Context by Inning
The table below shows inter-game and intra-game context by inning across all games for which I have calculated Player won-lost records.
Context by Inning
|
Context |
| Inning |
Inter-Game |
Intra-Game |
Combined |
| Top 1
| 0.9658 | 1.1927 | 1.1519 |
| Bottom 1
| 0.9843 | 1.2229 | 1.2036 |
| Top 2
| 0.9512 | 1.1520 | 1.0958 |
| Bottom 2
| 0.9478 | 1.1614 | 1.1008 |
| Top 3
| 0.9548 | 1.1212 | 1.0705 |
| Bottom 3
| 0.9457 | 1.1205 | 1.0597 |
| Top 4
| 0.9650 | 1.0784 | 1.0407 |
| Bottom 4
| 0.9494 | 1.0657 | 1.0118 |
| Top 5
| 0.9548 | 1.0373 | 0.9904 |
| Bottom 5
| 0.9305 | 1.0146 | 0.9442 |
| Top 6
| 0.9654 | 0.9895 | 0.9553 |
| Bottom 6
| 0.9429 | 0.9622 | 0.9072 |
| Top 7
| 0.9625 | 0.9456 | 0.9101 |
| Bottom 7
| 0.9300 | 0.9119 | 0.8481 |
| Top 8
| 0.9587 | 0.9024 | 0.8651 |
| Bottom 8
| 0.9213 | 0.8590 | 0.7914 |
| Top 9
| 0.9342 | 0.8566 | 0.8003 |
| Bottom 9
| 1.6186 | 0.8022 | 1.2984 |
| Top Extras
| 2.0429 | 0.5465 | 1.1164 |
| Bottom Extras
| 2.3238 | 0.5445 | 1.2653 |
This table takes some thought to understand. But working through it is well worth it, I think, as, in some ways, the results here are perhaps the most interesting and revealing results in all of my work.
Inter-Game Context
The first column of the above table shows inter-game context, which is comparable to the concept of Leverage. Not surprisingly, inter-game context is highest in extra innings. In fact, the only other inning with an average inter-game context above one is the bottom of the ninth inning. Interestingly, this means that in games in which the home team wins before their final at-bat, there are no innings in which the average inter-game context is above-average. Of course, this doesn’t mean that there are no individual at-bats which are above-average in context. For that matter, in any specific game, there are probably specific half-innings that are above average in context. But, in a typical game that doesn’t go into the bottom of the ninth inning, there’s simply no way to know which inning is likely to be the decisive inning of the game.
Looking only at the first 8-1/2 innings, two other facts are worth noting. First, after the first inning, inter-game contexts for the home team are an average of
2.2% lower than for the visiting team. This is in stark contrast to extra-inning games, where home-team inter-game context is
14% higher than for the visiting team. Overall, across all innings, the average inter-game context for the visiting team is
0.984; average inter-game context for the home team is
3.4% higher at 1.017.
Second, and I think more interesting, average inter-game context declines as the game progresses (until the bottom of the ninth inning and extra innings). The highest-context half-inning before the bottom of the ninth inning is the bottom of the first inning, with an average inter-game context of
0.984. The lowest-context half-inning, on average, is the bottom of the eighth inning at
0.921. Overall, through the first 8-1/2 innings of the game, the average inter-game context declines by an average of
0.7% per inning.
At first blush, this seems counter-intuitive. When people think of “clutch” situations, they often think of “close and late” situations – situations late in close games. Yet, on average, late situations are relatively un-“clutch” situations. In fact, these two ideas do not conflict. Late innings of close games are, indeed, high-context situations. For example, relief pitchers pitching in hold or save situations pitch in an average inter-game context of
2.020. Relief pitchers pitching in tie games pitch in an average inter-game context of
1.915. The reason why inter-game contexts decline as the game goes on, in spite of this, is because such situations are not the norm. For relief pitchers as a whole,
64.2% of all context-neutral Player decisions from
1916 - 2019 were earned in non-save/hold, non-tie situations. And these situations, not surprisingly, had an average inter-game context of
0.442.
In the early innings of a typical baseball game, there are no situations that have exceptionally high inter-game context. But, there are also very few situations that have exceptionally low inter-game context. As the game progresses, the chances of higher-context situations rises, but the chance of the game getting completely out of hand, leading to a complete lack of high-context situations, also increases. And, in fact, the latter, a game with nothing but low-context situations in the late innings, is more common in Major-League Baseball, than the former, a close game with high average inter-game contexts in the late innings.
