Previously, Suzuki and Beltre, two sets of Trout and Ramirez, OPS is the same but, I showed that the ratio of OBP and SLG is different.→figure 35, figure 36.
And, by the blow profile, it has shown that the effectiveness of IBB is different.
The last time, by using consecutive batter model to investigate the effectiveness of IBB.
This time I will examine the effectiveness of IBB due to the difference of the striking profile of the second batter.
FIG.46
Here, as a second batter, I will use of three data.
・Data obtained by aggregating 272 batter (OPS = 0.7). ・Data of 2005 Podsednik,S (CWS). ・Data of 2015 Hunter,T (MIN) .
FIG.47
As shown in Figure 47, the three data, OPS all 0.7 but there are differences in the content.
OBP Podsednik,S > OPS = 0.7 > Hunter, T SLG Podsednik,S > OPS = 0.7 > Hunter, T
Podsednik is hit mass production, but Hunter is a long-distance batter.
FIG.48
FIG.49
In FIG. 48, a graph of RP in the case of (2-b, 2) and (3-b, 2), in Figure 49, it shows a graph of the dot plot of RE and RP.
Important point.
・Ichiro, Berthollet, trout, Ramirez of relative position, almost the same in Figure 39,44,45 and 49.
・Effectiveness of IBB has become a Podsednik < OPS = 0.7 This time, unlike the case of figure 39, the effectiveness of IBB was greater the greater the SLG / OBP Second batter.
This is a natural result, when the runner enters the scoring position, batter directly linked to score but that it is a high hit probability batter.
Next situation that IBB is conceivable, in scoring situations, but when the batting order welcomes a hard hitter of number 5 (OPS > = 0.85).
FIG.43
Then, when the sixth batter of decent batter, (of course, the seventh since the batter is inferior more), but whether it should be IBB.
＊A batting order isn't when it was limited with this.
Here, as the fifth batter, using the data of the slugger the four earlier, the sixth batter, to compare, using OPS = 0.7 and OPS = 0.8.
The numerical value in case of (2-b,2), (3-b,2) and (2&3-b,2) is shown on the table 12 and the one by which a plot did these are shown on figure 43 and 44.
Table 12
FIG.44
FIG.45
Organize to show several points.
・And but of course, it is better weaker batter No. 6 batter, go up the effectiveness of IBB.
・It's when it's (3-b,2) and (2&3-b,2) by batter Ichiro, that both of RE and RP become plus.
・Number 5 assumes a slugger of 4 people as a batter, but the validity of IBB is different depending on blow profiles.
・The relative location by the plot is really similar by figure 39 and figure 44, 45.
・Considering that sacrificing RE, if a head-to-head, (3-b, 2), when the (2-b, 2), (2 & 3-b, 2), IBB can be a single strategy.
This time, let's consider a situation where IBB is carried out actually in baseball.
One of the situation, to have a runner in scoring position, batter of the bottom of batting order at-bat, the next batter is the case of the pitcher.
FIG.40
As shown in figure 41, there is actuary a large difference in the striking power to the pitcher and fielder.
Here, as the the batter of the bottom of batting order and the pitcher, I want to use three data of the following .
Two Batter: ・OPS = 0.5 and OPS = 0.7 are, but the same data as those shown in Table 8. OPS = 0.5 is a very bad performance batter. OPS = 0.7 is slightly worse performance than the average batter. Pitdher ・OPS = 0.35 is, but the same data as those shown in Table 8, which has almost the same performance as the pitcher average of MLB.
FIG.41
In Figure 42, the situation in the case of (3-b,2) is shown.
IBB : A pitcher (OPS=0.35) stands as at-bat by the situation of (3-b,2).
Fighting : DB, 1B, 2B, 3B, HR, the results of six kinds of Out is generated according to the probability. In each of the results situation, pitcher stands to bat.
Given the effectiveness of the IBB in the defensive side, from the RE and RP in the case of fighting, by subtracting those in the case of IBB, it should become a plus, so that it's effective.
