June 20, 2001

Aim For The Head

Response Rates

by Keith Woolner

This week's question comes from. uh. well, BP's Joe Sheehan, who wrote in last Monday's Daily Prospectus:

There's also something that reader Jim Cox mentioned to me that I have to say is very impressive to observe, if an unknown (or even a tautology) from an analytical standpoint. The Mariners score in a ridiculous percentage of their innings, and Cox points out that they seem to score in a ton of the innings that succeed an opponent's score.

During their 15-game winning streak, they scored in 41.7% of their at-bats (53 of 127); they scored 39.3% of the time when batting after the opposition scored. That sounds like a lot--two times in five, they answered runs with runs of their own--but I don't have comparative data, and am half-hoping Keith Woolner takes the bait for Tuesday's "Aim for the Head" column.

All right, Joe, just this once. This column is supposed to be for reader questions, you know. Next time at least have the decency to send me a question from a fake Hotmail or Yahoo mail account, OK?

There are really two different points in Joe's question: one about how frequently a team scores in any inning, and one about how often a team responds to allowing the opposition to score by scoring themselves in their next at bat (which we'll refer to as "answering" the opposition).

First, let's point out the obvious: teams that score lots of runs will score in a higher percentage of their innings. Similarly, by simple chance, a team that scores in a high percentage of innings would be expected to score in a comparably high percentage of innings that follow allowing runs.

In fact, assuming no dependency or influence between the two teams' chances of scoring, the likelihood of a team answering the opposition is exactly equal to the chance of scoring in any old randomly selected inning. In this way, the Mariners were underperforming a bit when in came to producing answering runs. They scored less often following giving up a run than they did across all innings. Though, as we'll see, both figures are well above any full-season performance of recent years.

How would we want to go about investigating which teams answer the opposition more than expected? We could just count the number of times a team answers the opposition. However, that has one large problem--teams that give up lots of runs will have more opportunities to answer than teams that surrender few runs. What we'll want to look at, then, is how often a team answers the opposition's scoring as a fraction of the number of innings in which they allow runs to score.

Let's illustrate this using a couple of examples:

In 1999, the Phillies scored in 28.9% of their innings. When the opposition scored in the previous half-inning, the Phillies scored 26.4% of the time, a rate 2.3% worse than their overall scoring. They were worse at answering the opposition than you'd expect.

The 2000 Yankees scored in 31.2% of their innings, but answered in 36.5% of their opportunities. They were more likely to answer the opposition by 5.3% over their overall chance of scoring in an inning.

I have data to determine scoring and answering rates for the seasons 1978 through 2000, so we can get a feel for how the 2001 Mariners fit. First, let's look at the teams who scored in the largest fraction of overall innings:

Score%: percentage of innings in which the team scored at least one run

Answer%: percentage of times the team scored when batting immediately after
allowing at least one run.

Teams with Score% of 33% or more are listed.

Year  Team   Score%   Answer%

1994  CLE     37.8%     36.1%
2000  CHA     37.0%     34.7%
1996  CLE     33.6%     34.3%
1998  NYA     35.5%     34.2%
1999  CLE     32.9%     33.9%
1997  SEA     33.9%     33.8%
1994  CHA     36.6%     33.7%
2000  SFN     34.4%     33.7%
2000  COL     34.0%     33.5%
1996  SEA     31.6%     33.5%
1996  COL     34.0%     33.5%
2000  HOU     32.2%     33.4%
2000  CLE     35.3%     33.4%
1995  CLE     34.9%     33.3%
1996  TEX     31.4%     33.3%
1997  CLE     32.9%     33.2%
1999  TEX     31.2%     33.1%
1996  BOS     34.5%     33.1%
1997  COL     33.8%     33.0%
1995  CAL     34.3%     33.0%
1995  COL     36.9%     33.0%

It's not surprising that the offensive explosion of the 1990s has produced all the teams who have scored in at least a third of their innings. The top representative for pre-1993 is the 1987 Tigers, who ranked #28 overall with a 32.5% scoring percentage. You have to go down to the 1982 Brewers in 41st place to find any other season represented.

By comparison, the worst teams on the list are the 1981 Blue Jays (20.2%), the 1981 Cubs (21.2%), and the 1985 Giants (22.0%).

Now let's look at the list of teams with an Answer% of 33% or better, remembering that we'd expect a comparable number of teams (and probably a lot of overlap with the teams above) by simple chance:

