(Presented at SABR-30, West Palm Beach, FL June 25, 2000)
There are many questions that can be asked about the game in these situations. How often and when do they occur? How are hitting and other events affected by the pressure? What differences are there between the two leagues? To answer such questions an objective definition of a game situation is needed. The observation that IBBs are often called for in these game critical situations suggests that IBBs can be used to define these situations.
Since the IBB is an official game statistic, the problem of identifying game situations becomes defining the circumstances used by managers to call for the IBB. The decision to give an IBB is a complex one, depending on much more than the presence of a base runner on second. An algorithmic decision method, one that can be programmed, is needed to insure consistency and to enable it to be applied to the more than 3,300,000 Plate Appearances (PA) in the 1979-1999 season records available as play-by-play files. Since IBBs are distinguished from the more common unintentional variety (UBB) in this record, a decision method using the game contexts of IBBs and UBBs is required. The observation that IBBs are given in a variety of situations as well as the observation that they are not offered in every candidate situation suggests a statistical decision method is appropriate.
The particular technique chosen to distinguish between IBB and UBB situations is a neural network (2), a technique for generating a classifier capable of making subtle distinctions. Its computational structure is diagramed in Figure 1. While the name suggests artificial intelligence or other exotic technologies a neural net is a well defined numerical computation. The name arise from the connection of all the input parameters, the numbers defining the game situation, to each hidden unit or "neuron" and the connection of all the outputs from the hidden units to the output unit. The particular neural net that is diagramed in Figure 1 is a two layer perceptron trained by an iterative procedure known as the back propagation of errors. The training procedure minimizes the sum of the squares of the classification error, the difference between the given value for an event and the value computed by the neural net from the game context. This is the same error criteria minimized in the more common linear regression procedure. Each neuron or computational unit, a single box in Figure 1, implements a two step computation. The first is a weighted sum of its inputs including a constant, completely equivalent to the evaluation of a similar sized linear regression formula. The second step subjects the value determined by the sum to a sigmoidal function, one that has output values limited to +1 and -1 and a slope of +1 at an input value of 0. Given a set of classified events (known IBBs and UBBs), the training procedure uses a gradient descent technique to minimize the misclassifications by determining the weights in each of these computational units. Additional information on the neural net classifier is given in (3).
Unlike a linear regression formula where the weights have an interpretation in terms of events used, there is no simple way to interpret the values of the weights in a neural net. A geometric interpretation of the decision function can be made but doing so is beyond the scope of this paper.
The game context is determined by 8 parameters. The first three are the presence of runners on each of the bases. The next two are the number of outs in the inning and the inning. All extra innings are given the value 10. The sixth parameter is the relative score, the difference between the offensive team and defensive team scores at the time of the event. The final two parameters are the hitting measure appropriate to the batter relieving the IBB and the on deck batter at that time. I have used a recent at bats slugging average for the hitting measure.
In the terminology of the neural net, there are 8 input units corresponding to the 8 quantities that define the context of the event. After considerable experimenting, I have decided that 9 hidden units is appropriate for this problem. The classification error goes down as the number of hidden units increases, but the gain in accuracy beyond the 9 used is very small. Thus the IBB/UBB classification neural net contains 91 numerical parameters or weights. A linear regression formula based on the same parameters would have 9 weights. A comparison between a linear regression and a neural net classifier is given in Table 2. The linear regression calculation weights and correlation coefficients provide insight into the relative importance of the input parameters. Table 1 lists this information.
Using the Retrosheet, Total Sports and Gary Gillette/Pete Palmer play-by-play game accounts for the 1979 to 1999 seasons all UBB (266270), IBB (26591) and Hit by Pitch, HP, (20069) events and their contexts were tabulated. Training sets were created by choosing a set of IBBs that meet some criteria (all, league, seasons) and a similar number of UBBs satisfying the same constraints. HP events are not used in the neural net training but are included in the analysis since their effect on the game is the same as a BB.
Table 1. Linear Regression Coefficients and Correlation Results parameter weight r*r Exclude constant -1.0470 runner on first -0.4228 0.108 0.1459 runner on second 0.7052 0.393 0.3571 runner on third 0.5181 0.185 0.2578 inning 0.0604 0.097 0.1063 outs 0.1184 0.094 0.0276 relative score 0.0364 0.088 0.0913 hitter getting BB 0.8198 0.013 0.0258 hitter on deck -0.7679 0.023 0.0243 Table 2. Classification of all 1979-1999 BBs, IBBs and HPs by the Neural Net (NN) and by Linear Regression (LR) UBB as IBB as UBB+IBB HP as UBB IBB frac IBB UBB frac UBB IBB frac UBB IBB frac NN 240656 25406 0.905 25488 1069 0.960 266144 26475 0.910 18129 1922 0.904 LR 218728 47334 0.822 25462 1095 0.959 244190 48429 0.834 16587 3464 0.827
The presence of a runner on second base is the most influential of the input parameters corresponding to accepted understanding in the game. The negative sign for the runner on first and on deck hitter weights indicates that these parameters tend to reduce the use of the IBB. The rather small values for the correlations, r2, with hitter abilities is perhaps surprising. A similar rank ordering is achieved by individually eliminating each of the input parameters from the neural net and repeating the training with the remaining seven. The amount the classification error is increased (column Exclude in Table 1) provides a measure of the importance of the parameter. The data in Table 2 shows that neural net reduces misclassifications by about 45% compared to a linear regression based classifier using the same game context parameters. The majority of this reduction is in reduced misclassifications of UBBs. HP events classify very similarly to UBBs.