Table 11
Table 11, shows the status of twelve cases above-mentioned value becomes positive. ( The remaining twelve cases IBB is not valid, it is not shown here.)
First batter is OPS = 0.5 or OPS = 0.7, in 4 case or 5 case resupectively, RE or RP is a plus.
FIG.42
Figure 43 shows, for the nine cases, the horizontal axis represents RE, and RP to the longitudinal axis, but a plot.
For OPS = 0.5, the value of RP, which is acquired by IBB is small, since none RE is a negative, the less effective IBB.
For OPS = 0.7, the value of RP, which is acquired by IBB is greater than 6%, since the RE small minus or plus, the effectiveness of IBB is high.
IBB is a valid situation. ・(2-b, 2) ・(3-b, 2) ・(2&3-b, 2) + ・(1&3-b, 2)→ This situation, note that RE is negative.
Of course, there is another road to the situation 1. In other words, in a time instead of the pitcher, it's the case, such as a pinch hitter to come out.
No longer validity of IBB that case, it would be to widen the attack side of the chance to reverse.
However, on the other hand, if reasonably good condition other party pitcher 4-6 innings, the defender dare to IBB, also to so as to issue a pinch hitter in the attack side, it can be good strategy.
And plus that give place to a good pitcher as soon as possible, it is trading between the minus greet pinch hitter in the scoring situation.
It is given in successive models, RE also RP also both came out or may be positive.
These are situations that can be a real baseball game.
In both NPB and MLB, considered as one of the reasons that IBB of the league without a DH system is large.
This time calculation, we have shown, simulates well the actual situation.
OPS = 0.35 is, in the aggregate data of 1072 pitcher, has almost the same performance as the pitcher average of MLB
OPS = 0.5 is, in the aggregate data of 430 fielder, this has become a very bad batter performance.
OPS = 0.7 is, in the aggregate data of 272 fielder, this has become a slightly worse performance than the average batter.
"Suzuki, I" shows his striking performance in SEA in 2004, which was 262 hit of that historic year.
"Beltre, A" shows hit striking performance in TEX in 2013.
"Trout, M" shows a striking performance in LAA in 2013
"Ramirez, M" shows a striking performance in BOS in 2005
It isn't 2011 - record in 2013, but it's a record good for a comparative target, so Suzuki and Ramirez will use.
FIG.35
For these seven batting performance, batting average, on-base percentage, slugging percentage, is shown using the on-base plus slugging.
There it is two points should be noted.
Suzuki and Beltre (0.87-0.88), OPS is almost same. And Trout and Ramirez (0.98-0.99) is too.
But the ratio of the OBP and SLG are different. Suzuki and Trout has a high ratio of OBP, Beltre and Ramirez has a high proportion of SLG.
FIG.36
Eight event probability of that may arise from these seven batting performance, I was calculated in the same manner as used in Table 7.
Describe the things of several points that can be read from this figure.
・Suzuki, single hit is extremely large, to the minute reverse, HR is less than OPS = 0.7.
・Beltre and Ramirez is in comparison to the Suzuki and Trout, the proportion of GDP is high, no three-base hit. It's due to the simple base-running ability.
・Trout, the proportion of HR is small compared to Ramirez ( with same OPS). In addition, the proportion of walks is high, the percentage of GDP is low. He has good batting eye, and also a distance (GO/AO is low), yet suggesting is fleet-footed.
So, in these batter, let's look at the effectiveness of IBB.
Table 9
First of all, it's state of the 12 that would probably be no validity of IBB.
Here, the batter of OPS = 0.35 and OPS = 0.5 are omitted (already calculated). Even one of ordinary, be seen, because not nearly IBB enabled by their batter.
When there are runners in scoring position, with two out in the context of the slugger, it is also seen when close to 0, but is not the case of the positive.
In these cases, IBB is not nearly effective.
Table 10
FIG.37
FIG.38
Table 10, figure 37 and 38 show the value of the remaining 12 of the situation RE (run expectation) and RP (run probability).
