

Of course, at this point we can’t say with confidence that that’s the real size of the advantage.  We would need to study this repeatedly, studying different pitchers, before we could definitively reach a conclusion that a tired closer reduces the winning percentage of his team by 50 or 60 points.  There could also be biases in the data which have not yet been called to our attention.   I’m just saying. . .that’s what this study shows, and it seems reasonable.   I thought it was interesting enough that I decided to add the daily “closer workload fatigue score” to the statistics section of the on line. 

The study also reached the following incidental conclusions, which I will pass along for what they are worth:

1)  Rivera’s strikeout rate declined significantly as his fatigue went up.   In the quartile study his strikeouts per nine innings were 8.47 in the bottom group, 6.82 when he was most fatigued, and in the sevens in the middle two groups (albeit it in the wrong order.)

2)  Rivera’s double play rate also dropped sharply when his fatigue score was high.   Rivera received the support of 40 double plays in 437.2 innings in the bottom two groups of the quartile study, when he was most rested.  This is .82 double plays per nine innings.  When his fatigue score was higher he received only 14 double plays in 269.1 innings, or .47 double plays per nine innings. 

3)  Rivera also allowed more home runs when he was tired, his rate per nine innings increasing from .37 to .50.   When he was more rested Rivera had 40 double plays against 18 home runs allowed.   When he was more tired he had 14 double plays and 15 homers.  

4)  However, Rivera’s WALK rate improved sharply when he was more tired.   Of course, Rivera’s walk rate is always fantastic.   Even when he was most rested, Rivera allowed only 2.00 walks per nine innings (not including intentional walks.)   But when he was most tired this figure was essentially cut in half, down to 1.10 walks per nine innings.  In the quintile split (split into five groups) Rivera allowed 1.08 and 1.11 un-intentional walks in the two “highest fatigue” groups. 

Presumably, Rivera’s control “improves” when he is more tired because

1.  There is more early contact, and

2.  His ball doesn’t move as much, meaning that it doesn’t jump out of the strike zone as often.