The table below shows the percentage of games in which the winning team took a lead which it held for the remainder of the game, by inning, from 2000 - 2009:
Percentage of Game-Winners with Lead They Never Relinquish through X Innings
|
Winning Team Takes Lead it Never Relinquishes |
| Inning
| In This Inning |
Through This Inning |
| 1 |
24.07% |
24.07% |
| 2 |
12.81% |
36.88% |
| 3 |
9.67% |
46.55% |
| 4 |
8.82% |
55.37% |
| 5 |
7.60% |
62.97% |
| 6 |
7.59% |
70.56% |
| 7 |
6.93% |
77.49% |
| 8 |
7.48% |
84.97% |
| 9 |
6.77% |
91.74% |
| 10+ |
8.26% |
100.00% |
That is, in 24.1% of all games, one of the two teams took a lead in the first inning which it proceeded to then hold for the remainder of the game. Note two things about this table. First, by far the most common inning for a team to take a lead which it never relinquished was actually the first inning. In fact, the second-most common inning for a team to take a lead which it never relinquished (again, by a fairly large margin over the third-most common inning) is the second inning. Second, over half of all games were decided by the end of the fourth inning – less than halfway through the game. In such games, there may be relatively few high-context situations in the later innings.
Intra-Game Context
The most striking result here and, frankly, the result which I had the hardest time wrapping my head around in all of this work, is that average intra-game context is extremely dependent on the inning. On average, through the first nine innings, intra-game context declines by approximately
4.1% per inning. Intra-game contexts by inning are shown in the table below.
| Inning |
Intra-Game Context |
| 1 |
1.2084 |
| 2 |
1.1568 |
| 3 |
1.1208 |
| 4 |
1.0721 |
| 5 |
1.0259 |
| 6 |
0.9758 |
| 7 |
0.9289 |
| 8 |
0.8809 |
| 9 |
0.8298 |
| Extras |
0.5455 |
At first blush, this makes no sense. Except for the bottom of the ninth and extra innings (where the intra-game numbers make sense to me), every game (except for rain-shortened games) includes every half-inning. Any official game will include a top of the first as well as a bottom of the fourth inning. How, then, can it make sense for the average intra-game context of the top of the first inning to be
12% higher than the average intra-game context of the bottom of the fourth?
To understand this, you have to really understand what intra-game context is. Intra-game context adjusts Player Decisions to reflect the fact that, at the end of the day, the game is the unit of value being measured here and all games have the same value. What does a high intra-game context mean? It means that a relatively low number of Player Decisions were accumulated within this particular game. Similarly, a low intra-game context means that a relatively high number of Player Decisions were accumulated within a particular game.
Examples of the latter are extra-inning games. There are more plate appearances than usual in extra-inning games and, because the game is tied late, there are likely to be an above-average number of situations within the game with very high inter-game context levels. Not surprisingly, then, extra-inning games generate nearly twice as many Player Decisions as nine-inning games. This is reflected in an average intra-game context of
0.545 for extra innings.
Extra-inning games or one-run games are good and fairly obvious examples of low intra-context games. What, then, are the characteristics of high intra-context games?
Basically, just the opposite of low intra-context games: games that are not particularly close, games with no lead changes, perhaps most notably, games in which one team jumps out to an early lead and never relinquishes it. I showed this table earlier, but I’ll show it again here: the percentage of games in which the winning team had taken the lead which it would never relinquish by inning. As I noted above, the most common inning for a team to take a lead which it would never relinquish was the first inning; the second-most common such inning was the second inning; in over half of all major-league games, the winning team has taken a lead which it will never relinquish by the end of the fourth inning.
Percentage of Game-Winners with Lead They Never Relinquish through X Innings
|
Winning Team Takes Lead it Never Relinquishes |
| Inning
| In This Inning |
Through This Inning |
| 1 |
24.07% |
24.07% |
| 2 |
12.81% |
36.88% |
| 3 |
9.67% |
46.55% |
| 4 |
8.82% |
55.37% |
| 5 |
7.60% |
62.97% |
| 6 |
7.59% |
70.56% |
| 7 |
6.93% |
77.49% |
| 8 |
7.48% |
84.97% |
| 9 |
6.77% |
91.74% |
| 10+ |
8.26% |
100.00% |
Plate appearances that result in runs scoring are, on average, higher inter-context plate appearances than plate appearances that do not result in runs scoring. Plate appearances that result in lead changes are extremely high inter-context plate appearances, on average. BUT, this is all much less true in the early innings of a game than in the late innings of a game. While, as noted above, the average inter-game context in the first inning is actually higher than in any subsequent innings before the bottom of the ninth, peak inter-game context in the first inning is the lowest of any inning. In 2009, for example, inter-game context by inning showed the same basic pattern as for the Retrosheet Era as a whole:
Inter-Game Context by Inning: 2009 American League
| Inning |
Average |
Std Deviation |
| 1
| 0.981
| 0.505
|
| 2
| 0.954
| 0.549
|
| 3
| 0.963
| 0.577
|
| 4
| 0.971
| 0.625
|
| 5
| 0.953
| 0.704
|
| 6
| 0.962
| 0.814
|
| 7
| 0.957
| 0.968
|
| 8
| 0.924
| 1.144
|
| 9
| 1.139
| 1.525
|
The last column here shows the standard deviation of inter-game context in the 2009 American League. Standard deviation is a statistical calculation which measures the spread of the inter-game context by inning.