If you look in terms of RE, is there validity to IBB is, it's two situations. ・(2&3-b, 2), Suzuki. (RE, RP) = (0.059, 5.5 %) ・(2&3-b, 2), Trouto. (RE, RP) = (0.010, 0.5 %)
FIG.39
When I thought by the absolute value of RE, I decided to think the occasion with the loss and the validity of IBB of more than 0.1 are damaged here.
To take a look at the entire picture, RP for the 11 cases to be positive and RE more than 0.1, the horizontal axis and RE, by RP to the vertical axis shows a plot in Figure 39.
(2-b, 2) and (3-b, 2) loses RE is small, if the game is close fight, is to be aspects emphasize RP.
(2-b, 2), (3-b, 2), in the case of (2&3-b, 2), the size of RP, Suzuki > Beltre > Trout has become the order of Ramirez, the value either do not take or take the IBB changes.
Since Suzuki has high RP and low RE, but rises validity of IBB, Ramirez will be vice versa, overall.
That was found here is that as follows.
・From the viewpoint of RE, nearly all situations, in some slugger, it has little validity.
・The head-to-head, although aspects of RP is emphasized is assumed, in such a situation, there is no small phase IBB is valid.
・When's this example, RP is a plus, as limiting the RE that loss to about 0.01, as the situation, (2-b, 2), it is effective (3-b, 2) is IBB.
Ichiro (2&3-b, 2), also in the context of (2 & 3-b, 2), but effective IBB, who has a lot of single hits extremely, is rare.
・In such a situation, rather than a long-distance batter, there is validity of IBB the batter a lot of hits type. In fact, Suzuki of 2004, out of the four batter, OPS is but the lowest, there is most often, 19 of IBB.
・The effectiveness of IBB is changed finely in a batter of hitting profile ( + of course, base-out situation). Ten number of AB, BB, HP, IBB, 1B, 2B, 3B, HR, SF and GDP is sufficient for calculation of this hitting profile here.
At the end. Considering the numerical values calculated in this carefully, with the exception of exceptions such as Ichiro of (2 & 3-b, 2), IBB since always accompanied by losses of RE, and a strategy selected in accordance with a situation is forced, it is not a simple effective strategy.
Well, for IBB, I think it is for the defensive side, what kind of situation, how much valid or, to be let to verify.
First, we will consider a simple situation.
The thinking here is, it's situation where one out runner first base second base (1&2-b, 0).
If you have reached the batter in this situation, pitcher whether should the IBB, let's think.
Here assumed batter grades, which was used in the previous calculation, but the overall average of 2011- 2014 of MLB. →Table 4
AVG : 0.254 OPB : 0.319 SLG : 0.400 OPS : 0.719
As expected, and whether there should not be IBB in this situation, it should not be how much in, let's see.
FIG.29
・IBB If the assumed pitcher chose IBB, It becomes situation (full-b, 1), the run expectation (RE) and run probability (RP) will be 1.533 and 65.3 % respectively. →Table 2, Table 3
(RE, RP) = (1.533, 65.3 %)
・Fighting a batter If the pitcher play against the batter, simple results will be DB (BB + HP-IBB), 1B, 2B, 3B, HR, SF, GDP and Out. Out is mainly strikeout and infield fly.
Here SH, defence's error, and base running mistake are not taken into consideration.
First, the context of (1&2-b, 1) is, in Table 7, corresponds to the case IV.
We will continue to calculate the EP and ER in each case.
Over the eight probability of the cases IV to the avobe number of each is summed to obtain the RE and RP of "Fitting a batter" as shown if FIG32.
As a result, (RE, RP) = (0.861, 39.7%) is obtained, when compared with that of the state of IBB, (RE, RP) = becomes (-0.672, -25.6%).
This is, in the context of (1&2-b, 1), when it reached the above batter,IBB 0.672 in the score expected value, 25.6% in the scoring chance, but that's a loss.
This loss, 1 out first base and alternate as much value, become the equivalent of losing it at once when viewed from the attacking side.
