Rubu's Hypothesis of Performance Interval

[Rubu]

All the cricket fans here tend to choose players depending on two separate methods. Group one, let us call them pro-talent, believes that class is permanent, and form is temporary. Therefore, it is talent that should matter most when choosing a player for the national team. The other group, let us call them pro-performance, believes that talent is just a mean to an end, performance. It does not matter what mean someone uses to perform, as long as he performs. Interestingly, both sides have quite a few valid arguments. As a result, the dispute goes on and on. Here is an adventurous effort from me to end this argument. I will call it the frequency interval hypothesis. Of course, not every one will agree with me, but I am hoping that at least some from both sides will.

Before I explain the hypothesis, let me state some background information. There are some players who are labeled as talented and perform on a regular basis. They are never part of this argument. Players such as Rafique, Mashrafee and Pilot might fall into this category. There are not our concerns here. There are another group of players who are not thought to be talented and they do not perform either. They are not our concerns as well. There are however, two more groups. One group of players are thought to be highly talented but do not performs very often. This is our interest group one. Let us call them the talented group. These players, even though they do not perform very often, can alter the result of a game on their day. These players, however, fails to have an impact on the game on other days. In short, either they perform well or do not perform at all. The other group of players, without being highly talented, always contributes a bit into the game. We can call them the utility players. These players can never change the outcome of a game single handedly like the other group, but will have some contribution more often than them.

The question is which group to choose? If we do choose the utility group, we will only have a better looking lose unless it is a close game. If we choose the talented group, we either win or loose miserably. The answer is it all depends on two main factors. How many close games are there, and what is the frequency of interval a player performs. Obviously, if the number of close games is high, a utility player would be preferable to a talented player. On the other hand, talented player is preferred when the outcome is heavily leaning toward the opponents. This is the frequency interval hypothesis in short, but I try to put it in a mathematical form.

The hypothesis is based on the fact that the main goal of a match is to win it. We should pick the squad in a way that will maximize the number of win. Let us take a hypothetical player X. Mr. X is a talented player who has the ability to change the outcome of a game single handedly. He comes ups up with those kind of match winning performance once in every 25 matches. In other 24 matches, his performance is below a utility player performance, say below 20 runs. Should we pick him? It all depends on how those 24 matches were. How many of them were close matches? Say, the number is 6. Here, say a utility player contributes once in every three matches. Now, if you add those runs of a utility player to a close match, you get a win. So, once in every three matches gives you two wins in those six close matches. Final outcome, two wins if you choose a utility player but one if you choose a talented player. But what if the talented player performs once in every 10 matches instead of 25? Everything else being equal, we get 2.5 wins using the talented player but 2 wins using utility player. In this case, the choice is the talented player.

It might sound a bit complicated to use, but all of it is simple math based on statistics. It can be actually done. Here, I would use it to analyze one special case, Rana v Kapali. One is a talented player, and the other is a utility player. I will consider a 50+ innings from the talented player (Kapali) as a difference making innings, and a 20+ innings from Rana as a utility innings. I will consider all the matches since Kapali’s debut to find out how many close matches are there. A loose below 25 runs, at the 47+ over or below 2 wickets will be considered a close match. Then I’ll use the difference making frequency from Kapali and utility frequency from Rana to figure out who would possibly bring in more wins. In this interval Bangladesh has played 61 ODI. Out of these 61 games, Bangladesh had 12 close games. The following are the ODI numbers that I considered close games: 2044, 2110, 2111, 2128, 2129, 2130, 2199, 2201, 2207, 2210, 2250 and 2257. Kapali had 43 innings so far and he scored above 50 four times. In other words his performance interval is 43/4 = 10.75. Given that in those 61 matches he would be able to make an impact in (61/10.75 = 5.67) matches. What about Rana? In his 18 innings, he scored utility runs (20+) 5 times. That gives him a utility interval of (18/5 = 3.6). So, how in how many matches, he would be able to make a difference? Since we know that there were 12 close matches, it will be (12/3.6 = 3.3) matches. What is the result? Considering pure batting only, Kapali has an advantage of (5.67 – 3.3) = 2.37 over Rana. This does not include any consideration of Rana’s bowling ability over Kapali’s, and probably Rana stays ahead there, but if are to pick one between this two as a “pure” batsman Kapali is the choice.

