weldone
Hall of Fame Member
As some of you know, I presented a paper in MathSports International 2017. The idea was well-received by the Mathematics community in general. Since then, I have developed the idea further to come up with full-blown ODI rankings. Below are some of the key aspects of the ranking:
1. Value Added: The paper was based on mainly this simple idea. We applied a concept from Financial Economics to value batting efforts. The similarity is that firms aim to maximise profits using limited resources; batsmen in ODI cricket aim to maximise runs using limited resources as well. Long story short, you can’t compare based on profit or runs alone; you can’t compare based on process efficiency alone either (profit/capital employed, or batting strike rate). The question to ask is if these resources (capital, or balls) were employed in an average venture, what would have been the return. In Financial Economics, we compute Economic Value Added = (Return on Capital Employed – Hurdle Rate) * Capital Employed. Similarly for batsmen, we can calculate Batsman Value Added = (Strike Rate – Par Rate) * Balls Faced/100. I shall discuss Par Rate in a separate point below. For this calculation now, imagine Par Rate is 70. Then a 40(50) innings will get 5 points, 45(50) will get 10 points, 80(100) will also get 10 points, and 36(60) will get -6 points according to the formula above. For bowlers, an equivalent formula will be (Par Rate – Economy Rate) * Balls Bowled/6. Imagine if Par Rate is 4.5 then 40 runs in 10 overs will fetch the bowler 5 points, 49 in 10 overs will get -4 points, and 20 in 6 overs will get 7 points.
2. Not Outs and Wickets: The premise is that not outs are inherently no better than outs if the batsman has played enough deliveries. If a batsman plays more than 1/10th of the available deliveries (slightly above 30 for 50-over matches, including no-balls) then he isn’t causing the team getting all-out. However, the less the number of balls a batsman plays (below 30) before getting out, the more impact he has towards the team getting all-out. So, 20*(25) is better than 20(25), 4*(2) is much better than 4(2), but there’s no difference between 35(40) and 35*(40). As a result, there is additional negative point for playing less deliveries depending on the number of deliveries played. Similarly, if a bowler takes less than 2 wickets in a 10-over spell then he’s not contributing towards getting the opposition all-out. Taking 3 wickets in 10-overs is better than taking 2-wickets, and so on. Taking 1 wicket in 5-overs is useful. The bonus points are designed accordingly.
3. Par Rate: The Par SR and Par ER are calculated based on the average first-innings performance of last 4 years (for era effect), the bowling strength of opposition (for batsmen), the batting strength of opposition (for bowlers), and pitch.
4. Pitch: Analysing pitches is the most difficult part. The same ground behaves differently at different times. Eden Gardens of today is not the same as Eden Gardens 30 years back. The Oval has changed drastically. Some pitches change within 2 consecutive matches. Unless someone watches all the 4000 ODIs and provides subjective opinion, the only other option is to deduce from scorecards. Long story short, I have divided the pitches in 6 categories based on scorecards – uneven pitch assists spinners but assists pacers more, crumbling pitch assists pacers but assists spinners more, dry pitch assists spinners but disadvantages pacers, green pitch assists pacers but disadvantages spinners, flat pitch disadvantages spinners but disadvantages pacers more, hard pitch disadvantages pacers but disadvantages spinners more.
5. Initial Rating: This is another area where this ranking is different from all other rankings. Because I use my ratings for predictive purpose, it is important to come up with accurate initial ratings. In all other rankings, players start from the same base in their debut match. But that is unfair and inaccurate. Because for example a South African debutant opening batsman has already achieved more than a debutant opening batsman from Scotland. The initial rating is decided based on the following 5 factors: team batting strength in last match (for batsmen), team bowling strength in last match (for bowlers), batting position, whether the player bowls at all in the debut match, and whether the player is a wicketkeeper.
6. Weightage per match: As this rating is predictive, the exact weightage is calculated such that the model has highest predictive power. The weightage follows geometric distribution. For example, if the last match has 3% weightage, then the 2nd last match is assigned 2.91% and 3rd last match 2.8227%, and so on. All the remaining weightage goes to ‘Initial Rating’. For bowlers, this weightage is also based on number of balls bowled (e.g. if the player has just bowled 2 overs in the last match, that won’t carry much weight).
7. How to read current ratings: I can explain the current ranking with the following example. If tomorrow AB de Villiers replaces an average batsman against an average bowling side on an average pitch then on average that replacement is expected to add 18 runs to the total score. Similarly, if tomorrow Hasan Ali replaces an average bowler against an average batting side on an average pitch then on average that replacement is expected to reduce 12 runs from the opposition total score. Only batsmen who have batted within last 1 year, and bowlers who have bowled within last 1 year have been included.
8. How to read career ratings: Career ratings are average rating of players across their career after adding some longevity bonus. The longevity bonus is calculated in similar way to how we designed it in PEWS’ test player rankings. As the final career rating points don’t mean anything specific, I have normalised them. So, Viv Richards had a batting career that is 3.87 standard deviations better than an average batting career. Muttiah Muralitharan had a bowling career that is 3.74 standard deviations better than an average bowling career. Career ranking includes only batsmen with 30+ ODI innings, and bowlers with 1800+ ODI balls bowled (equivalent to 10-over spells in 30 matches).
