Note the pattern of how the terms cancel one another out. In general, as long as

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Note the pattern of how the terms cancel one another out. In general, as long as k>n/2, this pattern will hold. Thus, under such circumstances the probability of a streak of k successes in n trials is This low probability suggests that DiMaggio's hitting streak is indeed an unusual and 4 When might the record be broken? can we expect this record to be broken? The natural follow-up question is: When When ksn/2 this expression will be in error only by terms of the order p*or greater. These will generally be negligible in the present problem. Data were compiled for all 245 players who played in at least 100 games in the 1993 baseball season. Again, while this criterion is arbitrary, it does make data collection manageable, and we estimate the probability of a non-regular player achieving an extended hitting streak to be negligible These data, and relevant calculations similar to the previous, are given in Table 2 on the last page Joe DiMaggio averaged playing in 134 games over the course of a 13-season career. Thus his chance of achieving a 56-game hitting streak irn any one season is (134-56+1) .792406)56- (134-56)*(.792406)57 00003771, We similarly compute the probability that someone would have achieved a 56-game hitting streak during the 1993 season as and the chance of a 56-game streak occurring at some time in his career is Pr(at least one 1-Pr(no streak)- 1-Product of terms in last column of Table 2 1-(1-00003771)13 00049. 1-.997303= .002697. 3. On the likelihood of the record: If the 1993 season is an any sense "typical", this would indicate a chance of somewhat less than three- tenths of one percent that the record will be broken in any given season. To extrapolate outward, the probability that the record will be broken in n years is then Career data were obtained on every player who had played in the major leagues for at least ten seasons. This criterion was chosen to make data collection a manageable task; we figure the chance of a short-term player achieving an extended hitting streak was negligible. These data are summarized in Table 1, on the next page Pr(record broken in n years)- 1-Pr(unbroken for n years)- 1-(1-.002697) Calculations similar to those in the previous section are done for each player grouping. The overall probability that someone would have achieved a 56-game hitting streak is Pr(at least one streak) 1 - Pr(no streak) 1 - Product of terms in last column of Table 1 - 1-.9273 = .0727 Values of this expression for selected values of n are given in Table 3·These calculations suggest that it will be a long time before DiMaggio's record is broken. Indeed, 257 seasons would need to elapse before we could reasonably expect this-barring strikes and other national disasters!

Explanation / Answer

Assumptions made:

Players follow previous streak

Conditions remain suitable for playing

Unbaised decisison making in game or in other words no match-fixing

Assumptions are reasonable to a certain extent as consistency comes with repeated practice and eventually performance increases

Without maintaining proper consistency and hard work result will not be good.

Given that, we should keep in mind that all matches are played with unbiasness

Moreoover, we need to consider that weather / climate and health conditions of players are at par with the playing necessity

Other assumptions that can be made:

Health condition check of players

Team motivaitonal activities

Effect: With improved health condition probability of hitting streak will go up.

Motivated players will deliver better output.

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