It would be interested to see how this works for Rajin and Tushar. But we cannot really identify either of them as talented or utility player. So, what needed to be done is to calculate both utility performance and difference making performance for both of them and add them together to get one number for each. Then see who scores more, Rajin or Tushar. (If no one else is interested in doing that I will try it latter)

How good this hypothesis can be in real life? Feedback wanted.

[al Furqaan]

i have not yet finished reading, but i must say...

...simply a marvelous piece.

and you know it was written by a desi for 2 reasons:

it analyzes cricket and
it provides a mathematical formula for that purpose.

I love it!!!

[al Furqaan]

i have a few critiques now that i have fully read it.

1) the assumption is that a talented innings (50+) is equal in magnitude to a utility innings (20+). while it may be so per player, per match it isn't 99% of the time. 50 > 20 always.

2) true kapali may have only scored 50 4 times out of 43, but sometimes a 25 ball 20 is as valuable as a well paced 50 (when other batsmen have scored 200).

3) while subjective things like talented players is rather objectively asessed on this forum, it is more difficult with individual innings. for example all on the forum would agree that ashraful's 100 against Australia was the single biggest determinant in our win. but what about ashraful's 34 ball 33 against india in a match in which we scored 257 (and lost)? that would be, in my estimation, a solid performance, but under your hypothesis, not so.

4) [this particular comment of mine might be flawed, but i do not have the brain power (at least not currently) to see if does or not, so i will have to rely on my fellow BC members to check it out for me. much thanks]

it is not guranteed that the utility player will perform (20 runs) in every exact match where the talented player under-performs or would under-perform.

the problem is that this conundrum cannot be solved purely mathematically. some element of the game will always be resigned to chance. our only wish is that the BCB use its best judgments in determining our best playing XI and that the players give 100% effort. in any case, your effort was as best as possible and still had the aforementioned shortcomings.

nonetheless, i really enjoyed reading your article, and i fully expect to see it on the front page of BC next time i log on. articles such as these are the reason for forums such as this.

[Rubu]

Al Furqaan, thanks for your feedback.

as it seems most of your criticism is about the numbers i picked. well, thats easy just need to adjust them.

>>>>the assumption is that a talented innings (50+) is equal in magnitude to a utility innings (20+). while it may be so per player, per match it isn't 99% of the time. 50 > 20 always

this is based on the assumption that a utility player will score 20 runs more frequently than a talented player who does not score that often. 50>20 is true always. but it all depends on how often u get the 50 and how often u get the 20. since u are more likely to get 20s from a utility player than a 50 from a talented player (of the defination above) the 20 is more welcome if the number of close matches are large.

2-3. true statements but hard to apply in this model.
4. that is based on the assumption that whatever patern went before will happen before. this is very close to true if the sampling fielding (number of data) is large. a player who played only a few games will not be good in this model. when the number is large, it does garentee (kind of ) that a utility player will score that 20 runs with a performance interval.

any more criticism? i'd like some more so that based on those i can keep chaning the hypothesis.

btw, one thing that got me hopeful about his idea is that, even though i'm baised about rana and don't like kapali my theory came up the other way. so, my personal choice probably did not effect it.

Edited on, July 31, 2005, 3:39 PM GMT, by Rubu.

[Rubu]

A comparison between tushar imran and rajin saleh on those same 61 matches where there were 12 close matches. i could pick a different sample but since i already know this its just easy to use.

Tushar Imran:

Difference Making Innings: 2

Difference Making Interval: (29/2) = 14.5.

Possible win as a telented player: (61/14.5) = 4.2

Utility innings: 12

Utility Interval: (29/12)=2.42

Possible win as utility player: (12/2.42) = 4.96.

total point: 4.2+4.96=9.16



Rajin Saleh:

Difference Making Innings: 5

Difference Making Interval: (31/5) = 6.2.