To further validate the neural net the data was separated into NL and AL subsets. Each set was used to train a classifier and the data not used in the training was classified. The resulting classifiers are almost as accurate as the complete data set classifier. The data was also separated into 1979-1989 and 1990-1999 sets. The training and classification were repeated with very similar results. For the results that follow the complete training set neural net classifier is used.
Another useful way to view the overall classification results is a histogram of numbers of events plotted against the neural net classifier output value. This is shown in Figure 2. In this figure the UBBs counts have been scaled by a factor of 10 enabling the IBB and HP trends to be clearly seen. The well defined peaks for each type of event and the large separation between them is additional evidence of the power of the neural net to identify IBB situations. The data presented clearly demonstrate that a neural net can be trained to recognize IBB situations with excellent accuracy.
The resulting IBB/UBB classifier was added to the play-by-play file processing program and used to classify all plate appearances. Various game events have been counted according to the neural net IBB/UBB situation defined when they occurred. The tabulations presented include all data from the 1979 to 1999 regular seasons by league. Figures 3 to 7 display various aspects of the IBB and neural net defined IBB situation distributions.
The observed number of IBBs per inning as a function of the inning is shown in Figure 3. In this and following plots, the right most column is for all the events occurring in 13th and later innings. The number of PAs per inning is roughly constant through the 8th inning showing the use of the IBB increases significantly towards the end of the game. The NL clearly uses the IBB tactic more than the AL.
Figure 4 shows the distribution of IBB situation PAs as a function of inning. Through the 8th inning the greater number of AL games included in the data is reflected in a larger number of IBB situations. However, in the 9th and extra innings a slightly larger fraction of NL than AL PAs are classified as IBB-like. Both the number of IBB situations and IBBs increases significantly as the game progresses.
Figure 5 shows the total number of IBB per PA as a function of the inning. There is a slow increase in the rate through the regulation innings and it jumps markedly in extra innings. Clearly, when a single run can decide a game, the use of the IBB is dramatically increased.
The interesting rate of IBBs offered as a fraction of IBB situations is shown in Figure 6. Obviously the IBB is only given in a fraction of the situations defined as IBB-like by the classifier. However, the fraction increases as the game progresses and approaches 1/4 in extra innings. While the neural net works very well for correctly classifying IBBs, a manager only calls for the intentional a small fraction of the time in situations matching those where the IBB is usually given.
The distribution of IBBs based on the relative score at the time of the event is shown in Figure 7. The IBB is predominantly given when the defensive team is behind or leading by at most one run.
Figures 8, 9 and 10 indicate how common hitting measures and certain error events depend on the type of game situation. The first of these displays batting average, slugging average and quantities related to Runners in Scoring Position (RSP). Obviously, the predominant indicator of an IBB is a runner in scoring position which accounts for the much higher RSP values in IBB situations. The most illuminating of these is the values for Runs/RSP (R/RSP in Figure 8), the average number of runs scored per runner in scoring position. While the RSP per PA is much higher in IBB situations, a significantly smaller fraction of these runners actually score in IBB situations. Batting and slugging averages improve slightly and the overall stronger hitting of the AL due to the designated hitter is clearly visible.
Figure 9 displays rates for some common error events. Since their effect on the game is the same Wild Pitches (WP) and Passed Balls (PB) are aggregated together. The rate of these events more than double in IBB situations. The rate of Balks (BK) is essentially unchanged. The category ER,B1 includes those fielding errors that allow a batter to reach first base. ER,RA are the fielding errors that allow a base runner to advance. In both cases, these rates are only slightly different. Using Student's T-test to check the significance of these differences confirms that they are significant for the WP+PB and ER,RA categories.
Figure 10 presents the data used to train the neural net in a slightly different fashion. The classification power of the net is evident in the greater than 100:1 difference (note the logarithmic Y axis) in rates for IBBs seen in the two classification categories. Both UBBs and HPs increase somewhat in IBB situations. Trends in both leagues are the same.
Summarizing, a study of when IBBs are offered using a neural net classifier trained by all ML regular season IBBs in the period 1979-1999 indicates that IBBs are given according to a well defined set of criteria. This follows from the 96% accuracy achieved in classifying IBB events by the neural net. The neural can be applied to all PAs defining a fraction of these as IBB situations. These IBB situations correspond to pressure or otherwise crucial game situations. Depending on the inning, managers appear to offer IBBs in 1/10 to 1/4 of the neural net classifier defined IBB situations.
In IBB situations the increased pressure is indicated by higher error rates and slightly higher batting and slugging rates and a slightly increased number of UBBs. However, the fraction of runners in scoring position that actually score decreases suggesting that the IBB tactic does reduce scoring.
The National League clearly uses the IBB at a higher rate than the American. Within IBB situations the changes from UBB situations are the essentially the same for both leagues.
(1) An Analysis of the Intentional Base on Balls, John F. Jarvis, SABR29 (Phoenix, AZ June 1999) presentation.
(2) "Neural Networks", Laurene Fausett, Prentice Hall, 1994
(3) "BBs, IBBs, HPs and Pitching Around in 1998", John F. Jarvis,
By the Numbers, Vol. 9, No. 4, November 1999, pp 11-13
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