In other words, inter-game contexts in the first inning range from 0.981 +/- 0.505 – i.e., they mostly fall between from 0.476 to 1.485. For the second inning, the range is 0.405 – 1.503. By the sixth inning, the range has increased to 0.148 – 1.776. And, by the seventh inning and later, the standard deviation is so large that it is actually greater than the mean. For the eighth and ninth innings, the mean plus one standard deviation for these innings is over 2 in both cases.
So, in games in which the winning team jumps out to an early lead, that early lead will likely occur in a relatively low inter-game context (as compared to a similar lead change that might occur later in a game). Then, in the late innings of such a game, the average inter-game context of the game could be very low. The result is that (a) the highest-context portion of the game will be the early innings when the lead was taken for good, and (b) the overall number of Player decisions will be exceedingly low. Because of (b), such games will have very high intra-game contexts, on average. For games in which the lead is taken late, on the other hand, the highest-context portion of the game will be in the late innings and the overall number of Player decisions is likely to relatively high, leading to low intra-game contexts. But note that, because the range of inter-game contexts is lower in the early innings than in the late innings, the difference in these two situations in early innings will be far less than in late innings.
A simple example might be helpful. We’ll simplify to two types of innings: early and late. Consider the following Player decisions for two games: one which was decided early and one which was decided late.
|
Early-Inning Decisions |
Late-Inning Decisions |
|
Context-Neutral |
Contextual |
Context-Neutral |
Contextual |
| Game decided early
| 1.5
| 1.8
| 1.5
| 0.5
|
| Game decided late
| 1.5
| 1.2
| 1.5
| 3.0
|
In this example, the first game has an early-inning inter-game context of 1.2 (1.8 / 1.5), a late-inning inter-game context of 0.3 (0.5 / 1.5), and an intra-game context of 1.3 (3 / 2.3).
The second game has an early-game context of 0.8 (1.2 / 1.5), a late-inning inter-game context of 2.0 (3.0 / 1.5), and an intra-game context of 0.7 (3 / 4.2).
Putting it all together, then, total early-inning decisions for the two games would equal
1.8*1.3 + 1.2*0.7 = 3.2
for an average early-inning intra-game context of 1.07 (3.2 / 3.0).
Total late-inning decisions for the two games would equal
0.5*1.3 + 3.0*0.7 = 2.8
for an average late-inning intra-game context of 0.80 (2.8 / 3.0).
This pattern in intra-game context across innings has important implications in valuing starting versus relief pitchers.
Total Context
Putting inter-game and intra-game context together, total context varies by inning as follows:
Total Context by Half-Inning
| Inning |
Total Context |
| Top 1
| 1.1519 |
| Bottom 1
| 1.2036 |
| Top 2
| 1.0958 |
| Bottom 2
| 1.1008 |
| Top 3
| 1.0705 |
| Bottom 3
| 1.0597 |
| Top 4
| 1.0407 |
| Bottom 4
| 1.0118 |
| Top 5
| 0.9904 |
| Bottom 5
| 0.9442 |
| Top 6
| 0.9553 |
| Bottom 6
| 0.9072 |
| Top 7
| 0.9101 |
| Bottom 7
| 0.8481 |
| Top 8
| 0.8651 |
| Bottom 8
| 0.7914 |
| Top 9
| 0.8003 |
| Bottom 9
| 1.2984 |
| Top Extras
| 1.1164 |
| Bottom Extras
| 1.2653 |
In order, the highest-context half-innings, on average, are the bottom of the ninth inning, the bottom of extra innings, the bottom of the first inning, the top of the first inning, and the top of extra innings. The lowest-context half-innings, on average, are the bottom of the eighth inning and the top of the ninth. This is not to say, of course, that all first-inning events are higher-context than later-inning events. On the contrary, as noted above, the standard deviation of context is much higher in later innings: there are many more much lower-context situations, but there are also more higher-context situations.
One way to get a feel for how inter-game and intra-game context interact with each other might be to consider two games won by the Los Angeles Dodgers at home in 2002, both of which ended with a final score of 1-0 with the only run scoring on a solo home run. These two games are compared in another article here.
All articles are written so that they pull data directly from the most recent version of the Player won-lost database. Hence, any numbers cited within these articles should automatically incorporate the most recent update to Player won-lost records. In some cases, however, the accompanying text may have been written based on previous versions of Player won-lost records. I apologize if this results in non-sensical text in any cases.
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