Year  Team   Score%   Answer%

1994  CLE    37.8%      36.1%
1999  HOU    37.3%      31.1%
2000  CHA    37.0%      34.7%
1995  COL    36.9%      33.0%
1994  CHA    36.6%      33.7%
2000  NYA    36.5%      31.2%
1993  PHI    35.9%      31.9%
1998  NYA    35.5%      34.2%
1994  DET    35.3%      32.1%
2000  CLE    35.3%      33.4%
1998  COL    35.0%      30.7%
1998  TEX    34.9%      31.1%
1995  CLE    34.9%      33.3%
1991  PIT    34.8%      29.2%
2000  TEX    34.8%      31.9%
1999  NYN    34.6%      32.4%
1996  BOS    34.5%      33.1%
1993  TOR    34.5%      32.6%
2000  SFN    34.4%      33.7%
1999  SEA    34.3%      31.0%
1995  CAL    34.3%      33.0%
2000  ANA    34.2%      32.2%
1999  TOR    34.1%      32.3%
1997  ANA    34.1%      31.5%
1999  SFN    34.1%      31.7%
1994  HOU    34.1%      32.1%
2000  COL    34.0%      33.5%
1996  COL    34.0%      33.5%
1978  BOS    34.0%      30.2%
1997  SEA    33.9%      33.8%
1997  COL    33.8%      33.0%
1991  DET    33.8%      29.7%
1994  BAL    33.7%      32.3%
1979  BAL    33.6%      29.6%
1996  CLE    33.6%      34.3%
2000  ATL    33.4%      32.7%
1995  BOS    33.3%      32.9%
1996  SDN    33.3%      28.1%
1991  TOR    33.2%      28.3%
1999  ARI    33.1%      31.9%
1998  TOR    33.1%      32.2%
1998  CHN    33.1%      30.4%
1999  TBA    33.0%      30.2%
1999  BAL    33.0%      31.8%
1979  CAL    33.0%      30.5%
1988  NYN    33.0%      28.5%
1994  KCA    33.0%      29.8%

Whoa! The 47 teams that answered back a third of time is more than double the size of the previous list. Six teams had higher Answer% than the best Score%, and 15 teams were better than the second best Score%. Why would this be?

Remember what I said earlier: assuming no dependency or influence between the two teams' chances of scoring, the likelihood of a team answering the opposition is exactly equal to the chance of scoring in any old randomly selected inning.

Is this really a reasonable assumption to make? I would suggest it's not because both teams are affected by the park environment, and if the game is played in a hitters' park, both teams are more likely to score. Thus, there are more expected opportunities to answer the opposition (since the opposition is scoring more often), as well as a better chance of answering (since you are also scoring more often). The chances of the two teams scoring are both being influenced by a common factor, and thus can't be said to be completely independent from each other.

Which is not to say that a team's basic scoring rate doesn't have primary influence over a team's answering rate. In fact, the two measures correlate with each other very well (R^2 of 0.79), and the graph below demonstrates the strength of the relationship far better than I could in words:

Getting back to the original question for a moment, the lists above clearly show that the Mariners' Score% of 41.7% and Answer% of 39.3% far exceed what any other team has been able to do for a whole season. Of course, teams also don't generally play .800 ball for two months, so we'd expect the Mariners to be remarkable in a lot of ways during such a stretch. But is it a good thing for teams to answer the opposition a large percentage of the time? Yes, if only because it means the team is scoring often in all situations.

So, what teams have "stepped up" the most to respond to the challenge of the opposition scoring? Here, I'll look at teams with the highest differential between their Answer% and their Score%. These are the teams who were the biggest surprises, relative to how often they put runs on the board:

Year  Team   Answer%   Score%   Diff

1999   HOU     37.3%    31.1%   6.2%
1991   PIT     34.8%    29.2%   5.6%
1980   CHN     29.7%    24.3%   5.4%
2000   NYA     36.5%    31.2%   5.3%
1996   SDN     33.3%    28.1%   5.2%
1991   TOR     33.2%    28.3%   4.9%
1978   SDN     29.7%    24.8%   4.9%
1988   NYN     33.0%    28.5%   4.5%
1992   NYA     30.7%    26.2%   4.5%
1993   SDN     30.7%    26.4%   4.3%
1998   COL     35.0%    30.7%   4.3%
1992   MIL     32.3%    28.0%   4.3%
1978   BAL     31.3%    27.0%   4.3%
1994   LAN     31.7%    27.5%   4.2%
1984   LAN     27.6%    23.4%   4.2%
1991   DET     33.8%    29.7%   4.1%
1979   BAL     33.6%    29.6%   4.1%
1988   BAL     26.9%    22.8%   4.1%
1993   PHI     35.9%    31.9%   4.0%
1984   CHA     30.5%    26.6%   4.0%

At first glance, it looks like good teams are able to answer the opposition proportionally more. The '99 Astros and the '91 Pirates both won their division, and the 2000 Yankees were World Champions. But it's not quite that easy. The #3 team on the list is the 1980 Cubs, who lost 98 games and finished last in their division. Buck Showalter's '92 Yankees were 10 games below .500. The fire-sale '93 Padres lost 101 games, yet answered the opposition better than their run scoring would predict.

Nor is there a clear pattern for park effects, though I'm just eyeballing the data here. The '99 Astros--the last year of the Astrodome--tops the list, but Coors Field ('98 Rockies) and Wrigley Field ('80 Cubs) are also represented.

Lastly we might ask whether the tendency for answering runs more often than the overall scoring rate would predict is persistent from year to year. It turns out that it probably isn't. There is a very small correlation between DIFF in one year to the next (R^2 of 0.03), and plotting one year versus the next doesn't show anything like the trend we saw earlier.

Of course, in all of the analysis we've done so far, there's been no consideration for whether being able to answer runs (beyond a team's ordinary scoring rate) has any value. Do winning teams tend to have Actual% > Score%? While I don't have time to address that this week, if there's sufficient interest, it may appear in a future column.

Thanks for writing, Joe. Now get back to work on tomorrow's Daily Prospectus!

Keith Woolner is an author of Baseball Prospectus.

Keith Woolner is an author of Baseball Prospectus. 
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