(1-b, 1) : (RE, RP) = (0.502, 26.7 %)
Of course, IBB should not be in (1&2-b, 1).
Next time, instead of the situation and the batter, as many as possible in the case, we will examine the efficiency of the IBB.
This time, to introduce a simple method for analyzing the probability of each state of the blow.
The result of a blow, here used, it is a thing of the following.
AB, 1B, 2B, 3B, HR, SF, GDP, SH, BB, HP, IBB
SF : sacrifice fly GDP : grounded into a double play SH : sacrifice hit
I show the actual batting performance of 2011-2013 of MLB in table 4.
Indicators of the blow, which is calculated from the numerical values shown here is as follows.
AVG : 0.254 OBP : 0.319 SLG : 0.400 OPS : 0.719
Table 4
Here, we put the assumption that, "SH not do."
And here, for the defense errors and base running mistake, these are not considered.
And we put two formulas that AB + SF = DA and BB + HP - IBB = DB. (＊ BB contains IBB.)
AB does not contain SF, SH, BB and HP. DB, 1B, 2B, 3B, HR, SF, GDP is independent event.
(A) of table 4 is actual number of 2011-2013 of MLB.
(B) of table 4 shows probability of two state of the blow, with or without SH.
Table 5
There are shown in Table 5, SF, GDP, the possible status of SH, the present invention which is divided into six kinds (I-VI) of state of 24.
The situations where no-runner (0-base, 0 or 1) or in a two-out (any-base, 2), sacrifice fly also sacrifice nor does not occur double play, which are indicated by (-), (-), (-).
*SH in (1&3-b, 0 or 1) and squeeze play are not taken into consideration.
And we will introduce the probability that PBOS.
PBOS : Probability of Base-Out State
For example, PBOS of "(0-base, 0 or 1) or (any-base, 2)" (case I) is calculated by adding the 10 numbers below. These number is come from Tabel 1.
This shows a method of calculating the number of digits.
DA was calculated by the following equation.
DA = 546376 × PBOS. 546376 is DA of the case of SH = 0 in table 4, (A).
For example, DA of "(0-base, 0) or (any-base, 2)"(case I) is calculated by 546376 × 0.729(32) = 398483.
DB, 1B, 2B, 3B, HR were calculated by the following equation.
DA × the number of green box in table 4, (B).
For example, 1B of "(0-base, 0 or 1) or (any-base, 2)"(case I) is calculated by 398483 × 15.520 × 0.01 = 61844.
SF and GDP were calculated by the following equation.
SF : 3716 × conditional probability of six situations. GDP : 10869× conditional probability of six situations.
For example, SF and GDP of "(1&2-base, 0 or 1)".
SF : 3716 × 0.198(6) = 738 GDP : 10869× 0.2011(8) =2187
In the calculated six situations thus shows the respective probabilities of hitting Table 7.
Table 7
As can be seen immediately, "B, 1B, 2B, 3B, HR" has also become the same probability in any situation.
It is the premise that "not to sacrifice", because it is so as will become, operating the calculation method.
SF is if the runner of second base, at 3.419 %, in the case of a third base is a 6.839 % of its two-fold.
If the GDP can occur, it is 10.132 % always.
Number of SF and GDP are not obtained from the actual data, it should be noted that it is one that has been assumed in this calculation.
If the actual data is available, to it it can be easily modified to apply a change as a parameter, how it fits the actual baseball game, it's verifiable.
Finally, calculation method shown here, AB, 1B, 2B, 3B, HR, BB, it is possible to HP, IBB, SF, DP, execution if availability numbers SH, but relatively simple.
Several times from this time, let's be discussed about IBB (Intentional bases on balls).
First of all, we compare IBB by NPB and MLB.
FIG.25
Average IBB/G in NPB of 1995-2014 is 0.153, and in MLB is 0.256, and its difference is 0.103, which significant by a probability of 99% statistically (p-value < 0.001).