In the next 4 posts, I shall post the current batsman ranking, current bowler ranking, career batsman ranking and career bowler ranking respectively.
1. Value Added: The paper was based on mainly this simple idea. We applied a concept from Financial Economics to value batting efforts. The similarity is that firms aim to maximise profits using limited resources; batsmen in ODI cricket aim to maximise runs using limited resources as well. Long story short, you can’t compare based on profit or runs alone; you can’t compare based on process efficiency alone either (profit/capital employed, or batting strike rate). The question to ask is if these resources (capital, or balls) were employed in an average venture, what would have been the return. In Financial Economics, we compute Economic Value Added = (Return on Capital Employed – Hurdle Rate) * Capital Employed. Similarly for batsmen, we can calculate Batsman Value Added = (Strike Rate – Par Rate) * Balls Faced/100. I shall discuss Par Rate in a separate point below. For this calculation now, imagine Par Rate is 70. Then a 40(50) innings will get 5 points, 45(50) will get 10 points, 80(100) will also get 10 points, and 36(60) will get -6 points according to the formula above. For bowlers, an equivalent formula will be (Par Rate – Economy Rate) * Balls Bowled/6. Imagine if Par Rate is 4.5 then 40 runs in 10 overs will fetch the bowler 5 points, 49 in 10 overs will get -4 points, and 20 in 6 overs will get 7 points.
2. Not Outs and Wickets: The premise is that not outs are inherently no better than outs if the batsman has played enough deliveries. If a batsman plays more than 1/10th of the available deliveries (slightly above 30 for 50-over matches, including no-balls) then he isn’t causing the team getting all-out. However, the less the number of balls a batsman plays (below 30) before getting out, the more impact he has towards the team getting all-out. So, 20*(25) is better than 20(25), 4*(2) is much better than 4(2), but there’s no difference between 35(40) and 35*(40). As a result, there is additional negative point for playing less deliveries depending on the number of deliveries played. Similarly, if a bowler takes less than 2 wickets in a 10-over spell then he’s not contributing towards getting the opposition all-out. Taking 3 wickets in 10-overs is better than taking 2-wickets, and so on. Taking 1 wicket in 5-overs is useful. The bonus points are designed accordingly.
3. Par Rate: The Par SR and Par ER are calculated based on the average first-innings performance of last 4 years (for era effect), the bowling strength of opposition (for batsmen), the batting strength of opposition (for bowlers), and pitch.
4. Pitch: Analysing pitches is the most difficult part. The same ground behaves differently at different times. Eden Gardens of today is not the same as Eden Gardens 30 years back. The Oval has changed drastically. Some pitches change within 2 consecutive matches. Unless someone watches all the 4000 ODIs and provides subjective opinion, the only other option is to deduce from scorecards. Long story short, I have divided the pitches in 6 categories based on scorecards – uneven pitch assists spinners but assists pacers more, crumbling pitch assists pacers but assists spinners more, dry pitch assists spinners but disadvantages pacers, green pitch assists pacers but disadvantages spinners, flat pitch disadvantages spinners but disadvantages pacers more, hard pitch disadvantages pacers but disadvantages spinners more.
5. Initial Rating: This is another area where this ranking is different from all other rankings. Because I use my ratings for predictive purpose, it is important to come up with accurate initial ratings. In all other rankings, players start from the same base in their debut match. But that is unfair and inaccurate. Because for example a South African debutant opening batsman has already achieved more than a debutant opening batsman from Scotland. The initial rating is decided based on the following 5 factors: team batting strength in last match (for batsmen), team bowling strength in last match (for bowlers), batting position, whether the player bowls at all in the debut match, and whether the player is a wicketkeeper.
6. Weightage per match: As this rating is predictive, the exact weightage is calculated such that the model has highest predictive power. The weightage follows geometric distribution. For example, if the last match has 3% weightage, then the 2nd last match is assigned 2.91% and 3rd last match 2.8227%, and so on. All the remaining weightage goes to ‘Initial Rating’. For bowlers, this weightage is also based on number of balls bowled (e.g. if the player has just bowled 2 overs in the last match, that won’t carry much weight).
7. How to read current ratings: I can explain the current ranking with the following example. If tomorrow AB de Villiers replaces an average batsman against an average bowling side on an average pitch then on average that replacement is expected to add 18 runs to the total score. Similarly, if tomorrow Hasan Ali replaces an average bowler against an average batting side on an average pitch then on average that replacement is expected to reduce 12 runs from the opposition total score. Only batsmen who have batted within last 1 year, and bowlers who have bowled within last 1 year have been included.
8. How to read career ratings: Career ratings are average rating of players across their career after adding some longevity bonus. The longevity bonus is calculated in similar way to how we designed it in PEWS’ test player rankings. As the final career rating points don’t mean anything specific, I have normalised them. So, Viv Richards had a batting career that is 3.87 standard deviations better than an average batting career. Muttiah Muralitharan had a bowling career that is 3.74 standard deviations better than an average bowling career. Career ranking includes only batsmen with 30+ ODI innings, and bowlers with 1800+ ODI balls bowled (equivalent to 10-over spells in 30 matches).
In the next 4 posts, I shall post the current batsman ranking, current bowler ranking, career batsman ranking and career bowler ranking respectively.
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