Possible win as a telented player: (61/6.2) = 9.84

Utility innings: 13

Utility Interval: (31/13)=2.38

Possible win as utility player: (12/2.38) = 5.04.

total point: 9.84+5.04=14.88

Rajin Saleh stay ahead of tushar imran by a huge 5.77.

Now, possible win does not mean we could win this match. but in everything else being equal, what would bring a win in those matches if we choose a utility player over a talented player in a close match, or other way around in a one sided match.

[al Furqaan]

i see...i do not have any more criticisms.

however, to be honest, i am against using mathematical models to select players.

i just believe in the highly subjective, most players should get in on talent (unless they never perform a la nafees iqbal) and some players based on utlity (rana in ODIs).

a good effort on your part. lets see what happens in Lanka.

[Orpheus]

Nicely done! Impressive.

I would rate this highly considering NOT so accurate statistical analysis is also done by number game of cricinfo! I will not dwell on the ones that will be more complex to have it in calculations for a layman but

Here is a flaw:

Your sample of 61? matches should be a sample that neither of the players played. Why (explained bottom) - but your sample was chosen from Kapali's debut when you were analyzing kapali tsk tsk!

Let's talk about Rajin

1) Suppose Rajin already played one of those matches where he contributed 50+ and it was a close game. Now according to your calculations, Both Rajin and Tushar would be valuable in that match as utility players..... But Rajin already played, so by including him the contribution is actually a big fat 0.

(also out of those matches these men didn't play, who are they replacing....their contribution is also being deducted.... but let's not get too complicated)

maybe you can do something like.... have Rajin compare to all the matches Tushar played where Rajin didn't play and have Tushar compare to all the matches Rajin played but Tushar didn't..... The deduct each of the respective players contribution to that match and then decide whether the match was close or not.. and blah blah blah... I just woke up and my head hurts... I will write more later if I can ok...

Edited on, July 31, 2005, 6:34 PM GMT, by Orpheus.
Reason: wrong smiley!! it is indeed impressive.

[israr]

Dam good Mathematics shouldn't be bought into rating talent, but my conjecture is that this can atleast give us somewhat kind of a notion of who is the better player, well at least. However, it's a job very well done. Iam impressed with the particular innovation and this piece of work is really commendable and really deserves some accolades. Job well done

[Rubu]

israr, thanks.

Orphy, see i did not call it a theory, but a hypothesis. that means there going to be changes and changes until a well excepted theory is established. I'll see how excluding the player in prospect effect the calculation. need some time.

[Tokai]

I also think if you take out the games a player had played then the model could be more useful. When calculating the numbers for Rajin, use a set of games (as many as possible) where Rajin did not play and figure out how many of them were close games. same goes for tushar and then compare them.

But I agree to the basic idea. when the number of close games are large, use utility players more than irregular talented player.

[akabir77]

What about the pitch/condition? how many of those matches were played in batting pitch where anyone can score 20. What i meant is sometime its harder to score 30+35 in a pitch where u can consider that to a 50 in a batting pitch...
Also when u r considering plyr to chose there has to be a gut feeling or 6th sense working for the player .. cause i bet you will use this formulla for the 11th man not the whole team... So the captain and coah might go with their gut feeling and be right instead of a formulla...
never the less great effort by mr rubu

Edited on, August 2, 2005, 3:52 PM GMT, by akabir77.

[Fazal]

... and what about when players get sick ( mental as well as physical), the weather (cold, hot, muggy, etc.), location, crowd noise, crown behavior (hostile vs. friendly), quality of umpiring, opponent fielding, mental instability due to external force?

We need to take into consideration of all those things to make this hypothesis into theory.

[Rubu]

Originally posted by Fazal
... and what about when players get sick ( mental as well as physical), the weather (cold, hot, muggy, etc.), location, crowd noise, crown behavior (hostile vs. friendly), quality of umpiring, opponent fielding, mental instability due to external force?

We need to take into consideration of all those things to make this hypothesis into theory.

Fine. u want me to give up?

Ok I give up.

[Fazal]

Originally posted by Rubu
Fine. u want me to give up?

Ok I give up.

Thukku... Sorry... Maf Chai.....

don't give up!!!! Its very entertaining.