In order to explore the cause of this difference, as shown in the figure16 and figure 17, on whether pitcher with a big difference to the striking power of a fielder can not stand or stand in the batter's box, you will see how different.
*NPB ; OPS of pitcher = 0.285, OPS of fielder = 0.736 MLB ; OPS of pitcher = 0.367, OPS of fielder = 0.761
To do this, it is sufficient to compare the two leagues with DH system.
FIG.26
NPB IBB/G in CL is 0.172, and in PL is 0.133, and its difference is 0.039, which significant by a probability of 99% statistically (p-value = 0.006,1995-2014).
MLB IBB/G in NL is 0.294, and in AL is 0.214, and its difference is 0.080, which significant by a probability of 99% statistically (p-value < 0.001,1995-2014).
Even NPB even MLB, (stand pitcher bat) with no DH system league is greater than the IBB / G.
Situations that can easily be imagined ; there are runners in scoring position (2 out), but if the following is pitcher of batter against.
FIG.27
In a situation where not getting the data of IBB of each batting order, let's explain this.
FIG.28
In this figure, it shows the IBB/G for each rank of OPS.
In PL and NL with DH system, IBB/G is larger for each rank of simply OPS.
On the other hand, in the CL and AL, also batter of OPS is low rank (OPS < 0.7), has taken a number of certain of IBB/G.
This is, in front of the pitcher, because the OPS is low batter, is kept away by the situation.
However, it is the first question, why, or shy away from that more than NPB in MLB has not been explained.
Leading reasons at present is that the difference between the scores/G is intact, is the difference in the number of IBB/G.
Because the situation to be the the IBB, is a scoring chance, it ie because tied the score.
Unfortunately, the situation probability that was introduced previously (table 1) is not missing in the NPB, where it can not be verified here.
In scoring the expected value table, when we look at the fine situation of base-out, because the special three situations comes into view, it should be easy to write.
The three situations, depending on the quality of the runners of base-running, before and after the event, the difference between the expected value is larger ones most.
FIG.22
(2-b, 2) → 1-base hit → 1 point + (1-b, 2) or (2-b, 2) → 1-base hit → 0 point + (1&3-b, 2)
As shown in the figure, on whether runner in the hit stops at either third base to home in, big difference comes out (0.74).
If the runner is by temporarily aggressive rush became out at home plate, scoring the expected value to be lost it 0.475.
Gain : 0.74 Loss : 0.475
FIG.23
(1-b, 2) → 2-base hit → 1 point + (2-b, 2) or (1-b, 2) → 2-base hit → 0 point + (2&3-b, 2)
Gain : 0.74 Loss : 0.573
FIG.24
(1&3-b,2) → GDP → 1 point + (0-b, 2) or (1&3-b,2) → GDP → 0 point + (3-b, 2)
Gain : 0.74 Loss : 0.357
In these situations, greater gain due success, loss due to failure is not so large.
Runner, in such circumstances, start quickly, aimed at home plate as possible.
It should be noted, also the same-base situation, if the out count is 1 out or 2 out, but that should not be excessive.
Here, we decide the rules to easily illustrate the situation of the out count and runner.
For example, about one out runner first base and second base, is to be written as (1 & 2, 1).
Table 1
Probability of Base-Out State
This table summarizes the base-out situation that occurs to the end from the start of the game when a new batter is standing in the batter's box, it used to express it as a percentage.
For example, the situation of (1 & 3, 1) base was generated in 1.15% of probability.
When added together all the numbers in this table, it is 100%.
Table 2
Run Expectations by Situation
Then, we will introduce the score expected value table.
In this table, its base-out conditions, indicating whether containing many points on average.
For example, when the situation of (1 & 3, 1), 1.142 points were brought on average.
Table 3
Run Probability By Situation
Finally, we introduce the scoring probability table.
The table, under the base-out status, indicates the probability whether the at least one point entered.
For example, in the situation of (1 & 3, 1), with a probability of 63.6%, the lowest one point entered.
And these three tables, based on the batting performance of the batter, the future, we will recommend the discussion.
